41 Finding a Percent of Name - LearningTOPSlearningtops.yolasite.com/resources/Crs1_Lessons041-050.pdf† To find a percent of a number: 1. Change the percent to a fraction or decimal

$Page 1: 41 Finding a Percent of Name - LearningTOPSlearningtops.yolasite.com/resources/Crs1_Lessons041-050.pdf† To find a percent of a number: 1. Change the percent to a fraction or decimal$
Saxon Math Course 1 L41-161 Adaptations Lesson 41

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Finding a Percent of a Number (page 216)

• You already know how to change a percent to a fraction. Rewrite the percent as a fraction with a denominator of 100 and reduce.

25% = 25

____ 100

= 1 __

4 5% =

5 ____

100 =

1 ___

20 150% =

150 ____

100 = 1

1 __

2

• To change a percent to a decimal, write the number as hundredths.

25% = 0.25 5% = 0.05 150% = 1.50

• To find a percent of a number:

1. Change the percent to a fraction or decimal.

2. Then solve.

Example: What number is 75% of 20?

Change the percent to a Change the percent to a fraction; then solve. decimal; then multiply.

is

__ of

3 __

4

___

20 = 15

Practice Set (page 218)

Write each of these percents as a reduced fraction.

a. 50% = b. 10% = c. 25% =

d. 75% = e. 20% = f. 1% =

Write the following percents as decimal numbers.

g. 65% = h. 7% = i. 30% =

j. 8% = k. 60% = l. 1% =

m. What number is 10% n. Find 25% of 48. o. How much money of 350? is 8% of $15.00?

is

__ of

1 ___

10

____

350 =

p. The sales-tax rate is 9 1

__ 2

%. Estimate the tax on a $9.98 purchase. How did you get your answer? 9 1

__ 2 %

rounds to % and $9.98 rounds to $ . % equals 1 ___

10 and

1 ___

10 times $ is $ .

q. Erika sold 80% of her 30 baseball cards. How many baseball cards did she sell?

80% = is

__ of

___

___ 30

Teacher Note:• Review “Fraction Decimal

Percent” on page 13 in the Student Reference Guide.

0.750× 20

15.00

$15 0.08

is __

of

1 __

4

___ =


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1. 80% of 20

Multiply the loop.

Divide by the outside number.

80% =

is

__ of

___

___

2. 8% of $8.50 $8.50 × $8.50

An 8% sales tax means

cents per dollar. $8.50 rounds to

$ ,so the tax should be close to

× = $ .

3. perimeter 4. Convert to a f ,

and m that number by .

5. 20 – = b

$20.00 9.18

6. 16 ∙ c = 288

Multiply the loop.

Divide by the outside number.

chairs

______ rows

___ ?

__ 1

7. average

126102

141

8. area

9. least to greatest

3 __

2 , 0, –1,

2 __

3

10. prime numbers

Written Practice (page 219)

, , , 2 , , , , , , ,

Use work area.


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11. Which does NOT divide 600?Use tests for divisibility.

A 2 B 3 C 5 D 9

12. win

____ loss

___

13. diameter 14.

a. parallel to Vine

b. perpendicular to Vine

15. Which is the measure of an acute angle?See the Student Reference Guide.

A 0° B 45° C 90° D 135°

16. (2.5)2 =

2.5 2.5

17. √___

81 = 18. reduced fraction

40% =

19. decimal number

9% =

$10 $10

20. reciprocal of 2

__ 3

Written Practice (continued) (page 220)

a.

b.


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21. 7m = 3500 22. $6.25 + w = $10.00

$10.00× $16.25

23. 2

__ 3 n = 1 24. x – 37 = 76

76× 37

25. 4.0 4.0

6.25 4.00

26. 3 3

__ 4

+ 2 3

__ 4

27. 4 __

4 –

3 __

3 = 28.

5 __

6 ∙

3 __

5 =

29. is

__ of

___

___ 48

30. estimate

9% %

$32.17 $

is

__ of

___

___


m =

n = x =

w =


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Renaming Fractions by Multiplying by 1 (page 221)

• To rename a fraction means to give an equivalent fraction.

• Multiply the fraction by a fraction equal to 1. The new fraction will be an equivalent fraction.

Example: Write a fraction equal to 1 _ 2 that has a denominator of 20.

1 __

2 =

? ___

20

1 __

2 ×

10 ___

10 =

10 ___

20

• You can do this easily with fraction manipulatives.

• When you do not have manipulatives, try the loop method.

Example: 2 __

3 =

___

15 (2 ∙ 15) ÷ 3 = 10

2 __

3 =

10 ___

15


a. 1

__ 3

=

___ 12

b. 2

__ 3 =

___

6

c. 3 __

4 =

___

8 d.

3 __

4 =

___

12

e. Shade 2 __

3 . Shade

1 __

4 .

Name each shaded rectangle as a fraction with a denominator of 12.

00

___ 12

00

___ 12

f. Write 2

__ 3 and

1 __

4 as fractions with denominators of 12. Then add the renamed fractions.

2

__ 3

=

___ 12

1 __

4 =

___

12

___

12 +

___

12 =

g. Describe how the rectangles you shaded in exercise e can help you add the fractions in f.

The shaded rectangles show the number of t in 2

__ 3

and 1

__ 4

. So I can count the

total number of t shaded fo find the s of the fractions.

h. Write 1

__ 6 as a fraction with 12 as the denominator. Subtract the renamed fraction from

5 ___

12 .

Reduce the subtraction answer.

1 __

6 =

___

12

5 ___

12

–

___ 12

=


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1. Answer with a mixed number.

