Place Value - I Love Algebra · 2018. 9. 6. · Name Date PeriodWorkbook Activity Chapter 1, Lesson 2 4 Rounding Whole Numbers Read the number. Round the number to the nearest tens

Name Date Period Workbook Activity

Chapter 1, Lesson 11

Place Value

Look at the place of the underlined digit.

Write the name of the place of the underlined digit. 198 tens

Directions Write the name of the place for each underlined digit.

© American Guidance Service, Inc. Permission is granted to reproduce for classroom use only. Basic Math Skills

EXAMPLE

1. 2,406 ______________

2. 128 ______________

3. 70,835 ______________

4. 17,501 ______________

5. 301,339 ______________

6. 10,002 ______________

7. 491,918 ______________

8. 46,023 ______________

9. 6,005 ______________

10. 59,700 ______________

11. 34,000 ______________

12. 500,069 ______________

13. 341 ______________

14. 10,000 ______________

15. 1,000,000 ______________

16. 3,902,885 ______________

17. 503 ______________

18. 16,030 ______________

19. 2,000,003 ______________

20. 73,999 ______________

21. 294 ______________

22. 5,020,007 ______________

23. 919,078 ______________

24. 4,009 ______________

25. 5,683 ______________

26. 687,633 ______________

27. 48,040 ______________

28. 384,995 ______________

29. 8,837 ______________

30. 23,000,821 _____________

31. 1,010,001 ______________

32. 53 ______________

33. 5,078 ______________

34. 708,583 ______________

35. 61,222 ______________

36. 701,865 ______________

37. 70,738 ______________

38. 501,775 ______________

39. 102,895 ______________

40. 71,990 ______________

41. 88,210 ______________

42. 90,909 ______________

43. 203,872,221 ____________

44. 910,573 ______________

45. 10,710 ______________

46. 737,098 ______________

47. 40,910 ______________

48. 10,002 ______________

49. 9,033,921 ______________

50. 810,022,033 ____________

51. 300,941 ______________

52. 2,671 ______________

53. 94,724 ______________

54. 803,921 ______________

55. 506 ______________

56. 1,034 ______________

57. 920 ______________

58. 1,023 ______________

59. 462,987 ______________

60. 10,935 ______________



Writing Numbers

Read the numeral. Write the numeral in words.

1,241 one thousand, two hundred forty-one

Directions Write the following numerals in words.

1. 1,208 _______________________________________________________________________

_______________________________________________________________________________

2. 204 _______________________________________________________________________

_______________________________________________________________________________

3. 4,801 _______________________________________________________________________

_______________________________________________________________________________

4. 80,026 _______________________________________________________________________

_______________________________________________________________________________

5. 92,224 _______________________________________________________________________

_______________________________________________________________________________

6. 44,659 _______________________________________________________________________

_______________________________________________________________________________

7. 602,875 _______________________________________________________________________

_______________________________________________________________________________

8. 6,096,089 _____________________________________________________________________

_______________________________________________________________________________

9. 673,218,003 _____________________________________________________________________

_______________________________________________________________________________

10. 830,002 _______________________________________________________________________

_______________________________________________________________________________


EXAMPLE



Number Translations

Read the amount written in words. Write the numeral for the amount.

Four thousand, one hundred ninety-two 4,192

Directions Write the following amounts in numerals.

1. Three thousand, five hundred thirty-six _____________________

2. Five hundred six _____________________

3. Seven hundred forty-nine _____________________

4. Five thousand, nine _____________________

5. Seven thousand, three hundred twenty-one _____________________

6. Nine thousand, two _____________________

7. Nine thousand, five hundred _____________________

8. Thirty-one thousand, four _____________________

9. Fifty-seven thousand, nine hundred _____________________

10. Eighty thousand, six hundred thirty-two _____________________

11. Forty-two thousand, three _____________________

12. Ninety-one thousand, four hundred eleven _____________________

13. Seven hundred thousand _____________________

14. Nine hundred thousand, sixty-four _____________________

15. Seven hundred seventy-one thousand, five hundred forty-nine _____________________

16. Four hundred fifty-five million _____________________

17. Three hundred five million, twenty-eight thousand, two _____________________

18. Eight thousand, eleven _____________________

19. Three hundred sixty-three thousand, five hundred four _____________________

20. Seventy thousand, nine hundred forty-two _____________________


EXAMPLE



Rounding Whole Numbers

Read the number. Round the number to the nearest tens place. Round numbers 5–9 up. Round numbers 1–4 down.

26 = 30

Directions Round these numbers to the nearest tens place.

Directions Round these numbers to the nearest hundreds place.

Directions Round these numbers to the nearest thousands place.


EXAMPLE

1. 48 = ______________

2. 305 = ______________

3. 4,056 = ______________

4. 408 = ______________

5. 9,911 = ______________

6. 72,099 = ______________

7. 5 = ______________

8. 803 = ______________

9. 617 = ______________

10. 61,092 = ______________

11. 777 = ______________

12. 290 = ______________

13. 4 = ______________

14. 18 = ______________

15. 102,005 = ______________

16. 4,506 = ______________

17. 9 = ______________

18. 61 = ______________

19. 693 = ______________

20. 349 = ______________

21. 9,012 = ______________

22. 7,521 = ______________

23. 43,071 = ______________

24. 102,009 = ______________

25. 29 = ______________

26. 3,002,091 = ____________

27. 71 = ______________

28. 91,029 = ______________

29. 6,018 = ______________

30. 33,951 = ______________

31. 34,988 = ______________

32. 89 = ______________

33. 129,999 = ______________

34. 10,891 = ______________

35. 509 = ______________

36. 780 = ______________

37. 199 = ______________

38. 499 = ______________

39. 1,500 = ______________

40. 25,509 = ______________

41. 999 = ______________

42. 90,098 = ______________

43. 1,058 = ______________

44. 501 = ______________

45. 99 = ______________

46. 301 = ______________

47. 298 = ______________

48. 78,475 = ______________

49. 470,512 = ______________

50. 19,000 = ______________



Addition of Whole Numbers

Write the problem in vertical form. Add.

18 � 162 � 171 � 8 = 359

Directions Rewrite the following addends in the vertical form and add.

Directions Solve the following word problems with addition.

34. Mark collects 178 pounds of scrap iron and 85 pounds of copper.Find the total weight of the metal. ___________________

35. Tara purchases 280 square feet of carpet for her living room and 250 square feet for her bedroom. Find the total number of square feet she purchases. ___________________


EXAMPLE1 1

18162171

� 8359

1. 32 � 141 � 68 � 122 = ______________

2. 4 � 37 � 812 � 774 � 1 = ______________

3. 8 � 35 � 77 � 273 � 65 = ______________

4. 54 � 76 � 90 � 725 = ______________

5. 701 � 33 � 83 � 61 � 374 = _____________

6. 7 � 837 � 504 � 91 � 522 = _____________

7. 93 � 705 � 866 � 73 = ______________

8. 45 � 38 � 401 � 5,000 = ______________

9. 86 � 59 � 63 � 27 � 105 = ______________

10. 395 � 57 � 82 � 273 � 88 = _____________

11. 304 � 771 � 826 � 776 = ______________

12. 366 � 8,261 � 8,837 � 912 = ____________

13. 6,372 � 75 � 908 � 76 = ______________

14. 874 � 7,601 �406 � 837 = ______________

15. 7,091 � 5,308 � 354 � 34 = ______________

16. 645 � 823 � 806 � 7,735 = ______________

17. 6,657 � 4,321 � 7,341 = ______________

18. 905 � 624 � 861 � 968 = ______________

19. 6,241 � 8,548 � 9,092 = ______________

20. 558 � 523 � 128 � 8,241 = ______________

21. 264 � 63 � 7,253 � 2 = ______________

22. 73 � 8,263 � 78 � 521 = ______________

23. 42 � 3,547 � 8,142 � 467 = ______________

24. 8,263 � 990 � 352 � 37 = ______________

25. 7,364 � 364 � 902 � 36 = ______________

26. 889 � 902 � 836 � 2,431 = ______________

27. 390 � 263 � 7,746 � 477 = ______________

28. 3,746 � 7,500 � 9,928 � 388 = ___________

29. 6,635 � 809 � 300 � 646 = ______________

30. 9,745 � 4,869 � 7,089 � 3,745 = __________

31. 36 � 2,006 � 215 � 116 = ______________

32. 2,117 � 3,591 � 6,711 � 2,883 = __________

33. 7,001 � 375 � 6 � 39 = ______________



Subtraction of Whole Numbers

Write the problem in vertical form. Subtract.

From 821 subtract 71. 750

Directions Rewrite these subtraction problems in the vertical form. Then subtract.

Directions Solve the following word problems with subtraction.

29. Van sells 185 tickets to the school’s Staff Talent Show.If he was given 350 tickets to sell, how many does he have left to sell? ____________________

30. Cassie plans a 475-mile trip. She drives 296 miles the first day.How many miles must she drive the second day to complete her trip? ____________________


EXAMPLE712

821� 71

750

1. 694 � 22 = _______________

2. From 384 subtract 75. _______________

3. 602 � 113 = _______________

4. From 102 subtract 89. _______________

5. 856 � 773 = _______________

6. Subtract 871 from 1,029. _______________

7. 552 � 498 = _______________

8. Subtract 528 from 717. _______________

9. 4,852 � 665 = _______________

10. From 3,810 subtract 1,922. ______________

11. 3,952 � 3,877 = _______________

12. Subtract 9,099 from 10,099.______________

13. 12,923 � 8,973 = _______________

14. From 16,242 subtract 10,987. ____________

15. 3,049 � 1,906 = _______________

16. Subtract 786 from 25,004. _______________

17. 46,974 � 18,860 = _______________

18. From 65,208 subtract 56,987. ____________

19. 7,890 � 5,699 = _______________

20. Subtract 61,098 from 87,987. ____________

21. 67,951 � 56,508 = _______________

22. From 10,001 subtract 9,802. _____________

23. 78,000 � 6,784 = _______________

24. Subtract 675 from 1,000. _______________

25. 362,900 � 87,098 = _______________

26. Subtract 81,321 from 601,030.____________

27. 70,981 � 69,673 = _______________

28. From 508,821 subtract 91,055. ____________



Multiplication Practice

Multiply the number in the left column by the number in the top row.

Directions Fill in the multiplication facts. Multiply each number in the left column by each number on the top row. Write the product of each pair of numbers in the box where the column and the row meet.

1.

2.


EXAMPLE4

3 12

� 0 1 2 3 4 5 6 7 8 9 10

0 0 0 0

1 0 1 2

2

3

4

5

6

7

8

9

10

� 6 2 3 0 9 10 8 7 5 4 1

2

9

5

4

8

0

7

6

3

1

10



Multiplication by Powers of Ten

When you multiply a number by 10, write the number. Then write a zero at the end. 235 � 10 = 2,350

When you multiply a number by 100, write the number. Then write two zeros at the end. 235 � 100 = 23,500

When you multiply a number by 1,000, write the number. Then write three zeros at the end. 235 � 1,000 = 235,000

Directions Multiply by these powers of ten.


1. 325 � 10 = ____________________

2. 421 � 100 = ____________________

3. 4,631 � 10 = ____________________

4. 6,023 � 100 = ____________________

5. 702 � 100 = ____________________

6. 3,011 � 1,000 = ____________________

7. 3,203 � 100 = ____________________

8. 26,190 � 10 = ____________________

9. 1,043 � 100 = ____________________

10. 50,783 � 1,000 = ____________________

11. 72 � 1,000 = ____________________

12. 38 � 1,000 = ____________________

13. 106 � 100 = ____________________

14. 81 � 100 = ____________________

15. 4,123 � 10 = ____________________

16. 3,007 � 1,000 = ____________________

17. 962 � 1,000 = ____________________

18. 300 � 10 = ____________________

19. 4,305 � 10 = ____________________

20. 4,020 � 1,000 = ____________________

21. 412 � 1,000 = ____________________

22. 906 � 1,000 = ____________________

23. 10,802 � 100 = ____________________

24. 104 � 100 = ____________________

25. 56 � 10 = ____________________

26. 13 � 100 = ____________________

27. 9 � 1,000 = ____________________

28. 83 � 1,000 = ____________________

29. 183 � 1,000 = ____________________

30. 7 � 1,000 = ____________________

31. 801 � 100 = ____________________

32. 334 � 10 = ____________________

33. 632 � 10 = ____________________

34. 4,567 � 100 = ____________________

35. 5 � 100 = ____________________

36. 20,304 � 100 = ____________________

37. 100 � 1,000 = ____________________

38. 20,011 � 100 = ____________________

39. 4,302 � 100 = ____________________

40. 10,001 � 100 = ____________________

EXAMPLES



Multiplication of Whole Numbers

Write the problem in vertical form. Multiply.

52 � 42 = 2,184

Directions Rewrite these multiplication problems in the vertical form and multiply.

Directions Solve the following word problems with multiplication.

29. Leah runs 4 miles every day before school for exercise.If she runs 179 days, how many miles will she run? ______________________

30. Each student in Mr. Brown’s class donates 15 sandwiches to the school picnic. If 38 students are in Mr. Brown’s class,how many sandwiches are donated? ______________________


EXAMPLE52

� 42104

+ 208 2,184

1. 24 � 22 = ______________________

2. 61 � 18 = ______________________

3. 201 � 43 = ______________________

4. 85 � 72 = ______________________

5. 712 � 66 = ______________________

6. 819 � 94 = ______________________

7. 465 � 20 = ______________________

8. 762 � 300 = ______________________

9. 301 � 300 = ______________________

10. 784 � 100 = ______________________

11. 629 � 150 = ______________________

12. 607 � 515 = ______________________

13. 5,763 � 501 = ______________________

14. 7,114 � 35 = ______________________

15. 920 � 724 = ______________________

16. 856 � 326 = ______________________

17. 3,021 � 307 = ______________________

18. 638 � 800 = ______________________

19. 4,160 � 110 = ______________________

20. 8,522 � 574 = ______________________

21. 5,021 � 4,000 = ______________________

22. 7,000 � 387 = ______________________

23. 5,448 � 673 = ______________________

24. 7,361 � 6,000 = ______________________

25. 4,000 � 3,000 = ______________________

26. 4,000 � 4,000 = ______________________

27. 3,500 � 5,100 = ______________________

28. 6,702 � 1,023 = ______________________



Division of Whole Numbers

Write the problem in standard form. Divide.

168 � 6 = 28

Directions Rewrite the following division problems in the standard form and divide.

Directions Solve these word problems with division.

29. The Jiffy Messenger Service travels a total of 2,954 miles in one 7-day week. How many miles do the messengers average each day? _______________________

30. Marvin collects 1,170 bottle tops over a 45-day period. How many bottle tops does he average per day? _______________________


EXAMPLE

1. 128 � 4 = ______________________

2. 477 � 9 = ______________________

3. 266 � 7 = ______________________

4. 480 � 5 = ______________________

5. 824 � 8 = ______________________

6. 864 � 4 = ______________________

7. 1,290 � 10 = ______________________

8. 1,771 � 7 = ______________________

9. 1,008 � 9 = ______________________

10. 3,069 � 9 = ______________________

11. 948 � 12 = ______________________

12. 1,472 � 16 = ______________________

13. 1,360 � 16 = ______________________

14. 2,160 � 12 = ______________________

15. 3,036 � 6 = ______________________

16. 8,844 � 11 = ______________________

17. 6,030 � 3 = ______________________

18. 5,400 � 6 = ______________________

19. 1,710 � 6 = ______________________

20. 1,820 � 13 = ______________________

21. 14,910 � 21 = ______________________

22. 15,625 � 25 = ______________________

23. 12,720 � 12 = ______________________

24. 13,797 � 27 = ______________________

25. 27,060 � 60 = ______________________

26. 21,350 � 35 = ______________________

27. 11,216 � 16 = ______________________

28. 12,030 � 30 = ______________________

286��1�6�8�– 12

48– 48

0



More Division of Whole Numbers

Write the problem in standard form.1,333 � 9 = __________ Divide.

Express the remainder as a fraction.Write the remainder over the divisor.

Directions Rewrite the following division problems in the standard form and divide. Express the remainders in fractional form.

Directions Solve these word problems with division. Express remainders in fractional form.

29. Maija’s mother owned her car for 9 years, driving a total of 136,910 miles. Find the average number of miles driven per year. ___________________

30. Daniel drove his car 816 miles using 22 gallons of gas. Compute Daniel’s gas mileage by dividing the number of miles driven by the number of gallons used. ___________________


EXAMPLE148

9��1�,3�3�3�– 9

43– 36

73– 72

1

�19�

1. 1,237 � 6 = ______________________

2. 898 � 6 = ______________________

3. 415 � 6 = ______________________

4. 2,115 � 11 = ______________________

5. 749 � 6 = ______________________

6. 1,218 � 12 = ______________________

7. 863 � 7 = ______________________

8. 3,017 � 15 = ______________________

9. 6,915 � 4 = ______________________

10. 812 � 82 = ______________________

11. 1,367 � 17 = ______________________

12. 3,575 � 28 = ______________________

13. 1,992 � 10 = ______________________

14. 2,115 � 63 = ______________________

15. 8,175 � 35 = ______________________

16. 7,167 � 20 = ______________________

17. 9,063 � 75 = ______________________

18. 10,613 � 53 = ______________________

19. 8,891 � 22 = ______________________

20. 7,776 � 78 = ______________________

21. 3,820 � 45 = ______________________

22. 29,666 � 30 = ______________________

23. 6,770 � 65 = ______________________

24. 41,080 � 80 = ______________________

25. 12,161 � 11 = ______________________

26. 58,775 � 40 = ______________________

27. 23,815 � 15 = ______________________

28. 91,090 � 90 = ______________________



Dividing Numbers by Powers of Ten

Write the problem in standard form and divide.

480 � 10 =

Or move the decimal point one place to the left for each zero in the divisor.

48.0 � 10 =

Directions Divide by these powers of ten.


EXAMPLE

4810��4�8�0�– 40

80– 80

0

1. 840 � 10 = __________________

2. 65,000 � 100 = __________________

3. 2,000 � 100 = __________________

4. 4,630 � 10 = __________________

5. 9,600 � 100 = __________________

6. 140,000 � 1,000 = __________________

7. 191,000 � 10 = __________________

8. 920,000 � 100 = __________________

9. 62,000 � 100 = __________________

10. 35,600 � 100 = __________________

11. 385,000 � 100 = __________________

12. 25,000,000 � 1,000 = __________________

13. 4,000,000 � 1,000 = __________________

14. 806,000 � 10 = __________________

15. 962,000 � 100 = __________________

16. 305,000 � 100 = __________________

17. 1,800,000 � 1,000 = __________________

18. 600,000 � 1,000 = __________________

19. 581,000 � 10 = __________________

20. 720,600 � 100 = __________________

21. 451,000 � 1,000 = __________________

22. 390,000 � 10 = __________________

23. 680,000 � 100 = __________________

24. 4,060,300 � 10 = __________________

25. 19,600 � 10 = __________________

26. 9,603,000 � 1,000 = __________________

27. 5,000,000 � 100 = __________________

28. 7,000,000 � 10 = __________________

29. 8,000,000 � 100 = __________________

30. 123,000 � 1,000 = __________________

31. 96,000,000 � 1,000 = __________________

32. 43,000 � 1,000 = __________________

33. 43,070,600 � 10 = __________________

34. 8,000,000 � 10,000 = __________________

35. 902,000 � 100 = __________________

36. 304,000,000 � 100 = __________________

37. 201,111,000 � 10 = __________________

38. 76,000,000 � 1,000 = __________________

39. 50,000 � 10,000 = __________________

40. 240,000 � 10,000 = __________________



Basic Operations with Whole Numbers

Add. Subtract. Multiply. Divide.

Directions Add.

Directions Subtract.

Directions Multiply.

Directions Divide. Write the remainders in the fractional form.


EXAMPLES23

� 44092

+ 92 1,012

2 2354356765

� 871,562

1 12 9 14

2,304� 567

1,737

1,1453��3�,4�3�5�– 3

04

– 313

– 1215

– 15

1. 243 � 321 � 132 � 68 = ___________

2. 5,067 � 23 � 505 � 40 = ___________

3. 1,102 � 705 � 4,033 = ___________

4. 5,122 � 567 � 504 � 3,402 = ___________

5. 30,304 � 4,030 � 20,300 � 1,102 = _______

6. 203,340 � 94,059 � 304,450 = ___________

7. 2,000 � 90,089 � 50,481 = ___________

8. 10,223 � 4,055 � 506 � 8,690 = __________

9. 2,304 � 567 = ________________

10. 304,119 � 4,053 = ________________

11. 30,400 � 19,234 = ________________

12. 102,556 � 9,806 = ________________

13. 134,505 � 5,968 = ________________

14. 900,800 � 203,788 = ________________

15. 6,578,009 � 456,801 = ________________

16. 340,599 � 9,875 = ________________

17. 23 � 44 = __________________

18. 304 � 32 = __________________

19. 579 � 23 = __________________

20. 3,011 � 44 = __________________

21. 4,503 � 23 = __________________

22. 4,053 � 206 = __________________

23. 5,098 � 2,304 = __________________

24. 40,577 � 3,092 = __________________

25. 3,435 � 3 = ____________________

26. 2,034 � 9 = ____________________

27. 49,571 � 9 = ____________________

28. 30,455 � 5 = ____________________

29. 46,570 � 45 = ____________________

30. 30,575 � 25 = ____________________



Averages

Find the average of these numbers: 25, 73, 80, 73, 33, 95

Step 1 Add. Step 2 Divide.

Directions Compute the averages for the sets of numbers. Round to the nearest tenth.

Directions Solve these word problems by computing the average.Round the answers to the nearest tenth.

19. Deborah works as a part-time car mechanic. She works 26 hours her first week. What is her average number of hours worked per day for four days? ___________________

20. The band sells 523 tickets to its annual concert. There are 13 ticket sellers.Find the average number of tickets sold by each seller. ___________________


EXAMPLE

1. 14, 12, 15, 11, 12, 13 ____________

2. 83, 78, 53, 92, 67, 27 ____________

3. 20, 28, 19, 31, 22, 18, 17, 30 ____________

4. 78, 98, 77, 67, 75, 90, 80,90, 80, 75, 70 ____________

5. 30, 31, 37, 33, 38, 35, 32,39, 34, 36 ____________

6. 44, 46, 64, 66, 62, 69, 41, 40 ____________

7. 103, 110, 152, 173, 177, 100,150, 175, 152 ____________

8. 205, 273, 198, 350, 220, 180,280, 220 ____________

9. 58, 74, 47, 83, 65, 36, 45, 46,70, 53, 55, 38 ____________

10. 163, 219, 300, 512, 375, 602,735, 638, 881 ____________

11. 3,004, 3,210, 3,387, 3,652,3,470, 3,521, 3,980, 3,922 ____________

12. 5,738, 5,755, 5,746, 5,789,5,736, 5,725, 5,756, 5,731 ____________

13. 230, 310, 222, 725, 600, 390,512, 525, 510, 400, 500, 683 ____________

14. 3,021, 5,361, 2,630, 6,110,4,002, 3,006, 4,102, 4,120,4,972, 3,500, 2,310 ____________

15. 4,589, 4,530, 4,520, 4,500,4,530, 4,528, 4,501, 4,554 ____________

16. 7,800, 7,853, 7,835, 7,850,7,812, 7,856, 7,851, 7,820 ____________

17. 35, 78, 95, 83, 62, 89, 35, 60,40, 66, 10, 31, 62, 89, 95 ____________

18. 1,239, 1,264, 1,220, 1,250,1,235, 1,260, 1,285, 1,240,1,200, 1,290, 1,206 ____________

2573807333

� 95379

63.16 � 63.26��3�7�9�.0�0�– 36

19– 18

1 0– 6

40– 36



Exponents

Read the number. Change the number into a problem and write the amount.

23 = 2 � 2 � 2 = 8

Directions Express the following without exponents.


EXAMPLE

1. 32 = _____________

2. 42 = _____________

3. 53 = _____________

4. 43 = _____________

5. 62 = _____________

6. 102 = _____________

7. 82 = _____________

8. 25 = _____________

9. 93 = _____________

10. 52 = _____________

11. 44 = _____________

12. 24 = _____________

13. 83 = _____________

14. 92 = _____________

15. 72 = _____________

16. 105 = _____________

17. 34 = _____________

18. 63 = _____________

19. 73 = _____________

20. 112 = _____________

21. 203 = _____________

22. 32 = _____________

23. 54 = _____________

24. 122 = _____________

25. 103 = _____________

26. 35 = _____________

27. 223 = _____________

28. 172 = _____________

29. 152 = _____________

30. 104 = _____________

31. 123 = _____________

32. 132 = _____________

33. 202 = _____________

34. 252 = _____________

35. 153 = _____________

36. 222 = _____________

37. 113 = _____________

38. 64 = _____________

39. 26 = _____________

40. 182 = _____________

41. 45 = _____________

42. 212 = _____________

43. 33 = _____________

44. 106 = _____________

45. 232 = _____________

46. 142 = _____________

47. 502 = _____________

48. 1002 = _____________

49. 192 = _____________

50. 332 = _____________

51. 133 = _____________

52. 162 = _____________

53. 253 = _____________

54. 173 = _____________

55. 143 = _____________

56. 55 = _____________

57. 107 = _____________

58. 114 = _____________

59. 124 = _____________

60. 109 = _____________



Order of Operations

Follow the order of operations. 2 � 4 � 2 = __________

2 � 8 = 10

Directions Find the answers. Perform the operations in the correct order.


EXAMPLE

1. 3 � 5 � 6 = ________________

2. 3 � 4 � 6 � 4 = ________________

3. 4 � 8 � 16 � 2 = ________________

4. 5 � 2 � 6 � 2 = ________________

5. 42 � 2 � 5 � 32 = ________________

6. 3 � 2 � 23 � 42 = ________________

7. 7 � 6 � 2 � 2 � 23 = ________________

8. 18 � 2 � 42 � 4 = ________________

9. 10 � 8 � 6 � 12 � 2 = ________________

10. 13 � 4 � 5 � 2 � 10 = ________________

11. 15 � 3 � 52 � 10 = ________________

12. 72 � 24 � 23 = ________________

13. 4 � 17 � 3 � 7 = ________________

14. 122 � 102 � 5 � 2 = ________________

15. 102 � 2 � 4 � 32 = ________________

16. 112 � 23 � 23 � 9 = ________________

17. 20 � 12 � 6 � 3 = ________________

18. 43 � 3 � 12 � 6 = ________________

19. 15 � 4 � 11 � 25 = ________________

20. 12 � 2 � 3 � 2 � 3 = ________________

21. 8 � 6 � 4 � 12 � 6 = ________________

22. 23 � 3 � 6 � 12 � 3 = ________________

23. 45 � 15 � 10 � 23 = ________________

24. 15 � 3 � 5 � 102 = ________________

25. 122 � 6 � 20 � 7 = ________________

26. 82 � 9 � 3 � 10 = ________________

27. 18 � 32 � 2 � 52 = ________________

28. 53 � 5 � 10 � 23 = ________________

29. 81 � 32 � 6 � 12 � 2 = ________________

30. 3 � 6 � 2 � 5 � 7 = ________________

31. 102 � 52 � 5 � 6 � 2 = ________________

32. 25 � 52 � 5 � 5 � 10 = ________________

33. 100 � 10 � 22 � 8 = ________________

34. 18 � 9 � 2 � 3 � 32 = ________________

35. 50 � 40 � 4 � 7 = ________________

36. 28 � 4 � 6 � 20 = ________________

37. 33 � 22 � 20 � 2 = ________________

38. 62 � 3 � 2 � 42 = ________________

39. 14 � 2 � 3 � 21 = ________________

40. 16 � 2 � 4 � 2 � 10 = ________________



Factors

Factor the number. Choose the correct factors.

F15 1 � 15 a. 1, 5, 10, 153 � 5 b. 1, 2, 3, 5

c. 1, 3, 5, 15d. 1, 3, 6, 12

Directions Circle the answer that has the correct factors.

1. 24 6. 52 11. 36a. 1, 2, 4, 6, 8, 12, 14 a. 1, 12, 24, 26, 30, 52 a. 2, 3, 4, 6, 8, 12, 24b. 1, 2, 4, 10, 12, 24 b. 26, 52 b. 1, 2, 3, 4, 6, 9, 12, 18, 36c. 1, 2, 3, 4, 6, 8, 12, 24 c. 1, 2, 4, 13, 26, 52 c. 1, 2, 4, 6, 8, 12, 36d. 2, 4, 6, 8, 10, 12, 24 d. 1, 13, 15, 52 d. 1, 3, 4, 6, 8, 12, 36

2. 16 7. 14 12. 12a. 1, 4, 8, 16 a. 2, 7, 11, 14 a. 2, 3, 4, 6, 12b. 1, 2, 4, 16 b. 1, 2, 7, 14, 28 b. 3, 4, 6, 12, 24c. 1, 2, 4, 8, 16 c. 2, 4, 7, 14 c. 2, 4, 6, 24d. 1, 2, 4, 8, 16, 32 d. 1, 2, 7, 14 d. 1, 2, 3, 4, 6, 12

3. 32 8. 42 13. 18a. 1, 2, 8, 16, 32 a. 1, 6, 7, 12, 21, 42 a. 1, 2, 3, 6, 9, 18b. 1, 2, 8, 16, 32, 64 b. 1, 2, 3, 6, 7, 14, 21, 42 b. 1, 2, 3, 6, 9, 18, 32c. 1, 2, 4, 8, 16, 32 c. 1, 6, 12, 42 c. 1, 2, 3, 6, 9, 18, 36d. 2, 4, 6, 8, 10, 32 d. 1, 2, 4, 12, 21, 42 d. 1, 2, 3, 4, 6, 7, 18

4. 8 9. 13 14. 20a. 2, 4, 8 a. 1, 7, 13 a. 2, 20b. 1, 2, 4, 8 b. 1, 13 b. 2, 5, 10, 15, 20c. 1, 2, 4, 8, 16 c. 1, 7, 13, 26 c. 1, 2, 5, 10, 15, 20d. 1, 2, 4, 8, 12, 24 d. 1, 2, 13, 19 d. 1, 2, 4, 5, 10, 20

5. 10 10. 26 15. 22a. 2, 5 a. 1, 2, 20, 26 a. 1, 11, 22b. 1, 2, 5, 10 b. 1, 13, 26 b. 1, 11, 22, 44c. 1, 2, 5, 10, 20 c. 1, 2, 13, 26 c. 1, 2, 11, 22d. 1, 2, 5 d. 1, 26 d. 1, 22, 44


EXAMPLE



Multiples

M4 Find the multiples of 4. Choose the correct multiples.

4 � 0 4 � 1 4 � 2 4 � 3 4 � 40 4 8 12 16

Directions Circle the answer that has the correct multiples. Note: Some multiples may be missing from a correct answer.

1. M2 6. M3 11. M5

a. 2, 4, 6, 8, 11 a. 0, 3, 5, 6, 9, 12 a. 0, 5, 10, 12, 15b. 0, 4, 6, 8, 12 b. 3, 6, 9, 12, 14 b. 0, 10, 15, 20, 30c. 0, 2, 4, 5, 6, 8 c. 0, 3, 6, 12, 15 c. 1, 5, 10, 15, 20d. 0, 2, 3, 4, 5, 6 d. 1, 3, 6, 9, 12, 15 d. 0, 10, 18, 20, 25

2. M11 7. M7 12. M10

a. 0, 1, 11, 22, 121 a. 0, 7, 14, 28, 56, 112 a. 0, 10, 15, 20, 25b. 0, 11, 22, 33, 44, 56 b. 0, 3, 7, 14, 28, 35 b. 0, 5, 10, 15, 20c. 11, 22, 33, 111 c. 0, 7, 11, 22, 33, 44 c. 10, 15, 20, 25, 30d. 0, 11, 22, 33, 121 d. 1, 7, 14, 28, 35, 40 d. 0, 10, 30, 50, 100

3. M4 8. M9 13. M12

a. 0, 2, 4, 6, 8, 16 a. 0, 9, 18, 27, 36 a. 0, 12, 24, 36, 44b. 4, 8, 16, 32, 36 b. 0, 9, 27, 38, 45 b. 0, 12, 16, 24, 28c. 0, 4, 6, 8, 12, 20 c. 0, 19, 38, 76 c. 0, 12, 24, 36, 48d. 0, 14, 28, 56, 100 d. 0, 1, 2, 3, 4, 5 d. 0, 10, 12, 14, 16

4. M6 9. M20 14. M13

a. 0, 2, 4, 6, 8, 9 a. 0, 20, 40, 60, 80 a. 13, 29, 39, 52b. 0, 6, 12, 18, 24 b. 0, 20, 30, 40, 50 b. 0, 13, 23, 39c. 1, 6, 12, 18, 24 c. 1, 20, 40, 60, 80 c. 1, 13, 26, 52d. 1, 3, 6, 9, 18, 24 d. 1, 10, 20, 30, 40 d. 0, 13, 26, 39

5. M30 10. M40 15. M50

a. 0, 10, 30, 60, 90 a. 0, 40, 80, 120, 160 a. 1, 50, 100, 150b. 0, 30, 60, 90, 120 b. 1, 40, 80, 120, 160 b. 0, 50, 100, 150c. 0, 15, 30, 45, 60 c. 1, 20, 40, 60, 80 c. 1, 25, 50, 75d. 1, 15, 30, 40, 60 d. 0, 20, 40, 60, 80 d. 0, 10, 15, 25


EXAMPLE

a. 0, 1, 2, 4b. 0, 4, 10, 12c. 0, 1, 4, 8d. 0, 4, 8, 12



Prime and Composite Numbers

Identify all the factors of a number. F9 = 1, 3, 9

Tell whether the number is a prime or composite number.

9 has three factors, so it is a composite number.

Directions Write prime or composite for each number given.

1. 23 _________________ 19. 21 _________________ 37. 12 _________________

2. 25 _________________ 20. 44 _________________ 38. 7 _________________

3. 45 _________________ 21. 17 _________________ 39. 58 _________________

4. 19 _________________ 22. 26 _________________ 40. 98 _________________

5. 84 _________________ 23. 102 _________________ 41. 62 _________________

6. 29 _________________ 24. 77 _________________ 42. 60 _________________

7. 73 _________________ 25. 42 _________________ 43. 22 _________________

8. 37 _________________ 26. 54 _________________ 44. 49 _________________

9. 55 _________________ 27. 4 _________________ 45. 31 _________________

10. 78 _________________ 28. 100 _________________ 46. 1 _________________

11. 15 _________________ 29. 27 _________________ 47. 400 _________________

12. 220 _________________ 30. 79 _________________ 48. 2 _________________

13. 110 _________________ 31. 55 _________________ 49. 3 _________________

14. 6 _________________ 32. 204 _________________ 50. 300 _________________

15. 120 _________________ 33. 41 _________________

16. 72 _________________ 34. 155 _________________

17. 350 _________________ 35. 29 _________________

18. 410 _________________ 36. 57 _________________


EXAMPLE



Sets of Numbers

Identify the set of even numbers. Even numbers are multiples of 2.1, 2, 3, 5, 6, 8, 10, 12

Set of even numbers 2, 6, 8, 10, 12

Directions Write the sets from the given numbers.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,

21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37,

38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50

1. The set of even numbers

_______________________________________________________________________________

2. The set of odd numbers

_______________________________________________________________________________

3. The set of prime numbers

_______________________________________________________________________________

4. The set of numbers that will divide into 100 with zero as a remainder

_______________________________________________________________________________

5. The set of numbers that is multiples of 3 _________________________________________




9. The set of numbers that is factors of 100 _________________________________________








EXAMPLE



Prime Numbers

List prime numbers from the given set.2, 3, 4, 5

Identify prime numbers, which are numbers that have exactly 2 factors.2 has 2 factors3 has 2 factors4 has 3 factors5 has 2 factors

Prime numbers are 2, 3, 5.

Directions Write the sets from the given numbers.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,

21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37,

38, 39, 40, 41, 42, 43, 44, 45

1. List the prime numbers in order from smallest to largest from the set given.

_______________________________________________________________________________

2. List the even numbers in order from smallest to largest from the set given.

_______________________________________________________________________________

3. List the odd numbers in order from smallest to largest from the set given.

_______________________________________________________________________________

4. Add pairs of prime numbers. Exclude 2 from your additions.

Can you predict an odd or even answer? ______________ Summarize your results.

_______________________________________________________________________________

5. Add pairs of odd numbers. Can you predict an odd or even answer? ______________Summarize your results.

_______________________________________________________________________________

6. Add pairs of even numbers. Can you predict an odd or even answer? ______________Summarize your results.

_______________________________________________________________________________

Find the three prime addends for each of the following numbers.

7. 12 = ____________ 9. 14 = _____________

8. 19 = ____________ 10. 21 = _____________


EXAMPLE



Divisibility Tests

Use the divisibility test to determine if this number is divisible by 3.

123 Add the digits. 1 + 2 + 3 = 6

Determine if the sum is a multiple of 3. 6 is a multiple of 3.123 is divisible by 3.

Directions Perform the divisibility test to complete the chart.Write Yes or No for each space.


EXAMPLE

Number Divisible by 2? Divisible by 3? Divisible by 5?

1. 12,034

2. 31,241

3. 21,453

4. 3,040,511

5. 989,798

6. 10,233

7. 20,394

8. 3,012,211

9. 50,321

10. 293,100

Number Divisible by 4? Divisible by 9? Divisible by 10?

11. 20,349

12. 13,536

13. 12,350

14. 182,340

15. 125,350

16. 30,451

17. 10,800

18. 100,237

19. 584,750

20. 95,832



Prime Factorization

Complete factor trees to find prime factorization.

Find prime factors for 45 and 34.

45 34

9 � 5 2 � 17

3 � 3 � 5

Directions Complete factor trees for these numbers.

1. 48 4. 36 7. 39 9. 72

2. 44 5. 32 8. 38 10. 52

3. 64 6. 28


EXAMPLES



Least Common Multiple

Find the LCM (12, 6).

M12 = 12, 24, 36

M6 = 6, 12, 18, 24

LCM (12, 6) = 12

Directions Find the least common multiple and show the steps.

1. Find the LCM (10, 15). 6. Find the LCM (36, 12).

___________________ ____________________

___________________ ____________________

___________________ ____________________


___________________ ____________________

___________________ ____________________

___________________ ____________________


___________________ ____________________

___________________ ____________________

___________________ ____________________


___________________ ____________________

___________________ ____________________

___________________ ____________________


___________________ ____________________

___________________ ____________________

___________________ ____________________


EXAMPLE



Least Common Multiple/Greatest Common Factor

Find the factors. Underline greatest common numbers in both sets.

LCM (3, 5) GCF (10, 25)

M3 = {0, 3, 9, 12, 15, . . .} F10 = {1, 2, 5, 10}

M5 = {0, 5, 10, 15, 20, . . .} F25 = {1, 5, 25}

LCM (3, 5) = 15 GCF = 5

Directions Find the least common multiple and show the steps.


___________________ ____________________

___________________ ____________________

___________________ ____________________


___________________ ____________________

___________________ ____________________

___________________ ____________________

Directions Find the greatest common factor.

5. GCF (18, 16) _______________ 11. GCF (12, 20) _______________

6. GCF (8, 36) _______________ 12. GCF (32, 36) _______________

7. GCF (12, 15) _______________ 13. GCF (12, 16) _______________

8. GCF (6, 26) _______________ 14. GCF (20, 8) _______________

9. GCF (18, 4) _______________ 15. GCF (20, 15) _______________

10. GCF (14, 4) _______________


EXAMPLES



Using Prime Factorization

LCM (10, 15) GCF (10, 15)

10 15 10 15

2 � 5 3 � 5 2 � 5 3 � 5

10 = 2 � 5 10 = 2 � 5

15 = 3 � 5 15 = 3 � 5

2 � 3 � 5 = 30 5 GCF = 5

Directions Find the least common multiple (LCM) for these pairs of numbers.



Directions Find the greatest common factor (GCF) for each pair of numbers.

5. GCF (10, 25) 8. GCF (14, 8)

6. GCF (20, 30) 9. GCF (22, 55)

7. GCF (22, 77) 10. GCF (44, 48)


EXAMPLES

↓ ↓↓ ↓



Comparing Fractions

Cross-multiply numerators and denominators. Compare the products.12 10 10 12

�23� �

45� �

23� �

45� �

23� �

45�

3 � 4 � 12 2 � 5 � 10 10 � 12

Directions Compare the fractions in each pair. Use < or > for each pair.


1. �35� �

47�

2. �56

� �78

�

3. �57

� �78

�

4. �25

� �41

�

5. �133� �

260�

6. �38

� �290�

7. �161� �

59

�

8. �58

� �11

07�

9. �12

� �151�

10. �123� �

145�

11. �11

56� �

11

67�

12. �123� �

134�

13. �18

� �123�

14. �251� �

13

81�

15. �125� �

261�

16. �173� �

362�

17. �15

� �19

�

18. �221� �

331�

19. �13

� �27

�

20. �67

� �81

�

21. �35

� �12

�

22. �28

� �147�

23. �160� �

15

�

24. �150� �

12

01�

25. �47

� �151�

26. �35

� �161�

27. �45

� �220�

28. �161� �

252�

29. �12

� �28

�

30. �141� �

281�

31. �190� �

45

�

32. �172� �

170�

33. �69

� �11

27�

34. �142� �

27

�

35. �133� �

16

�

36. �185� �

11

56�

37. �38

� �153�

38. �11

02� �

11

46�

39. �26

� �144�

40. �112� �

244�

41. �161� �

153�

42. �24

� �12

02�

43. �180� �

440�

44. �67

� �12

80�

45. �46

� �180�

46. �160� �

24

�

47. �21

31� �

23

21�

48. �195� �

13

81�

49. �11

01� �

22

03�

50. �48

� �151�

51. �12

03� �

13

52�

52. �11

31� �

157�

53. �190� �

11

34�

54. �171� �

182�

55. �37

� �59

�

56. �56

� �11

67�

57. �121� �

23

�

58. �18

� �455�

59. �12

30� �

15

�

60. �170� �

165�

EXAMPLE



Working with Fractions

Divide to find out how many times one denominator goes into the other. Multiply the numerator by the quotient.

�25� � Divide 25 by 5. 25 � 5 � 5

�25� � �

55� � �

1205�

�25� � �

1205�

Directions Express these fractions in higher terms.


EXAMPLE

1. �35

� �

2. �13

� �

3. �56

� �

4. �78

� �

5. �78

� �

6. �37

� �

7. �29

� �

8. �15

� �

9. �14

� �

10. �151� �

11. �49

� �

12. �131� �

13. �23

� �

14. �170� �

15. �34

� �

16. �67

� �

17. �173� �

18. �58

� �

19. �123� �

20. �19

� �

21. �11

21� �

22. �185� �

23. �169� �

24. �47

� �

25. �11

35� �

26. �187� �

27. �11

09� �

28. �113� �

29. �11

01� �

30. �11

56� �

31. �154� �

32. �223� �

33. �57

� �

34. �143� �

35. �150� �

36. �197� �

37. �141� �

38. �23

30� �

39. �37

� �

40. �136� �

41. �11

25� �

42. �56

� �

43. �184� �

44. �12

83� �

45. �292� �

46. �58

� �

47. �251� �

48. �352� �

49. �368� �

50. �37

50� �

51. �360� �

52. �133� �

53. �151� �

54. �46

50� �

55. �11

58� �

56. �582� �

57. �166� �

58. �172� �

59. �299� �

60. �251� �

50

18

24

32

56

21

36

30

20

121

72

44

18

80

16

42

39

64

52

99

60

45

76

63

105

34

38

65

55

64

56

92

210

39

1,000

51

99

90

84

80

60

54

42

92

220

96

105

160

380

280

390

65

121

480

72

156

80

156

145

126

25



Renaming Fractions

Rename fractions by expressing them in lowest terms. Divide the numerator and denominator by their greatest common factor.

�11

04� � �

Directions Express these fractions and mixed numbers in their lowest terms.

5�7

10 � 2�14 � 2


EXAMPLE

1. �195� � _______

2. �297� � _______

3. �12

82� � _______

4. 13 �11

05� � _______

5. 2 �11

24� � _______

6. �12

00� � _______

7. �13

39� � _______

8. �24

80� � _______

9. �15

00� � _______

10. 6 �450� � _______

11. 13 �78

00� � _______

12. 27 �15024

� � _______

13. �33

03� � _______

14. 9 �24

46� � _______

15. �291� � _______

16. �12

50

00

� � _______

17. 20 �15

87� � _______

18. �45

62� � _______

19. �12280

� � _______

20. �11

02

28

� � _______

21. �12

72

80

� � _______

22. 8 �29

32� � _______

23. 51 �16261

� � _______

24. 9 �13

53� � _______

25. �14048

� � _______

26. 9 �36

12� � _______

27. 6 �673� � _______

28. �16

64� � _______

29. �18281

� � _______

30. �56

84� � _______

31. 11 �69

22� � _______

32. 18 �23255

� � _______

33. �25

84� � _______

34. �25

05� � _______

35. �33

68� � _______

36. �14520

� � _______

37. �22

05� � _______

38. �81

81� � _______

39. �33

39� � _______

40. �18182

� � _______

41. �35

86� � _______

42. �15

54� � _______

43. �15068

� � _______

44. �13086

� = _______

45. �12555

� � _______

46. �41580

� � _______

47. �22

18

00

� � _______

48. �16640

� � _______

49. �37

02� � _______

50. �44

58

00

� � _______

51. �24

22� � _______

52. �12

48

00

� � _______

53. �13

50

00

� � _______

54. �89

46� � _______

55. �56

08� � _______

56. �17084

� � _______

57. �24015

� � _______

58. �26097

� � _______

59. �14222

� � _______

60. �35050

� � _______



Mixed Numbers

Rename 1�23� as an improper fraction 3 � 1 � 3 3 � 2 � 5 1 �

23� � �

53�

Multiply the whole number by the denominator. Then, add the numerator.Write the new numerator over the same denominator.

Directions Rename these mixed numbers as improper fractions.


EXAMPLE

1. 2 �16

� � _________

2. 1 �12

� � _________

3. 2 �15

� � _________

4. 1 �56

� � _________

5. 4 �15

� � _________

6. 3 �25

� � _________

7. 1 �16

� � _________

8. 9 �27

� � _________

9. 4 �34

� � _________

10. 2 �151� � _________

11. 1 �59

� � _________

12. 13 �27

� � _________

13. 20 �12

� � _________

14. 6 �29

� � _________

15. 3 �47

� � _________

16. 2 �23

� � _________

17. 15 �13

� � _________

18. 6 �141� � _________

19. 15 �34

� � _________

20. 6 �25

� � _________

21. 7 �15

� � _________

22. 33 �23

� � _________

23. 17 �12

� � _________

24. 2 �127� � _________

25. 9 �151� � _________

26. 8 �153� � _________

27. 18 �35

� � _________

28. 3 �129� � _________

29. 9 �11

01� � _________

30. 2 �11

34� � _________

31. 3 �11

67� � _________

32. 4 �129� � _________

33. 5 �79

� � _________

34. 5 �122� � _________

35. 6 �133� � _________

36. 4 �113� � _________

37. 7 �11

01� � _________

38. 8 �11

35� � _________

39. 1 �272� � _________

40. 3 �151� � _________

41. 4 �250� � _________

42. 2 �232� � _________

43. 5 �11

61� � _________

44. 21 �621� �_________

45. 5 �12

30� � _________

46. 7 �22

03� � _________

47. 5 �650� � _________

48. 1 �123� � _________

49. 3 �151� � _________

50. 7 �225� � _________

51. 4 �239� � _________

52. 4 �322� � _________

53. 1 �178� � _________

54. 11 �151� �_________

55. 20 �116� �_________

56. 10 �127� �_________

57. 11 �251� �_________

58. 5 �11

21� � _________

59. 7 �320� � _________

60. 2 �263� � _________



Renaming Improper Fractions

Express the improper fractions as mixed numbers. Divide the numerator by the denominator.Simplify if necessary.

�798�

Solution: 8 �69� or 8 �

23�

Directions Rename the improper fractions as mixed numbers.Simplify if necessary.


EXAMPLE

1. �175� � __________

2. �269� � __________

3. �53

10� � __________

4. �383� � __________

5. �41

40� � __________

6. �21

00� � __________

7. �325� � __________

8. �288� � __________

9. �587� � __________

10. �52

33� � __________

11. �71

70� � __________

12. �41

23� � __________

13. �61

21� � __________

14. �81

21� � __________

15. �31

91� � __________

16. �83

73� � __________

17. �11

81� � __________

18. �71

28� � __________

19. �71

14� � __________

20. �51

73� � __________

21. �11

90� � __________

22. �52

40� � __________

23. �42

60� � __________

24. �61

61� � __________

25. �51

30� � __________

26. �31

42� � __________

27. �683� � __________

28. �694� � __________

29. �21

98� � __________

30. �998� � __________

89��7�8�– 72

6 remainder is 6



Improper Fractions to Mixed Numbers

Rename �153�. Divide the numerator by the denominator.

Simplify if necessary.

Directions Rename these improper fractions as mixed numbers.Simplify if necessary.


EXAMPLE

1. �164� � _________

2. �176� � _________

3. �278� � _________

4. �125� � _________

5. �343� � _________

6. �158� � _________

7. �245� � _________

8. �662� � _________

9. �370� � _________

10. �385� � _________

11. �188� � _________

12. �340� � _________

13. �72

55� � _________

14. �71

20� � _________

15. �236� � _________

16. �71

29� � _________

17. �690� � _________

18. �11210

� � _________

19. �31

67� � _________

20. �597� � _________

21. �31

96� � _________

22. �357� � _________

23. �127� � _________

24. �62

08� � _________

25. �31

30� � _________

26. �139

5� � _________

27. �21

02

00

� � _________

28. �22

51� � _________

29. �61

32� � _________

30. �11320

� � _________

31. �368� � _________

32. �157� � _________

33. �11

81� � _________

34. �223� � _________

35. �51

41� � _________

36. �952� � _________

37. �31

63� � _________

38. �359� � _________

39. �51

11� � _________

40. �41

64� � _________

41. �252� � _________

42. �81

72� � _________

43. �51

72� � _________

44. �61

21� � _________

45. �71

30� � _________

46. �981� � _________

47. �776� � _________

48. �81

91� � _________

49. �42

83� � _________

50. �94

86� � _________

51. �82

83� � _________

52. �11055

� � _________

53. �268� � _________

54. �10

70

� � _________

55. �439� � _________

56. �625� � _________

57. �81

57� � _________

58. �599� � _________

59. �91

90� � _________

60. �436� � _________

25��1�3�– 10

3

�35�



Multiplication of Fractions

Multiply numerators. Multiply denominators.Simplify if necessary.

Directions Multiply these fractions. Simplify the answers to the lowest terms.


EXAMPLE

1. �15

� � �34

� � ____________

2. �45

� � �11

01� � ____________

3. �69

� � �13

� � ____________

4. �25

� � �140� � ____________

5. 8 � �67

� � ____________

6. �79

� � 1 �12

� � ____________

7. �29

� � 1 �18

� � ____________

8. �131� � 3 �

23

� � ____________

9. �173� � �

153� � ____________

10. �181� � �

15

� � ____________

11. �25

� � �127� � ____________

12. �58

� � �38

� � ____________

13. �46

� � �23

� � ____________

14. �13

� � �160� � ____________

15. �12

� � �35

� � ____________

16. �33

58� � �

45

� � ____________

17. �161� � 2 �

56

� � ____________

18. �172� � �

37

� � ____________

19. �16

� � �25

� � ____________

20. �25

� � 2 �25

� � ____________

21. 1 �37

� � �58

� � ____________

22. �163� � 2 �

16

� � ____________

23. 3 �15

� � �131� � ____________

24. 4 �15

� � 7 � ____________

25. 5 �25

� � 10 � ____________

26. 5 �123� � �

16

� � ____________

27. 3 �45

� � 65 � ____________

28. 2 �14

� � 4 � ____________

29. 2 �15

� � 5 �12

� � ____________

30. 7 �25

� � 5 �27

� � ____________

31. 2 �210� � 20 �

150� =

32. 5 �163� � 1 �

12

� = ____________

33. 7 �15

� � �67

52� � ____________

34. 5 �27

� � 1 �12

� � ____________

35. 7 �58

� � 2 �34

� � ____________

36. 5 �122� � 1 �

12

� �___________

37. 5 �141� � 1 �

13

� �___________

38. 3 �45

� � 1 �12

� � ____________

39. 8 �89

� � �12

80� � ____________

40. 3 �15

� � 5 �13

� � ____________

41. 3 �13

� � �15

� � ____________

42. 2 �37

� � �11

47� � ____________

43. 3 �56

� � �14

26� � ____________

44. 5 �27

� � 5 � ____________

45. 7 �25

� � 1 �15

� � ____________

__________

�35� � �

78� � �

21�40

3 � 7�5 � 8



Multiplying Mixed Numbers

Change mixed numbers to improper fractions.Multiply. Simplify if necessary.

2 �15� � �

15� �

�151� � �

15� � �

1215�

Directions Multiply these fractions.


EXAMPLE

1. 4 �25

� � 1 �35

� �

___________________

2. 1 �16

� � 1 �27

� �

___________________

3. 3 �13

� � 1 �35

� �

___________________

4. �37

� � 1 �15

� �

___________________

5. �17

� � 2 �14

� �

___________________

6. 1 �113� � 2 �

37

� �

___________________

7. 2 �14

� � 2 �13

� �

___________________

8. 1 �13

� � 3 �12

� �

___________________

9. 2 �23

� � �16

� �

___________________

10. 1 �13

� � 2 �25

� �

___________________

11. �15

� � 2 �13

� �

___________________

12. 2 �56

� � 1 �57

� �

___________________

13. 2 �13

� � 3 �15

� �

___________________

14. 2 �23

� � 3 �13

� �

___________________

15. �35

� � 3 �13

� �

___________________



Dividing Fractions

Invert the divisor. Multiply. Simplify if necessary.

�25� � �

37� �

�25� � �

73� � �

1145�

Directions Divide these fractions. Remember to invert the divisor.Show your work. See the example.


EXAMPLE

1. �130� � �

45

� �

2. �11

32� � �

11

58� �

3. �59

� � �182� �

4. �75

� � �11

05� �

5. �142� � �

68

� �

6. �89

� � �67

� �

7. �152� � �

78

� �

8. �170� � �

11

05� �

9. �27

� � �78

� �

10. �17

� � �134� �

11. �194� � �

12

81� �

12. �11

24� � �

67

� �

13. �89

� � �69

� �

14. �67

� � �29

� �

15. �45

� � �12

60� �

16. �16

� � �152� �

17. �15

� � �35

� �

18. �11

45� � �

11

45� �

19. �37

� � �190� �

20. �11

46� � �

12

50� �



Division of Fractions

Invert the divisor. Multiply and simplify if necessary.

�35� � �

25� � �

35� � �

52�

� �35� � �

52�

�

� �32� = 1 �

12�

Directions Divide these fractions. Simplify the answers to the lowest terms.

3 � 1�1 � 2


EXAMPLE

1. �37

� � �17

� � ____________

2. �67

� � �29

� � ____________

3. �153� � �

22

56� � ____________

4. �11

56� � �

38

� � ____________

5. �163� � �

123� � ____________

6. �130� � 1 �

45

� � ____________

7. �161� � 2 �

15

� � ____________

8. �45

� � �22

45� � ____________

9. �57

� � �11

45� � ____________

10. �12

� � �13

� � ____________

11. �52

� � 1 �12

� � ____________

12. �43

� � 2 �15

� � ____________

13. �15

� � �34

� � ____________

14. �190� � �

25

� � ____________

15. �25

� � �18

� � ____________

16. 5 �28

� � �18

� � ____________

17. �11

27� � �

12

51� � ____________

18. �13

� � 2 �12

� � ____________

19. 2 �34

� � �11

61� � ____________

20. 5 �35

� � 2 �110� �____________

21. 2 �15

� � �15

� � ____________

22. 3 �27

� � �42

61� � ____________

23. 1 �25

� � 2 �23

� � ____________

24. 1 �28

� � 2 �12

� � ____________

25. �156� � 1 �

12

� � ____________

26. 7 �12

� � 22 �12

� � ___________

27. 5 �23

� � 1 �152� �____________

28. �37

� � 1 �131� � ____________

29. 2 �16

� � 1 �12

� � ____________

30. 3 �153� � �

23

29� � ____________

31. 5 � 1 �16

� � ____________

32. 11 � 3 �343� � ____________

33. 4 �131� � 6 � ____________

34. 4 �12

� � �33

68� � ____________

35. 3 �27

� � 1 �12

� � ____________

36. 2 �56

� � 17 � ____________

37. 1 �59

� � 1 �25

� � ____________

38. 2 �35

� � �15

� � ____________

39. 5 �38

� � 1 �116� �____________

40. 1 �131� � 5 � ____________

1

1



Addition of Fractions with Like Denominators

Add numerators. Keep the denominator.

Directions Add these fractions. Simplify the answers.


EXAMPLE

1. �27

�

+ �47

�

2. �136�

+ �126�

3. �155�

+ �135�

4. �271�

+ �271�

5. �89

�

+ �59

�

6. 5 �23

�

+ 2 �13

�

7. �29

�

+ �39

�

8. �127�

+ �157�

9. �230�

+ �220�

10. 2 �128�

+ 3 �138�

11. 6 �170�

+ �190�

12. 12 �171�

+ 3 �121�

13. �153�

+ �183�

14. �178�

+ �128�

15. �260�

+ �250�

16. 4 �263�

+ 5 �12

73�

17. 5 �256�

+ �22

46�

18. 35 �56

�

+ 5

19. 4

+ 6 �25

�

20. 7 �123�

+ �11

31�

�152�

+ �162�

�11

12�



Addition of Fractions with Unlike Denominators

To add fractions and mixed numbers with unlike denominators, find the least common multiple of the denominators. Raise the fraction to higher terms and add.



EXAMPLE

1. �49

�

+ �13

�

2. �178�

+ �13

�

3. 5 �37

�

+ 2 �114�

4. 10 �27

�

+ 3 �354�

5. 25 �365�

+ 4 �730�

6. �59

�

+ �148�

7. �241�

+ �17

�

8. 6 �230�

+ 4 �25

�

9. 23 �17

�

+ 2 �154�

10. 38 �112�

+ 2 �640�

11. �265�

+ �45

�

12. �385�

+ �27

�

13. 8 �230�

+ �34

�

14. 37 �48

�

+ 5 �274�

15. 3 �35

�

+ 2 �210�

16. �13

25�

+ 7 �2710�

17. 18 �16

�

+ 3 �712�

18. 8 �231�

+ 2 �17

�

19. 8 �15

�

+ 10 �515�

20. 12 �258�

+ 4 �556�

�56� � �

1158�

+ �128� � + �1

28�

� �1178�




1. �21

01�

+ �47

�

2. �151�

+ �47

�

3. 2 �57

�

+ 5 �68

�

4. 5 �49

�

+ 3 �121�

5. 16 �152�

+ 4 �35

�

6. �133�

+ �15

�

7. �37

�

+ �99

�

8. �152�

+ 6 �140�

9. 6 �133�

+ 4 �56

�

10. 9 �151�

+ 6 �25

�

11. �262�

+ �45

�

12. �171�

+ �11

02�

13. 2 �173�

+ 9 �130�

14. 3 �57

�

+ 2 �191�

15. 4 �173�

+ 2 �35

�

16. 3 �47

�

+ 7 �38

�

17. 28 �57

�

+ 6 �49

�

18. 4 �112�

+ 6 �27

�

19. 35 �149�

+ 2 �130�

20. 12 �185�

+ �14

�

More Addition of Fractions

To add fractions and mixed numbers with unlike denominators, find the least common multiple of the denominators. Raise the fraction to higher terms and add.


�59� � �

3653�

+ �37� � + �

2673�

� �6623�

EXAMPLE



Addition of Mixed Numbers

Add the fractions. Find the lowest common multiple if necessary.Add the whole numbers. Simplify to lowest terms.

Directions Add these fractions. Simplify the answers to the lowest terms.

Directions Rewrite the fractions in the standard form and add.Simplify the answers to the lowest terms.


EXAMPLE

1. 2 �130�

+ 3 �110�

2. 18 �156�

+ 3 �18

�

3. 81 �125�

+ 2 �23

�

4. 18 �121�

+ 4 �56

�

5. 23 �47

�

+ 8

6. 4 �25

�

+ 3 �15

�

7. 7 �14

�

+ �13

�

8. 17

+ 2 �15

�

9. 29 �25

�

+ 3 �56

�

10. 16 �133�

+ �349�

11. 6 �251�

+ 2 �17

�

12. 13 �156�

+ 2 �14

�

13. 10 �37

�

+ 2 �45

�

14. 13 �232�

+ 5 �434�

3 �123�

+ 4 �113�

7 �133�

15. 1 �12

� � 2 �131� = __________

16. 2 �35

� � 4 �16

� = __________

17. 7 �17

� � 5 �18

� = __________

18. 6 �29

� � 1 �130� = __________

19. 10 � 2 �16

� = __________

20. 5 �122� � �

110� = __________



Subtraction of Fractions with Like Denominators

Subtract numerators. Keep denominators.Simplify if necessary.

Directions Subtract these fractions and simplify your answers.


EXAMPLE

1. �13

85�

� �395�

2. 3 �172�

� 2 �122�

3. 8 �11

35�

� 3 �145�

4. 16 �21

01�

� �260�

5. 7 �323�

� 5

6. �11

36�

� �156�

7. 5 �11

58�

� 2 �138�

8. 11 �14

21�

� 5 �461�

9. 8 �258�

� 5

10. 13 �11

78�

� 4 �188�

11. �12

01�

� �271�

12. 11 �140�

� �110�

13. 30 �13

83�

� 5 �373�

14. 31 �12

47�

� 4 �257�

15. 15 �136�

� 4 �116�

16. 13 �249�

� 3 �229�

17. 8 �35

36�

� 2 �556�

18. 33 �34

75�

� �425�

19. 13 �13

78�

� �378�

20. 25 �373�

� 4 �343�

�78�

� �38�

�48� � �

12�



Subtraction of Fractions Without Renaming

Raise fractions to higher terms. Subtract numerators and whole numbers.Simplify if necessary.

Directions Subtract these fractions. Simplify the answers to the lowest terms.


EXAMPLE

1. 25 �18

�

� 24 �19

�

2. 28 �11

25�

� 4 �25

�

3. 52 �130�

� 2 �157�

4. 3 �12

51�

� 1�15

�

5. 51 �59

�

� 4 �140�

6. 22 �78

�

� 3 �214�

7. 26 �49

�

� 4 �18

�

8. 14 �151�

� 7 �27

�

9. 7 �128�

� 5 �210�

10. 28 �241�

� 4 �17

�

11. 25 �13

28�

� 9 �139�

12. 33 �47

�

� 6 �17

�

13. 4 �11

61�

� 2 �332�

14. 16 �278�

� 5 �238�

15. 16 �130�

� 2 �15

�

16. 8 �12

�

� 5 �39

�

17. 42 �67

�

� 5 �16

�

18. 2 �13

�

� 1 �125�

19. 5 �113�

� 2 �115�

20. 14 �125�

� �116�

15 �23� � 15 �

1241�

� 6 �27� � � 6 �2

61�

� 9 �281�



Subtraction of Fractions with Renaming

Rename the fractions and subtract them. Subtract the whole numbers.Simplify if necessary.



EXAMPLE

1. 13 �18

�

� 1 �78

�

2. 28 �13

�

� 5 �23

�

3. 13 �129�

� 2 �159�

4. 14 �127�

� 5 �137�

5. 26 �258�

� 4 �268�

6. 28 �27

�

� 5 �57

�

7. 4 �39

�

� �59

�

8. 6 �141�

� 1 �161�

9. 29 �157�

� 28 �197�

10. 42 �15

60�

� 2 �25

50�

11. 12 �127�

� 3 �157�

12. 6

� �132�

13. 8 �231�

� 5 �271�

14. 32 �13

35�

� 5 �13

55�

15. 32

� 4 �252�

16. 7

� 5 �11

12�

17. 67

� 5 �11

78�

18. 8 �270�

� 5 �21

01�

19. 5

� 2 �12

70�

20. 9 �21

01�

� 5 �12

20�

19 �15� � 18 �

65�

� 2 �35� � � 2 �

35�

16 �35�



More Subtraction of Fractions with Renaming

Rename the fractions and subtract them. Subtract the whole numbers.Simplify if necessary.

Directions Subtract these fractions. Simplify the answers.


EXAMPLE

1. 4 �34

�

� 3 �56

�

2. 14 �29

�

� 5 �78

�

3. 11 �15

�

� �14

�

4. 38 �121�

� 4 �252�

5. 45 �191�

� 4 �22

12�

6. 6 �143�

� 5 �22

56�

7. 16 �193�

� 4 �12

86�

8. 29 �115�

� 2 �34

�

9. 12

� 2 �11

01�

10. 11 �116�

� �12

�

11. 4

� 2 �35

�

12. 3 �12

�

� 2 �67

�

13. 18 �125�

� 5 �34

�

14. 13 �136�

� 4 �78

�

15. 23 �47

�

� 22 �194�

16. 9 �13

�

� 4 �11

31�

17. 12 �11

45�

� 10 �23

90�

18. 10 �25

�

� 5 �11

01�

19. 10 �27

�

� 8 �11

41�

20. 4 �156�

� 2 �38

�

3 �25� � 3 �

1460� � 2 �

5460�

� 2 �78� � � 2 �

3450� � � 2 �

3450�

�2410�



Subtraction of Fractions

Change to common denominators if necessary. Rename top mixed number if necessary. Subtract numerators. Simplify if necessary.


Directions Rewrite the fractions in the standard form and subtract.Simplify the answers to the lowest terms.


EXAMPLE

1. �178�

� �138�

2. 16 �11

23�

� 3 �216�

3. 33 �15

�

� 2 �34

�

4. 23 �178�

� �732�

5. 2 �153�

� �143�

6. 4 �11

56�

� 2 �38

�

7. 18

� 5 �27

�

8. 5 �110�

� 2 �175�

9. 16 �27

�

� 2 �37

�

10. 10 �12

34�

� 2 �16

�

11. 13

� 2 �131�

12. 12

� 6 �133�

13. 16 �130�

� 1 �150�

14. 7 �151�

� 3

15. 59 �115�

� 2 �435�

16. 12 �136�

� 5 �41

81�

1 �178� � 1 �1

78� � �

2158�

� �59� � � �

11

08� � � �

1108�

�1158� � �

56�

17. 3 �14

� � 2 �78

� = _______________________

18. 13 �125� � 3 �

45

� = _______________________

19. 6 �152� � 4 �

15

� = _______________________

20. 38 � 2 �37

� = _______________________



Basic Operations with Fractions and Mixed Numbers


Directions Add.



Directions Divide.


�34�

+ �34�

�64� � 1 �

12�

1 �58�

– 1 �38�

�28� � �

14�

�23� � �1

30� � �

15� �

14� � �

78� � �

14� � �

87� � �

27�

1. 2 �13

� � 3 �13

� = ________________

2. 4 �18

� � 2 �28

� = ________________

3. 1 �15

� � �110� = ________________

4. 2 �16

� � 3 �23

� = ________________

5. 4 �17

� � 1 �134� = ________________

6. 1 �18

� � 2 �16

� = ________________

7. 5 �28

� � 1 �14

� = ________________

8. 2 �23

� � 1 �12

� = ________________

9. 4 �78

� � 1 �34

� = ________________

10. 6 �28

� � 2 �34

� = ________________

11. 35 � 6 �27

� = ________________

12. 41 �35

� � 6 = ________________

13. �56

� � �23

� = ________________

14. �141� � �

21

20� = ________________

15. �12

� � �23

� = ________________

16. 2 �35

� � 1 �13

� = ________________

17. 6 �29

� � �12

� = ________________

18. 1 �18

� � 2 �35

� = ________________

19. �68

� � �12

84� = ________________

20. �56

� � �23

50� = ________________

21. �141� � �

12

80� = ________________

22. 1 �12

� � �36

� = ________________

23. 2 �14

� � �190� = ________________

24. 2 �35

� � �23

60� = ________________

25. 1 �29

� � 1 �12

� = ________________

1 1

1 5

2

1

EXAMPLES



Place Value

Look at the underlined digit. Write the place value for the underlined digit.

3.754 hundredths

Directions Write the place value for each underlined digit.

Directions Underline the place value indicated.


EXAMPLE

1. 2.34 ________________________

2. 1.20345 ________________________

3. 1.02301 ________________________

4. 12.01012 ________________________

5. 0.00012 ________________________

6. 12.00200 ________________________

7. 1.22008 ________________________

8. 840.88940 ________________________

9. 2.10769 ________________________

10. 502.001 ________________________

11. 3.4001 ________________________

12. 7.3309 ________________________

13. 1.0023 ________________________

14. 0.002003 ________________________

15. 3.00410 ________________________

16. 23.00019 ________________________

17. 12.0002 ten-thousandths

18. 0.012 tenths

19. 0.00023 hundred-thousandths

20. 0.00012 thousandths

21. 1.02304 tenths

22. 102.0023 tenths


24. 0.010102 millionths



27. 530.0002 tenths


29. 0.0112887 millionths

30. 1.0234 tenths



Reading and Writing Numerals

Look at the underlined digit. Write the name of the place.

3.143 thousandths

Start at the left. Write the word for the numerals. Use and to stand for the decimal point.

1.63 one and sixty-three hundredths

Directions Write the name of the place for each underlined digit.

Directions Write the following numerals in words.

25. 9.032 _____________________________________________________________________

_____________________________________________________________________

26. 0.0024 _____________________________________________________________________

_____________________________________________________________________

27. 102.10245 _____________________________________________________________________

_____________________________________________________________________

28. 0.010139 _____________________________________________________________________

_____________________________________________________________________

29. 40.044 _____________________________________________________________________

_____________________________________________________________________

30. 410.00003 _____________________________________________________________________

_____________________________________________________________________


1. 12.18 ______________

2. 0.920 ______________

3. 1.034 ______________

4. 3.0578 ______________

5. 64.2381 ______________

6. 0.003 ______________

7. 152.9 ______________

8. 24.02231 ______________

9. 8.0263 ______________

10. 4.0005 ______________

11. 4.59021 ______________

12. 295.11 ______________

13. 5.02848 ______________

14. 45.92210 ______________

15. 394.0264 ______________

16. 385.04485 ______________

17. 3.04 ______________

18. 0.003705 ______________

19. 0.00304 ______________

20. 59.0492 ______________

21. 83.39051 ______________

22. 19.46031 ______________

23. 44.912 ______________

24. 5.61056 ______________

EXAMPLES



Translation of Decimal Numbers

Read the amount. Write it in numerals. Remember, and stands for the decimal point.

Five and seventy-one hundredths 5.71

Directions Write the following amounts in numerals.

1. Twenty-three and six tenths ____________________

2. Forty-one and three hundredths ____________________

3. Seventy-two thousandths ____________________

4. Five and eight tenths ____________________

5. Six and three thousandths ____________________

6. One hundred two thousandths ____________________

7. Four hundred three thousandths ____________________

8. Two and two hundredths ____________________

9. Six hundred thirty-four ten-thousandths ____________________

10. Six thousand, three hundred forty-eight hundred-thousandths ____________________

11. Twenty thousand, four hundred five hundred-thousandths ____________________

12. One hundred two and seven hundredths ____________________

13. Eight hundred two and seven hundred fifty-one thousandths ____________________

14. One thousand, nine hundred three and seven hundredths ____________________

15. Two thousand and twenty-six thousandths ____________________

16. Four thousand three and seven ten-thousandths ____________________

17. Two hundred six thousandths ____________________

18. Three hundred-thousandths ____________________

19. Thirty-four hundred-thousandths ____________________

20. One and fifty-nine hundredths ____________________


EXAMPLE



Comparing and Rounding Decimals

Order numbers from least to greatest.Least Greatest

1.059 0.0159 0.159 0.0159 0.159 1.059

Directions Arrange each set in order from least to greatest.

1. 0.6234 62.350 0.7406 ______________ ______________ ______________

2. 0.0045 0.0450 0.0040 ______________ ______________ ______________

3. 2.0049 2.0050 2.034 ______________ ______________ ______________

4. 0.1024 0.1031 0.113 ______________ ______________ ______________

5. 23.0045 23.004 2.30045 ______________ ______________ ______________

6. 304.097 300.999 304.102 ______________ ______________ ______________

7. 3.00495 30.0495 0.300495 ______________ ______________ ______________

8. 9.00603 9.00599 9.000999 ______________ ______________ ______________

9. 0.356924 0.350899 0.400001 ______________ ______________ ______________

10. 5.04592 6.001 0.939401 ______________ ______________ ______________

Round to the nearest hundredth. Round up if thousandth is 5 or greater.5.1365.14

Directions Round the following numbers to the nearest:

Tenth Hundredth Thousandth


EXAMPLE

EXAMPLE

11. 245.44 _____________

12. 4.091 _____________

13. 2.0399 _____________

14. 0.048 _____________

15. 30.9199 _____________

16. 0.048539 _____________

17. 5.0555 _____________

18. 49.952 _____________

19. 0.0394 _____________

20. 199.051 _____________

21. 6.34499 _____________

22. 0.995 _____________

23. 666.034 _____________

24. 394.091999 ____________

25. 0.0951 _____________

26. 495.0495 _____________

27. 40.0495 _____________

28. 0.08931 _____________

29. 0.00592 _____________

30. 10.122309 _____________

31. 0.39 _____________

32. 390.0485 _____________

33. 3,998.0002 _____________

34. 8.89099 _____________

35. 4.76842 _____________



Addition of Decimals

Write the problem in vertical form. Then add.

2.3 � 4 � 0.09 � 59 �

Directions Rewrite the following addends in vertical form and add.

Directions Solve the following word problems with addition.

29. Compute the total amount deposited if Lance’s deposits are $15, $1.90, $121, and $2.65. ________________________

30. It rains three times during the first week of summer vacation.Compute the total amount if it rains 2.05 inches, 0.29 inches,and 3 inches. ________________________


EXAMPLE

2.34.0.09

� 59. 65.39

1. 3.4 � 5 � 0.18 � 17 � _____________

2. 0.056 � 3.02 � 4 � 1.2 � _____________

3. 19 � 9.3 � 0.049 � 3 � _____________

4. 30.9 � 5 � 0.91 � 0.922 � _____________

5. 0.08 � 1 � 1.1 � 6.2 � _____________

6. 2.331 � 0.1123 � 7 � 1.8 �_____________

7. 16 � 4.05 � 5 � 4.77 � _____________

8. 65.94 � 4.7 � 1 � 7.2 � _____________

9. 5.906 � 0.071 � 44.581 � _____________

10. 3.045 � 0.045 � 84.3 � _____________

11. 0.9639 � 0.0082 � 5.03 � _____________

12. 7.304 � 1.5 � 8.33 � 2 � _____________

13. 7004.1 � 35.066 � 0.06 � _____________

14. 93 � 0.739 � 2.38 � 0.1 � _____________

15. 4.4 � 3.5 � 23.49 � 6 � _____________

16. 6.06 � 33 � 0.045 � 3 � _____________

17. 5 � 6 � 6.9 � 0.082 � _____________

18. 6.112 � 4.7 � 6 � 0.0001 �_____________

19. 9.9 � 5.03 � 5.5 � 0.002 � _____________

20. 47.05 � 6.2 � 0.4 � 1 � _____________

21. 54 � 2.2 � 0.01 � 6.9 � _____________

22. 2.334 � 0.1128 � 8.3 � _____________

23. 4.056 � 3.5 � 7 � 0.92 � _____________

24. 5 � 6.1 � 55.6 � 0.01 � _____________

25. 6.001 � 4.9 � 3 � 0.05 � _____________

26. 1 � 2.1 � 5.66 � 0.031 � _____________

27. 9.9 � 3.4 � 0.56 � 0.012 � _____________

28. 6.035 � 3.4 � 5 � 0.057 � _____________

2.304.000.09

� 59.00 65.39



Subtraction of Decimals

Write the problem in vertical form. Then subtract.

1.03 � 0.94 �

Directions Rewrite these problems in vertical form. Then subtract.

Directions Solve the following word problems with subtraction.

29. Diana saves $25 for school clothes and purchases a blouse costing $9.96. How much money does she have left? ________________________

30. Ross drives 298.6 miles on a two-day vacation. If he drives 150 miles on the first day, how many miles does he drive on the second day? ________________________


EXAMPLE

0 9 13

1.03– 0.94

0.09

1. 6.34 � 0.14 � _________________________

2. From 23.034 subtract 0.0341 _____________

3. 20 � 0.934 � _________________________

4. Subtract 12.92 from 27.104 ______________

5. 103.506 � 94 � _______________________

6. Subtract 0.607 from 2 ___________________

7. 2.3941 � 0.2852 � _____________________

8. From 1.0182 subtract 0.81818 ____________

9. 34.8 � 5.0837 � _______________________

10. From 2 subtract 1.9283 __________________

11. 0.0238 � 0.003856 � ___________________

12. Subtract 9.9 from 10.005 ________________

13. 1.3 � 1.0953 � ________________________

14. Subtract 0.0056 from 0.9 ________________

15. 58.3 � 12.923 � _______________________

16. From 4.95 subtract 2.5 __________________

17. 71 � 5.341 � _________________________

18. Subtract 0.3945 from 6 __________________

19. 0.304 � 0.0433 � ______________________

20. From 205.5 subtract 0.56 ________________

21. 4.59 � 2.4 � __________________________

22. Subtract 2.3 from 5 _____________________

23. 4.5 � 0.0954 � ________________________

24. From 6.94 subtract 0.9567 _______________

25. 49 � 5.607 � _________________________

26. Subtract 0.0384 from 1.991 ______________

27. 3 � 0.4581 � _________________________

28. From 86 subtract 0.86 __________________



Multiplication of Decimals by Powers of Ten

Write the problem in vertical form. Then multiply. Remember the decimal point.

2.63 � 10 �

Directions Rewrite the following problems in vertical form and multiply.


EXAMPLE2.63

� 10

26.30

1. 6.25 � 10 � _________________

2. 5.638 � 10 � _________________

3. 0.06 � 100 � _________________

4. 0.072 � 100 � _________________

5. 1.061 � 10 � _________________

6. 5.63 � 100 � _________________

7. 3.14 � 100 � _________________

8. 1.414 � 1,000 � _________________

9. 0.00627 � 1,000 � _________________

10. 0.2802 � 10 � _________________

11. 0.0605 � 100 � _________________

12. 0.7701 � 100 � _________________

13. 1.101 � 1,000 � _________________

14. 7.6 � 100 � _________________

15. 5.1 � 1,000 � _________________

16. 8.81 � 10,000 � _________________

17. 3.7 � 10,000 � _________________

18. 2.05 � 10,000 � _________________

19. 0.0001 � 1,000 � _________________

20. 5.6 � 100 � _________________

21. 69.1 � 1,000 � _________________

22. 0.777 � 1,000 � _________________

23. 0.201 � 10,000 � _________________

24. 0.028 � 10 � _________________

25. 0.002 � 1,000 � _________________

26. 1.1 � 1,000 � _________________

27. 10 � 1.67 � _________________

28. 1,000 � 0.003 � _________________

29. 100 � 0.1505 � _________________

30. 10 � 1.688 � _________________

31. 1,000 � 3.9 � _________________

32. 100 � 3.702 � _________________

33. 10 � 0.1 � _________________

34. 1,000 � 0.11 � _________________

35. 3.44 � 100 � _________________

36. 1.112 � 1,000 � _________________

37. 0.00232 � 10,000 � _________________

38. 0.012 � 10,000 � _________________

39. 3.033 � 10 � _________________

40. 8.014 � 1,000 � _________________

41. 0.0556 � 10,000 � _________________

42. 5.5 � 100 � _________________

43. 0.6709 � 100 � _________________

44. 0.0021 � 1,000 � _________________

45. 23.1 � 100 � _________________



Multiplication of Decimals

Write the problem in vertical form. Then multiply. Remember the decimal point.

1.2 � 0.04 �

Directions Rewrite the following problems in vertical form and multiply.

Directions Solve the following word problems with multiplication.

29. Lionel works part-time with a construction company and earns $24.50 per day. How much will Lionel earn working 5 days? ____________________

30. Regina earns $7.50 per hour straight time. Compute Regina’s time and one-half rate by finding the product of $7.50 and 1.5. ____________________


EXAMPLE 1.2

� .04

48

00

0.048

1. 3.5 � 0.11 � ____________________

2. 48 � 1.5 � ____________________

3. 4.05 � 0.03 � ____________________

4. 3.6 � 0.93 � ____________________

5. 56.7 � 0.31 � ____________________

6. 0.059 � 0.12 � ____________________

7. 9.01 � 1.03 � ____________________

8. 5.8 � 0.0004 � ____________________

9. 0.0034 � 23 � ____________________

10. 6.12 � 3.4 � ____________________

11. 7.81 � 56 � ____________________

12. 5.25 � 0.01 � ____________________

13. 6.79 � 8.3 � ____________________

14. 0.044 � 0.9 � ____________________

15. 0.09 � 0.04 � ____________________

16. 7.05 � 0.3 � ____________________

17. 98 � 0.11 � ____________________

18. 0.931 � 100 � ____________________

19. 7.02 � 5.1 � ____________________

20. 0.034 � 0.0048 � ____________________

21. 1,000 � 0.00342 � ____________________

22. 405 � 1.52 � ____________________

23. 8.8 � 6.7 � ____________________

24. 13.5 � 4.7 � ____________________

25. 69.1 � 0.001 � ____________________

26. 10.4 � 10.5 � ____________________

27. 0.059 � 0.0691 � ____________________

28. 0.101 � 121.1 � ____________________



Scientific Notation with Positive Exponents

Write in scientific notation. 2,300,000 � 2.3 � 106

Directions Rewrite the following numbers using scientific notation.


EXAMPLE an exponent

a power of tena number

between oneand ten

1. 4,200 � ____________________

2. 6,250 � ____________________

3. 82,100 � ____________________

4. 50,000 � ____________________

5. 72,300 � ____________________

6. 15,080 � ____________________

7. 1,800 � ____________________

8. 29,000 � ____________________

9. 500,000 � ____________________

10. 600,000 � ____________________

11. 700,000,000 � ____________________

12. 7,800,000 � ____________________

13. 10,000 � ____________________

14. 35,600 � ____________________

15. 81.52 � ____________________

16. 17.63 � ____________________

17. 236.5 � ____________________

18. 3,800 � ____________________

19. 19,000 � ____________________

20. 16.12 � ____________________

21. 610,000,000 � ____________________

22. 400,000,000 � ____________________

23. 790,000 � ____________________

24. 25.33 � ____________________

25. 1,420,000 � ____________________

26. 1,000,000,000 � ____________________

27. 34,000,000 � ____________________

28. 103,000 � ____________________

29. 23,000 � ____________________

30. 450,000,000 � ____________________

31. 11,000 � ____________________

32. 401,300 � ____________________

33. 311,400 � ____________________

34. 102.3 � ____________________

35. 927,000 � ____________________

36. 211,400 � ____________________

37. 100,000 � ____________________

38. 10,000 � ____________________

39. 344,000,000,000 � ____________________

40. 42,000,000,000 � ____________________

41. 12,000,000 � ____________________

42. 41,000,000 � ____________________

43. 764,200,000 � ____________________

44. 911,400,000 � ____________________

45. 102,000 � ____________________



Scientific Notation with Negative Exponents

Write in scientific notation. 0.006 � 6 � 10–3



EXAMPLE a negative exponent

a power of tena number

between oneand ten

1. 0.008 � ____________________

2. 0.0715 � ____________________

3. 0.0062 � ____________________

4. 0.0007 � ____________________

5. 0.02 � ____________________

6. 0.0321 � ____________________

7. 0.0805 � ____________________

8. 0.0006 � ____________________

9. 0.00005 � ____________________

10. 0.03051 � ____________________

11. 0.00091 � ____________________

12. 0.0000007 � ____________________

13. 0.000003 � ____________________

14. 0.00000021 � ____________________

15. 0.0061 � ____________________

16. 0.00054 � ____________________

17. 0.000003 � ____________________

18. 0.00101 � ____________________

19. 0.000005 � ____________________

20. 0.000052 � ____________________

21. 0.000735 � ____________________

22. 0.0001433 � ____________________

23. 0.00021 � ____________________

24. 0.00093 � ____________________

25. 0.000000004 � ____________________

26. 0.00000000062 � ____________________

27. 0.423 � ____________________

28. 0.00316 � ____________________

29. 0.005071 � ____________________

30. 0.000078 � ____________________

31. 0.002103 � ____________________

32. 0.0000000005 � ____________________

33. 0.00000123 � ____________________

34. 0.00203 � ____________________

35. 0.000222 � ____________________

36. 0.0121 � ____________________

37. 0.10203 � ____________________

38. 0.000204 � ____________________

39. 0.0691 � ____________________

40. 0.0000203 � ____________________

41. 0.0000000304 � ____________________

42. 0.3044 � ____________________

43. 0.00077 � ____________________

44. 0.002058 � ____________________

45. 0.0004058 � ____________________



Scientific Notation in Standard Form

Write in standard form. 5.1 � 102 5.1 � 10–2

5 . 1 0 . � 510 0 . 0 5 . 1 � 0.051

Directions Rewrite each scientific notation in standard form.


2 21 1

1. 5.6 � 102 � ______________________

2. 1.5 � 102 � ______________________

3. 2 � 104 � ______________________

4. 8 � 103 � ______________________

5. 4.65 � 103 � ______________________

6. 1.73 � 104 � ______________________

7. 6.203 � 105 � ______________________

8. 2.414 � 105 � ______________________

9. 8.5 � 107 � ______________________

10. 3 � 107 � ______________________

11. 2 � 101 � ______________________

12. 5.16 � 102 � ______________________

13. 8.2 � 103 � ______________________

14. 1.2 � 101 � ______________________

15. 7.502 � 102 � ______________________

16. 3.0052 � 102 � ______________________

17. 2.61 � 103 � ______________________

18. 5.85 � 104 � ______________________

19. 7.05 � 104 � ______________________

20. 6 � 104 � ______________________

21. 3.008 � 103 � ______________________

22. 1.9 � 102 � ______________________

23. 4.002 � 104 � ______________________

24. 7 � 1010 � ______________________

25. 1.9 � 10–8 � ______________________

26. 3 � 10–9 � ______________________

27. 5.03 � 10–1 � ______________________

28. 4.06 � 10–4 � ______________________

29. 6.003 � 10–5 � ______________________

30. 1.01 � 10–5 � ______________________

31. 4.5 � 10–5 � ______________________

32. 5.012 � 10–3 � ______________________

33. 6 � 10–5 � ______________________

34. 7.01 � 10–4 � ______________________

35. 2.34 � 10–3 � ______________________

36. 4.535 � 10–2 � ______________________

37. 1 � 10–8 � ______________________

38. 1.024 � 10–2 � ______________________

39. 4.441 � 10–5 � ______________________

40. 7.002 � 10–4 � ______________________

41. 2.001 � 10–8 � ______________________

42. 3.3 � 10–3 � ______________________

43. 6.77 � 10–4 � ______________________

44. 4.001 � 10–3 � ______________________

45. 5 � 10–10 � ______________________

EXAMPLES



Scientific Notation

Write in scientific notation. 0.00563 � 0 . 0 0 5 . 6 3 � 5.63 � 10–3


Write in standard form. 5.63 � 10–3 � 0 . 0 0 5 . 6 3 � 0.00563

Directions Write the following numbers in standard form without exponents.


EXAMPLE

2

2

1

1

3

1. 2,300,000 � _________________

2. 59,000 � _________________

3. 0.0005 � _________________

4. 0.0000039 � _________________

5. 23.41 � _________________

6. 453 � _________________

7. 25,400,000 � _________________

8. 0.000000000843 � _________________

9. 1,900,000,000 � _________________

10. 39,400,000 � _________________

11. 0.00000837 � _________________

12. 567.2 � _________________

13. 0.0001 � _________________

14. 4,000 � _________________

15. 0.00495 � _________________

16. 567,000,000,000,000 � _________________

3

17. 2.3 � 103 � ________________________

18. 4.29 � 105 � ________________________

19. 8 � 106 � ________________________

20. 5.7 � 105 � ________________________

21. 4.94 � 10–8 � ________________________

22. 7.03 � 10–7 � ________________________

23. 6.1 � 1010 � ________________________

24. 5.5 � 10–3 � ________________________

25. 6.832 � 106 � ________________________

26. 8.11 � 10–2 � ________________________

27. 3 � 1012 � ________________________

28. 1.35 � 10–5 � ________________________

29. 1.39 � 107 � ________________________

30. 9.04 � 10–4 � ________________________

EXAMPLE



Division of Decimals by Powers of Ten

Write in standard form. Divide 53 � 10 �

Directions Rewrite the following division problems in the standard form and divide.


EXAMPLE

1. 62 � 10 � ____________________

2. 7.7 � 100 � ____________________

3. 0.07 � 100 � ____________________

4. 39 � 1,000 � ____________________

5. 3 � 10 � ____________________

6. 4.07 � 100 � ____________________

7. 3.02 � 100 � ____________________

8. 8.4 � 1,000 � ____________________

9. 100 � 1,000 � ____________________

10. 5.6 � 10 � ____________________

11. 7 � 100 � ____________________

12. 6.2 � 1,000 � ____________________

13. 1.8 � 1,000 � ____________________

14. 94 � 100 � ____________________

15. 5 � 1,000 � ____________________

16. 13 � 1,000 � ____________________

17. 2.6 � 1,000 � ____________________

18. 8.6 � 100 � ____________________

19. 0.0023 � 10 � ____________________

20. 2 � 1,000 � ____________________

21. 3.8 � 100 � ____________________

22. 4.02 � 10,000 � ____________________

23. 566 � 1,000 � ____________________

24. 2,963 � 1,000 � ____________________

25. 8,203 � 10,000 � ____________________

26. 4,002 � 100 � ____________________

27. 0.706 � 10 � ____________________

28. 9 � 1,000 � ____________________

29. 0.04 � 100 � ____________________

30. 0.3006 � 100 � ____________________

31. 0.35 � 1,000 � ____________________

32. 4.02 � 100 � ____________________

33. 17 � 1,000 � ____________________

34. 1 � 1,000 � ____________________

35. 4.2 � 10,000 � ____________________

36. 0.02 � 10,000 � ____________________

37. 45.7 � 10,000 � ____________________

38. 5,023.5 � 10,000 � ____________________

39. 51.5 � 1,000 � ____________________

40. 6.66 � 10,000 � ____________________

41. 3.02 � 1,000 � ____________________

42. 728 � 10 � ____________________

43. 936 � 10,000 � ____________________

44. 641.02 � 10,000 � ____________________

45. 5.5 � 100 � ____________________

5.310 �5�3�.0�

– 503 0

– 3 00



Division of Decimals

Write in standard form. Move decimal. Divide 23.4 by 0.1 �

Directions Rewrite the following division problems in the standard form and divide. Round each quotient to the nearest hundredth.

Directions Solve the following word problems with division.

29. Kathleen purchases tomatoes for lunch. If the tomatoes are priced at 4 pounds for $4.24, how much will she pay for one pound?

30. A carton of six colas sells for $4.62. How much does one cola cost?


EXAMPLE

1. 14.4 � 0.7 � _____________________

2. 0.46 � 0.4 � _____________________

3. 0.98 � 0.8 � _____________________

4. 10 � 5.5 � _____________________

5. 1.5 � 0.9 � _____________________

6. 2.6 � 1.5 � _____________________

7. 0.06 � 0.7 � _____________________

8. 40 � 1.2 � _____________________

9. 7.7 � 0.03 � _____________________

10. 5.6 � 0.12 � _____________________

11. 12.3 � 1.1 � _____________________

12. 6.99 � 1.2 � _____________________

13. 9.12 � 0.9 � _____________________

14. 28.04 � 0.7 � _____________________

15. 3.5 � 3 � _____________________

16. 6.33 � 0.07 � _____________________

17. 1 � 0.9 � _____________________

18. 2.2 � 13 � _____________________

19. 30 � 89 � _____________________

20. 5.06 � 1.2 � _____________________

21. 5 � 1.5 � _____________________

22. 49.9 � 3.4 � _____________________

23. 2 � 4.5 � _____________________

24. 0.506 � 0.403 � _____________________

25. 4.06 � 2.02 � _____________________

26. 0.0008 � 0.04 � _____________________

27. 0.045 � 0.08 � _____________________

28. 3.91 � 2.6 � _____________________

2340.1 �2�3�.4�

– 203

– 30 4– 4

0



Basic Operations with Decimals


Directions Add.



Directions Divide. Round the quotients to the nearest hundredths.


1. 2.3 � 5.67 � ______________

2. 45 � 9.97 � 0.055 � ______________

3. 3.04 � 0.056 � 0.7 � ______________

4. 67.3 � 34.09 � 4.45 � ______________

5. 0.0745 � 0.45 � 0.087202 �_____________

6. 3.45 � 0.0923 � 3.07 � _____________

7. 2.33 � 0.76 � 74.9 � 4.4 � _____________

8. 0.0348 � 0.2 � 4 � 4.45 � _____________

2.3+ 5.67

7.97

5 9 10

36.00– 0.93

35.07

2.2

� .9

1.98

.38229 �3�.4�4�0�0�– 2 7

74– 72

20– 18

20– 18

2

9. 36 � 0.93 � _____________________

10. 4.5 � 2.09 � _____________________

11. 5.943 � 0.56 � _____________________

12. 0.0982 � 0.039 � _____________________

13. 2.9 � 0.8033 � _____________________

14. 50.4 � 28.48 � _____________________

15. 1 � 0.97 � _____________________

16. 345 � 23.9 � _____________________

17. 2.2 � 0.9 � _____________________

18. 34 � 5.2 � _____________________

19. 6.7 � 0.67 � _____________________

20. 45.3 � 0.23� _____________________

21. 30.5 � 4.5 � _____________________

22. 3.409 � 0.42 � _____________________

23. 90.4 � 2.11 � _____________________

24. 5.63 � 0.941 � _____________________

25. 3.44 � 9 � _____________________

26. 98.3 � 20 � _____________________

27. 1.304 � 1.1 � _____________________

28. 36 � 0.7 � _____________________

29. 3 � 1.7 � _____________________

30. 5.606 � 25 � _____________________

EXAMPLES



Decimals to Fractions

Rename 0.6 as a fraction. Simplify if necessary.

0.6 � �160� � �

35�

Directions Rewrite each decimal as a fraction or a mixed number.Simplify the answers to the lowest terms.


EXAMPLE

1. 0.51 � _____________

2. 0.07 � _____________

3. 0.5 � _____________

4. 0.2 � _____________

5. 0.003 � _____________

6. 0.007 � _____________

7. 0.75 � _____________

8. 0.82 � _____________

9. 0.15 � _____________

10. 1.5 � _____________

11. 0.62 � _____________

12. 0.085 � _____________

13. 0.008 � _____________

14. 0.001 � _____________

15. 2.6 � _____________

16. 0.022 � _____________

17. 0.04 � _____________

18. 20.6 � _____________

19. 5.03 � _____________

20. 4.1 � _____________

21. 200.6 � _____________

22. 0.0012 � _____________

23. 0.041 � _____________

24. 0.101 � _____________

25. 0.9 � _____________

26. 0.102 � _____________

27. 0.052 � _____________

28. 0.0071 � _____________

29. 0.004 � _____________

30. 0.38 � _____________

31. 15.1 � _____________

32. 3.75 � _____________

33. 0.25 � _____________

34. 2.25 � _____________

35. 1.82 � _____________

36. 0.21 � _____________

37. 1.002 � _____________

38. 0.52 � _____________

39. 0.42 � _____________

40. 2.125 � _____________

41. 0.54 � _____________

42. 0.0085 � _____________

43. 4.48 � _____________

44. 1.53 � _____________

45. 10.5 � _____________

46. 1.18 � _____________

47. 24.5 � _____________

48. 0.0002 � _____________

49. 0.353 � _____________

50. 7.2 � _____________

51. 0.0004 � _____________

52. 0.1004 � _____________

53. 46.85 � _____________

54. 0.999 � _____________

55. 0.122 � _____________

56. 0.01 � _____________

57. 0.106 � _____________

58. 0.004 � _____________

59. 0.147 � _____________

60. 54.06 � _____________

61. 1.85 � _____________

62. 9.43 � _____________

63. 7.78 � _____________

64. 4.14 � _____________

65. 0.335 � _____________

66. 1.38 � _____________

67. 0.34 � _____________

68. 0.554 � _____________

69. 0.332 � _____________

70. 0.246 � _____________



Fractions to Decimals

Rename �23� as a decimal.

Round to nearest hundredth.

Directions Write each fraction as a decimal rounded to the nearest hundredth.


EXAMPLE

1. �115� � _____________

2. �136� � _____________

3. �110� � _____________

4. �45

� � _____________

5. �117� � _____________

6. �11

34� � _____________

7. �69

� � _____________

8. �19

� � _____________

9. �190� � _____________

10. �35

� � _____________

11. �154� � _____________

12. �34

� � _____________

13. �12

� � _____________

14. �166� � _____________

15. �11

21� � _____________

16. �131� � _____________

17. �210� � _____________

18. �11

45� � _____________

19. �25

� � _____________

20. �251� � _____________

21. �132� � _____________

22. �67

� � _____________

23. �37

� � _____________

24. �111� � _____________

25. �18

� � _____________

26. �125� � _____________

27. �11

57� � _____________

28. �133� � _____________

29. �136� � _____________

30. �156� � _____________

31. �127� � _____________

32. �13

� � _____________

33. �129� � _____________

34. �16

� � _____________

35. �230� � _____________

36. �21

01� � _____________

37. �191� � _____________

38. �169� � _____________

39. �171� � _____________

40. �11

01� � _____________

41. �56

� � _____________

42. �176� � _____________

43. �153� � _____________

44. �163� � _____________

45. �89

� � _____________

.666 → 0.673 �2�.0�0�0�– 1 8

20– 18

20– 18

2



Changing Fractions to Decimals

Change the fraction to a decimal. Divide to 3 decimal places.Then round to 2 places.

Hint: Try to simplify the fraction before division.

�122� � �

16

� � 6�1�.0�0�0� � 0.166 � 0.17

Directions Change these fractions to decimals. Divide to 3 places.Then round to 2 places.


EXAMPLE

1. �79

� � _______________________

2. �59

� � _______________________

3. �161� � _______________________

4. �79

� � _______________________

5. �11

01� � _______________________

6. �11

21� � _______________________

7. �78

� � _______________________

8. �11

23� � _______________________

9. �120� � _______________________

10. �49

� � _______________________

11. �132� � _______________________

12. �125� � _______________________

13. �18

� � _______________________

14. �19

� � _______________________

15. �23

00� � _______________________

16. �27

55� � _______________________

17. �56

00� � _______________________

18. �13

26� � _______________________

19. �12

24� � _______________________

20. �15150

� � _______________________

21. �34

50� � _______________________

22. �23

23� � _______________________

23. �278� � _______________________

24. �396� � _______________________

25. �27

05� � _______________________

26. �133� � _______________________

27. �13

74� � _______________________

28. �134� � _______________________

29. �350� � _______________________

30. �245� � _______________________



Writing Ratios

Show a ratio in its three forms.

�12� � 1:2 � 1 to 2

Directions Express the ratios using the other two forms.

Directions Count the number of like symbols and write the ratios for each.

21. Write the ratio of the number of @’s to #’s. ____________________

22. Write the ratio of the number of @’s to %’s. ____________________

23. Write the ratio of the number of @’s to $’s. ____________________

24. Write the ratio of the number of @’s to *’s. ____________________

25. Write the ratio of the number of #’s to %’s. ____________________

26. Write the ratio of the number of #’s to *’s. ____________________

27. Write the ratio of the number of #’s to @’s. ____________________

28. Write the ratio of the number of *’s to @’s. ____________________

29. Write the ratio of the number of *’s to $’s. ____________________

30. Write the ratio of the number of %’s to #’s. ____________________


EXAMPLE

1. �43

� ____________________

2. 4:7 ____________________

3. 9 to 12 ____________________

4. �58

� ____________________

5. 12:16 ____________________

6. 5 to 15 ____________________

7. �93

� ____________________

8. �11

25� ____________________

9. �11

67� ____________________

10. �21

21� ____________________

11. 23:80 ____________________

12. 3 to 7 ____________________

13. 4 to 9 ____________________

14. 5 to 18 ____________________

15. 26:27 ____________________

16. 32:42 ____________________

17. �34

45� ____________________

18. 2 to 18 ____________________

19. 33:34 ____________________

20. �273� ____________________

@ # % $ # * & $ $# @ $ * & & # @# @ * & & * * # @& # @ $ $ $ $ #@ @ $ % % & * *& * % % $ # $ %& * & $ # @ @ ## $ $ % % * & * &* & * & * * * & $ $# # @ @ # # * *



Proportions

Do �78� and �

23

82� form a proportion?

The cross products are both 224. The cross products are equal,so the ratios form a proportion.

�78� � �

2382�

8 � 28 7 � 32224 224

Directions Use cross products to decide if the ratios are equal. Write an equal

sign (�) if the ratios form a proportion. Write an inequality symbol

() if the ratios do not form a proportion.


EXAMPLE

1. �13

� �142�

2. �18

50� �

745�

3. �27

� �28

46�

4. �11088

� �138�

5. �255� �

12550

�

6. �23

� �192�

7. �11

06� �

58

�

8. �78

� �11

56�

9. �34

� �68

�

10. �156� �

28

56�

11. �19860

� �13

60�

12. �24

� �48

�

13. �342� �

16

64�

14. �192� �

23

76�

15. �135� �

495�

16. �75

24� �

97

�

17. �39

� �297�

18. �14

� �24

�

19. �13

� �56

�

20. �45

� �22

05�

21. �11

09� �

33

09�

22. �36

� �150�

23. �14

� �28

�

24. �58

� �34

�

25. �27

� �28

44�

7 28

8 32



Ratios and Proportions

14 books to 2 readers

Write the ratio as a fraction. Simplify if necessary.

�124� � �

71�

Directions Write a ratio to compare each of the following. Simplify to lowest terms.

Cross-multiply. Divide.

�7n2� � �

82�

8n � 72 � 2 8n = 144 n � 144 � 8n � 18

Directions Solve these proportions using the cross-product method.Express improper fractions as mixed numbers.


EXAMPLE

1. 12 music CD’s to 4 tapes

_______________________

2. 10 automobiles to 13 bikes

_______________________

3. 24 apples to 8 oranges

_______________________

4. 125 miles to 5 gallons of gas

_______________________

5. 22 cats to 33 dogs

_______________________

6. 24 baseballs to 38 players

_______________________

7. 14 lb of flour to 7 shoppers

_______________________

8. 8 students to 18 tables

_______________________

9. 28 TV’s to 56 radios

_______________________

10. 22 planes to 11 trains

_______________________

11. �n7

� � �11

40�

12. �12

84� � �

n2

�

13. �11

05� � �

2n5�

14. �11

13� � �

3n9�

15. �41

80� � �

n5

�

EXAMPLE



Using Proportions

Cross-multiply. Compare products.

�23� �

11

15� 2 � 15 � 30 3 � 11 � 33

�23� �

11

15�

Directions Use cross products and use �, , or � for each.

Directions Use the cross-product method to solve for the unknown.

Directions Write and solve proportions using the cross-product method.Round your answers to the nearest tenths place.

13. Eldo can ride his bike 15 miles in 2 hours. How many miles can he ride in 7 hours?

14. Lacy can in-line skate 9 miles an hour. How many hours will it take her to do 30 miles?

15. Karen and Patrick worked together stringing beads for necklaces. If they can string 50 beads in 9 minutes,how long will it take for them to string 725 beads?


EXAMPLE30 33

1. �11

21� �

190�

2. �170� �

23

02�

3. �24

20� �

23

03�

4. �183� �

23

20�

5. �89

� �11

35�

6. �12

51� �

11

78�

7. �13

40� � �

9n0�

8. �n3

� � �21

52�

9. �2n7� � �

69

�

10. �1n8� � �

132�

11. �n7

� � �25

86�

12. �596� � �

n4

�

�



Meaning of Percent

Shade the boxes to show percent.

16% � 16 out of 100

Shade 16 boxes.

Directions Shade these percents.

1. 23% 5. 33% 9. 95% 13. 55%

2. 75% 6. 80% 10. 45% 14. 12%

3. 30% 7. 9% 11. 60% 15. 68%

4. 40% 8. 17% 12. 100%


EXAMPLE



Changing Percents to Decimals and Fractions

14% Write as a decimal. Drop percent sign. Add decimal point.14% � 0.14

14% Write as a fraction. Drop percent sign.Write number as a numerator over denominator of 100.Simplify if necessary.

14% � �11040

� � �570�

Directions Write these percents as decimals.

Directions Write these decimals as fractions. Simplify your answers.

Directions Write these percents as decimals and fractions.Simplify your answers.


1. 17% � ___________

2. 33% � ___________

3. 60% � ___________

4. 22% � ___________

5. 41% � ___________

6. 46% � ___________

7. 90% � ___________

8. 37% � ___________

9. 55% � ___________

10. 75% � ___________

11. 61% � ___________

12. 80% � ___________

13. 39% � ___________

14. 66% � ___________

15. 48% � ___________

16. 34% � ___________

17. 100% � ___________

18. 1% � ___________

19. 0.37 � ___________

20. 0.18 � ___________

21. 0.11 � ___________

22. 0.05 � ___________

23. 0.08 � ___________

24. 0.01 � ___________

25. 0.33 � ___________

26. 0.09 � ___________

27. 0.40 � ___________

28. 0.50 � ___________

29. 0.68 � ___________

30. 0.10 � ___________

31. 0.02 � ___________

32. 0.88 � ___________

33. 0.25 � ___________

34. 0.35 � ___________

35. 0.90 � ___________

36. 0.55 � ___________

37. 24% � ____________________________

38. 30% � ____________________________

39. 23% � ____________________________

40. 33% � ____________________________

41. 70% � ____________________________

42. 72% � ____________________________

43. 87% � ____________________________

44. 95% � ____________________________

45. 74% � ____________________________

EXAMPLES



Decimals to Percents

Rename 0.63 as a percent by moving the decimal point two placesto the right and adding the percent symbol.

0.63 � 63%

Directions Rewrite each decimal as a percent.


EXAMPLE

1. 0.36 � _____________

2. 1.35 � _____________

3. 0.05 � _____________

4. 0.6 � _____________

5. 0.78 � _____________

6. 0.45 � _____________

7. 0.0088 � _____________

8. 0.035 � _____________

9. 0.122 � _____________

10. 0.02 � _____________

11. 0.4 � _____________

12. 0.21 � _____________

13. 2.09 � _____________

14. 2.3 � _____________

15. 6.12 � _____________

16. 4.5 � _____________

17. 0.065 � _____________

18. 0.0081 � _____________

19. 0.205 � _____________

20. 0.244 � _____________

21. 0.0045 � _____________

22. 0.6031 � _____________

23. 5.05 � _____________

24. 0.2207 � _____________

25. 0.41 � _____________

26. 0.2246 � _____________

27. 0.032 � _____________

28. 0.01 � _____________

29. 0.1 � _____________

30. 0.112 � _____________

31. 0.172 � _____________

32. 1.75 � _____________

33. 2 � _____________

34. 62 � _____________

35. 4.09 � _____________

36. 3.1 � _____________

37. 9.21 � _____________

38. 0.155 � _____________

39. 80.0 � _____________

40. 7.02 � _____________

41. 25.0 � _____________

42. 3.44 � _____________

43. 22.332 � _____________

44. 5.556 � _____________

45. 2.33 � _____________

46. 0.75 � _____________

47. 15.02 � _____________

48. 0.0062 � _____________

49. 30.452 � _____________

50. 73.1 � _____________

51. 33.4 � _____________

52. 1.433 � _____________

53. 43.14 � _____________

54. 12.06 � _____________

55. 48.045 � _____________

56. 2.332 � _____________

57. 2.398 � _____________

58. 12.124 � _____________

59. 42.46 � _____________

60. 0.0056 � _____________



Major Elements of a Percent Sentence

15% of what number is 52? Rate Base Percentage

15% n 52

What percent of 22 is 11? n 22 11

Directions Identify the rate, base, and percentage for the following percent sentences. Use the letter n to represent a missing value.

Rate Base Percentage

1. 56% of 90 is what number? __________________________________________________

2. What percent of 50 is 40? __________________________________________________


4. 88% of 50 is what number? __________________________________________________

5. 100% of what number is 176? __________________________________________________

6. 200% of 50 is what number? __________________________________________________

7. 90% of what number is 64? __________________________________________________


9. 70% of 50 is what number? __________________________________________________

10. 80% of 20 is what number? __________________________________________________



13. 150% of what number is 300? __________________________________________________

14. 6% of 33 is what number? __________________________________________________

15. 12% of what number is 70? __________________________________________________



18. 9% of 56 is what number? __________________________________________________

19. 33% of 129 is what number? __________________________________________________

20. 3% of what number is 27? __________________________________________________


EXAMPLES



Find the Percentage

8% of 20 is _________

8% of 20 is n0.08 � 20 � n

1.6 � n

Directions Solve for the percentage.


EXAMPLE

1. 9% of 50 is ______________________

2. 4% of 53 is ______________________

3. 28% of 4 is ______________________

4. 6% of 125 is ______________________

5. 2% of 86 is ______________________

6. 43% of 14 is ______________________

7. 75% of 92 is ______________________

8. 21% of 34 is ______________________

9. 92% of 62 is ______________________

10. 53% of 80 is ______________________

11. 15% of 28 is ______________________

12. 92% of 65 is ______________________

13. 3% of 2.1 is ______________________

14. 40% of 3.5 is ______________________

15. 7% of 0.7 is ______________________

16. 6% of 2.3 is ______________________

17. 122% of 42 is ______________________

18. 136% of 5 is ______________________

19. 200% of 73 is ______________________

20. 0.4% of 96 is ______________________

21. 7.2% of 48 is ______________________

22. 5.3% of 70 is ______________________

23. 0.8% of 245 is ______________________

24. 1.6% of 1.4 is ______________________

25. 2.8% of 9.02 is ______________________

26. 2.4% of 76 is ______________________

27. 5% of 0.083 is ______________________

28. 0.6% of 435 is ______________________

29. 0.7% of 7.49 is ______________________

30. 129% of 4.2 is ______________________

31. 0.03% of 141 is ______________________

32. 0.8% of 0.2 is ______________________

33. 0.82% of 403 is ______________________

34. 245% of 2.6 is ______________________

35. 10% of 45 is ______________________

36. 3.4% of 500 is ______________________

37. 45% of 100 is ______________________

38. 23.4% of 300 is ______________________

39. 140% of 62 is ______________________

40. 7% of 250 is ______________________

41. 0.46% of 746 is ______________________

42. 6.5% of 30 is ______________________

43. 7.9% of 500 is ______________________

44. 200% of 0.33 is ______________________

45. 9% of 9 is ______________________



Find the Base

5% of ________ is 1.4

5% of n is 1.40.05 � n � 1.4

n � 1.4 � 0.05n � 28

Directions Solve for the base.


EXAMPLE 280.5�1�.4�0�

– 1 040

– 40

1. 5% of __________ is 4.1

2. 2% of __________ is 3.6

3. 6% of __________ is 1.8

4. 3% of __________ is 0.27

5. 7% of __________ is 0.196

6. 4% of __________ is 1.28

7. 50% of __________ is 2.7

8. 35% of __________ is 30.8

9. 6% of __________ is 0.078

10. 8% of __________ is 0.32

11. 2.5% of __________ is 0.15

12. 7.3% of __________ is 2.044

13. 120% of __________ is 50.4

14. 3.4% of __________ is 2.38

15. 9% of __________ is 0.315

16. 5% of __________ is 0.13

17. 5% of __________ is 0.0235

18. 41% of __________ is 0.82

19. 3% of __________ is 0.045

20. 245% of __________ is 191.1

21. 9% of __________ is 0.0594

22. 0.3% of __________ is 0.135

23. 0.75% of __________ is 0.9

24. 0.8% of __________ is 0.4

25. 4% of __________ is 0.0176

26. 0.21% of __________ is 0.0735

27. 150% of __________ is 135

28. 125% of __________ is 62.5

29. 5.2% of __________ is 0.0988

30. 3.4% of __________ is 0.3094

31. 0.5% of __________ is 1.19

32. 0.21% of __________ is 0.0147

33. 0.32% of __________ is 0.32

34. 0.75% of __________ is 7.5

35. 8% of __________ is 0.416

36. 1.4% of __________ is 0.196

37. 6% of __________ is 0.138

38. 5% of __________ is 0.115

39. 120% of __________ is 102

40. 1% of __________ is 0.03

41. 0.9% of __________ is 1.35

42. 6.3% of __________ is 0.252

43. 8% of __________ is 16

44. 4% of __________ is 0.024

45. 1.6% of __________ is 3.376



Find the Rate

________% of 80 is 4.8

n% of 80 is 4.8 orn � 0.80 = 4.8

n = 4.8 � 0.80n = 6%

Directions Solve for the rate.


EXAMPLE6

0.80�4�.8�– 4 8

0

n � 80 = 4.8

n = �48.08�

n = 0.06 = 6%

1. __________ % of 25 is 5

2. __________ % of 35 is 1.05

3. __________ % of 70 is 3.5

4. __________ % of 30 is 1.8

5. __________ % of 80 is 5.6

6. __________ % of 20 is 1.8

7. __________ % of 80 is 0.56

8. __________ % of 200 is 102

9. __________ % of 20 is 7

10. __________ % of 300 is 45

11. __________ % of 100 is 9

12. __________ % of 2,000 is 360

13. __________ % of 35 is 2.8

14. __________ % of 305 is 48.8

15. __________ % of 20 is 30

16. __________ % of 64 is 112

17. __________ % of 10.5 is 0.84

18. __________ % of 250 is 70

19. __________ % of 38 is 1.14

20. __________ % of 72 is 1.08

21. __________ % of 206 is 16.48

22. __________ % of 500 is 4.5

23. __________ % of 2.06 is 0.1442

24. __________ % of 600 is 420

25. __________ % of 700 is 9.8

26. __________ % of 40 is 0.32

27. __________ % of 200 is 0.14

28. __________ % of 3,000 is 1.8

29. __________ % of 2.5 is 0.9

30. __________ % of 4.2 is 0.546

31. __________ % of 4 is 0.12

32. __________ % of 400 is 0.08

33. __________ % of 22 is 56.1

34. __________ % of 30 is 106.5

35. __________ % of 80 is 14

36. __________ % of 15 is 0.56

37. __________ % of 90 is 5.4

38. __________ % of 50 is 100

39. __________ % of 23 is 2.3

40. __________ % of 120 is 300

41. __________ % of 22 is 0.33

42. __________ % of 30 is 2.85

43. __________ % of 70 is 4.9

44. __________ % of 0.16 is 0.000136

45. __________ % of 50 is 9



Percent Sentences

Percentage Base Rate

25% of 80 is _____ 25% of _____ is 52 _____% of 44 is 1125% � 80 � n 25% � n = 52 n% � 44 = 110.25 � 80 � 20 0.25n = 52 n � 0.44 = 11

n = 208 n = 11 � 0.44n = 25%

Directions Solve for the percentage.

Directions Solve for the base.

Directions Solve for the rate.

Directions Complete each percent sentence.


1. 25% of 60 is __________

2. 82% of 50 is __________

3. 90% of 60 is __________

4. 35% of 36 is __________

5. 92% of 100 is __________

6. 20% of 30 is __________

7. 15% of __________ is 9

8. 60% of __________ is 15

9. 20% of __________ is 8

10. 62% of __________ is 10.54

11. 53% of __________ is 106

12. 92% of __________ is 23

13. __________ % of 9.5 is 7.6

14. __________ % of 70 is 21

15. __________ % of 45 is 4.05

16. __________ % of 30 is 21

17. __________ % of 80 is 72

18. __________ % of 26 is 0.65

19. __________ % of 2.5 is 0.375

20. 5.5% of __________ is 0.2475

21. 0.5% of 75 is __________

22. 2.8% of __________ is 18.2

23. __________ % of 240 is 192

24. 75% of __________ is 225

25. 10% of __________ is 0.26

EXAMPLES



Using Proportions

Find base. Find rate. Find percentage.

25% of n is 17.5 n% of 40 is 24 7% of 80 is n

�12050

� = �17

n.5� �

10n0

� = �2440� �

1700� = �

8n0�

100 � 17.5 = 25n 100 � 24 = 40n 100n = 7 � 80

1,750 = 25n 2,400 = 40n 100n = 560

�1,

27550� = �

2255n

� �2,

44000� = �

4400n

� �110000n

� = �516000

�

70 = n 60 = n n = 5.6

Directions Write proportions and solve for the unknown.


1. 20% of n is 9.6 ______________

2. n% of 35 is 5.6 ______________

3. 70% of 32 is n ______________

4. 30% of n is 120 ______________

5. n% of 50 is 11.5 ______________

6. 85% of 36 is n ______________

7. 90% of n is 270 ______________

8. n% of 97 is 48.5 ______________

9. 80% of 40 is n ______________

10. 23% of n is 73.6 ______________

11. n% of 60 is 24 ______________

12. 35% of n is 24.5 ______________

13. 18% of 350 is n ______________

14. n% of 29 is 2.03 ______________

15. 9% of n is 4.68 ______________

EXAMPLES



Discount

Find the sale price of a music CD that lists for $18.50, if the discount rate is 20%.

Step 1 $18.50 list price Step 2 $18.50 list price� .20 � 3.70 discount

$3.70 discount $14.80 price after discount

Find the discount rate if a $25.00 DVD is on sale for $21.25.

Step 1 $25.00 list price

� 21.25 discount price

$3.75 discount

Directions Solve these discount problems. When necessary round answers to the nearest cent.


.15 = 15% discount rate25�3�.7�5�– 2 5

125– 125

1. $175.00 list price10% discount rate

Discount _______

Sale price _______

2. $80.00 list price20% discount rate

Discount _______

Sale price _______

3. CD list price $22.0015% discount rate

Discount _______

Sale price _______

4. Videotape list price $50.00Sale price $20.00

Discount _______

Discount rate _______

5. Computer list price $950.00Discount rate 10%

Discount _______

Sale price _______

6. Radio list price $75.00Discount rate 15%

Discount _______

Sale price _______

7. Stereo list price $150.00Sale price $120.00

Discount _______

Discount rate _______

8. Disk drive list price $150.00Discount rate 20%

Discount _______

Sale price _______

9. Television list price $395.00Discount rate 10%

Discount _______

Sale price _______

10. Jeans list price $34.95Discount rate 10%

Discount _______

Sale price _______

EXAMPLES



Sales Tax

Compute 6% sales tax on $13.05

$13.05 cost before tax� .06 tax rate0.78300.79The tax is $0.79 or 79 cents.

Directions Compute sales tax.

Directions Compute sales tax and total cost.


EXAMPLE

1. $2.75 at 5% _________

2. $6.15 at 7% _________

3. $24.95 at 7% _________

4. $120.00 at 5% _________

5. $1,200.00 at 6% _________

6. $16.75 at 6% _________

7. $100.00 at 6% _________

8. $30.10 at 7% _________

9. $0.45 at 5% _________

10. A book for $17.95

6% tax rate

Tax _________

Cost plus tax _________

11. Clock for $75.00

5% tax rate

Tax _________


12. Television for $299.99

7% tax rate

Tax _________


13. Table for $98.00

5% tax rate

Tax _________


14. Used car for $11,960.00

6% tax rate

Tax _________


15. Electric stove for $699.00

5% tax rate

Tax _________


Tax always rounds up.



Simple Interest

Compute the simple interest on a principal of $125.00 at an interest rate of 7% for 3 years.

$125.00 principal $8.75 interest for one year� .07 � 3 for 3 years$8.7500 interest for one year $26.25 interest for 3 years

Compute the simple interest on $200.00 at a rate of 6% for 9 months.$200.00 principal� .06

$12.00 interest for 1 year

$9.00 is the interest for 9 months.

Directions Compute the simple interest.


EXAMPLE

1. Compute the simple interest for $750.00 at 7% for 5 years. _________________________

2. Compute the simple interest for $800.00 at 6% for 6 months. _________________________

3. Compute the simple interest for $1,200.00 at 9% for 10 years. _________________________





8. Compute the simple interest for $4,500.00 at 7% for 9 months._________________________



�$112

� � �192�

�112� � �

34� � �

346� � 9

Write 9 months over 12months to express timeas years.



Installment Buying

Find the finance charge and balance with a 2% finance rate for $400.00.

Step 1 $400.00 previous balance Step 2 $400.00 previous balance� .02 finance rate � 8.00 finance charge

$8.0000 finance charge $408.00

Step 3 $408.00

� 25.00 first month’s payment

$383.00 new balance

Directions Complete the installment chart for a TV that cost $400.00. The monthly payments will be $25.00 and a 2% finance charge will be added to the unpaid balance.

Directions Complete the installment chart for a TV that cost $400.00 with a 1% finance charge added to the unpaid balance. The monthly payments are $25.00.


EXAMPLE

New balance beforefirst payment

Previous Finance Before Monthly NewMonth Balance Charge Payment Payment Balance

June $400.00 $8.00 $408.00 $25.00 $383.00

July $383.00

August

September

October

Previous Finance Before Monthly NewMonth Balance Charge Payment Payment Balance

June

July

August

September

October



Commission

Compute the commission for a real estate agent who sells a house for $95,000 and the commission rate is 3%.

$95,000.00 sale price� .03 commission rate

$2,850.00 commission

Directions Compute the following sales commissions.


EXAMPLE

1. Amount is $4,500.00

Commission rate 5%

Commission _________

2. Amount is $48,000.00

Commission rate 3%


3. Amount is $3,400.00

Commission rate 3%


4. Amount is $500.00

Commission rate 5%


5. Amount is $1,000.00

Commission rate 3%


6. Amount is $1,600.00

Commission rate 3%


7. Amount is $450.00

Commission rate 5%


8. Amount is $1,700.00

Commission rate 4%


9. Amount is $3,400.00

Commission rate 5%


10. Amount is $950.00

Commission rate 10%


11. Amount is $560.00

Commission rate 5%


12. Amount is $880.00

Commission rate 4%


13. Amount is $234.00

Commission rate 11%


14. Amount is $911.00

Commission rate 4%


15. Amount is $260.00

Commission rate 9%




Tips

Compute a 15% tip on a meal that costs $23.50.

$23.50 meal cost $23.50 meal cost� .15 tip rate � 3.53 tip

11750 $27.03 total2350

$3.5250 round to nearest cent

$3.53 rounded to nearest cent

Directions Compute the tip for each meal. Use 15% as a tip rate for each meal.

Directions Compute the tip for each meal and round to the nearest dollar.


EXAMPLE

1. Meal cost $20.00

Tip _________

Meal total _________

2. Meal cost $27.20

Tip _________


3. Meal cost $37.00

Tip _________


4. Meal cost $25.00

Tip _________


5. Meal cost $45.20

Tip _________


6. Meal cost $18.00

Tip _________


7. Meal cost $5.50

Tip _________


8. Meal cost $11.90

Tip _________


9. Meal cost $4.50

Tip _________


10. Meal cost $4.60

Tip _________


11. Meal cost $15.50

Tip _________



Tip _________



Tip _________


14. Meal cost $5.50

Tip _________


15. Meal cost $7.95

Tip _________




Points, Lines, and Angles

Make a construction to represent AB.

A B B A

Rays can be drawn from either direction. The beginning point must be A as indicated AB.

Directions Use the baseline provided to construct the following geometric constructions.


EXAMPLE

• • • •

1. BA _____________________

2. �ABC _____________________

3. �XYZ _____________________

4. AD _____________________

5. D�Z� _____________________

6. Vertex G _____________________

7. Vertex H _____________________

8. RT _____________________

9. point B _____________________

10. �QRS _____________________

→

→

↔

→

→



Identifying Angles

Construct an acute angle.

Directions Construct these angles on the baselines given.

1. acute 4. reflex

_________________ ___________________

2. straight 5. right

_________________ ____________________

3. obtuse

_________________


EXAMPLE

∠ABC is acute because ∠Bis less than 90 degrees.

•

• •

A

B

C



Measuring Angles

Place protractor on the angle so that the center is on the angle’s vertex and the baseline is on one of the rays.

Make sure second ray crosses the scale. Read the scale.

45°

Directions Use a protractor to measure these angles to the nearest degree.If necessary, use a straightedge to extend the sides of the angle.

1. __________________ 4. __________________

2. __________________ 5. __________________

3. __________________


EXAMPLE



Polygons

Count the number of sides. Name the polygon.

quadrilateral

Directions Count the number of sides for each polygon. Use the chart to classify each polygon.

1. 5.

__________________ __________________

2. 6.

__________________ __________________

3. 7. 9.

__________________ __________________ __________________

4. 8. 10.

__________________ __________________ __________________


EXAMPLE

Number Name of of Sides Polygon

3 triangle

4 quadrilateral

5 pentagon

6 hexagon

7 heptagon

8 octagon

9 nonagon

10 decagon

12 dodecagon



Solid Figures

Look at the solid figure. Identify it.

cone

Directions Identify these solid figures.

1. 5. 9.

__________________ __________________ __________________

2. 6. 10.

__________________ __________________ __________________

3. 7.

__________________ __________________

4. 8.

__________________ __________________


EXAMPLE

Documents

Place Value - I Love Algebra · 2018. 9. 6. · Name Date PeriodWorkbook Activity Chapter 1, Lesson 2 4 Rounding Whole Numbers Read the number. Round the number to the nearest tens