1 __

2

2 __

3

___ 6

+

___ 6 =

2. two hundred billion

3. area

120 rounds to and times 40

is . This is close to my answer.

4. 40% of 30

40% =

is

__ of

___

___

5. 1 __

2 =

___

8 6.

1 __

2 =

___

10

7. 4.324.32

4.32

8. 6.300 4.030

9. (0.15)2 = 10. reciprocal of 6

__ 7



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11. 12,345.8967.89

12. LCM of 3, 4, and 6

13. 5 3 __

5

+ 4 4 __

5

14. √___

36 – 4 2

__ 3

=

– 4 2__ 3

15. 8 __

3 ×

1 __

2 = 16.

6 __

5 ×

___ =

17. 1 1 _ 4

– 1 __

4

18. 10

___ 10

– 5

__ 5

=

19. 1 __

3 =

___

6

___

9

___

12 20. prime numbers


, Use work area.


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21. estimate the average

12,643 9,870

14,261

Round the scores to , , and .

A the scores to get ; then

d by to find the average.

22. estimateCancel the matching zeros.

8176 41

Round 8176 to and 41 to . Then

d .

23. is

__ of

___

___

25. perimeter 26. area

27. fact family

r – d = s r – = s + = d + =

28. Divisor is .

Dividend is .

Quotient is .

29. 2 1

__ 2 hours after 11:45 p.m.

time now

Count hours.

Count minutes.

30. a. How many 5 __

6 s are in 1?

b. How many 5

__ 6

s are in 3?


Regular

Fact Family

DiscountSale

Use work area.

_____

24. 3

__ 4 =

___

8

7 __

8

+ 7 __

8 Now subtract.

Use work area.

Use work area.

a.

b.


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Equivalent Division Problems Finding Unknowns in Fraction and Decimal Problems (page 225)

• If you multiply or divide the dividend and the divisor by the same number, the quotient does not change. You make an equivalent division problem.

• Short division is much easier than long division. With two-digit division problems, try to cut the numbers in half; then you have an easy short division problem.

Example: Make an equivalent division problem; then divide.

16 ) ______

1200 8 ) ______

6 0 40

Divide both numbers by 2. 7 5

• Finding unknowns with fractions and decimals is exactly the same as with whole numbers. See “Missing Numbers” in the Student Reference Guide.


a. 5 1 __

3

(× 3) (× 3)

÷ =

b. Half of:

266 14

c. 5.d– d

3.2

5.0+ 3.2

d = d. f

– 1

__ 5

4 __

5

4 __

5

– 1

__ 5

f =

e. m

+ 1 1 __

5

40

4 4 __

5

– 1 1 __

5

m = f. 3 __

8 w = 1 w =

_____


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1. total cost

$120 $120

$120.00 $120.00

2. 150 – = d

150 128

3. 19.73 old record19.32 new record

4. 2

__ 3

=

___ 6

5. 1

__ 2 =

___

6 6.

2 __

3 n = 1

7. 6 – w = 1 4 __

5

6 3

__ 8

+ 1 4

__ 5

8. m – 4 1

__ 4 = 6

3 __

4

6 3 __

4

+ 4 1 __

4

9. c – 2.45 = 3

3.45+ 2.45

10. 12 – d = 1.43

12.43+ 11.43


w = m =

c = d =

n =


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11. 5 __

8 ×

1 __

5 = 12.

3 __

4 ×

___ =

13. 3 7

__ 8

– 1 3 __

8

14. NOT primeSee the Student Reference Guide.

A 23 B 33 C 43

15. 2 __

2

2 __

2 ×

2 __

2 16. 12-yard loss

17. nine and twelve hundredths 18. 67, 4 92,384

19. 0.37 × 102

shift 0.3700 0

20. (0.6 × 0.4) × 0.2 =


.


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21. perimeter 80 ft

each side

area

22. Answer with a reduced mix number.

100

23. a. Answer with a mixed number.

100

____ 16

(÷ 4)(÷ 4)

100

____ 16

=

b. 4 1 __

2

1 __

2

(× 2) (× 2)

÷

24. LCM of 4, 6, and 8

25. Complete the sequence of 1 ___

16 s.

Remember to reduce fractions.

... 1 __

4 ,

5 ___

16 , 3

__ 8

,

7 ___

16 , , ,

4 __ 16 6 __ 16 __ 16 __ 16

26. Measure to the nearest eighth of an inch.

27. What mixed number? 28. 1 __

2

___

10

1

__ 5

+

___ 10

29. 40% = of 20 seats

is

__ of

___

___

30. acute, right, or obtuse

a. angle A

b. angle B

c. angle C

d. angle D


=

Use work area.

a.

b.

, ,


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Simplifying Decimal Numbers

Comparing Decimal Numbers (page 231)

• Zeros at the end of a decimal number do not change the value of the number.

0.3 = 0.300 = 0.3000

• To simplify decimal numbers:

Get rid of the extra zeros in front and back.

Keep the zero in front of the decimal.

Do not remove a zero that has value.

Examples:

02.0100 = 2.01

0.4200 = 0.42

• To compare decimal numbers:

1. Rewrite the numbers vertically and line up the decimal points.

2. Compare the greatest place value first (start on the left).

Example: 0.3 0.209 0.3 0.3 > 0.209 0.209


Write these numbers in simplified form:

a. 0.0500 . b. 50.00

c. 1.250 . d. 4.000

Compare these decimal numbers:

e. 0.2 0.15 0.20.15

f. 12.5 1.25 12.501.25

g. 0.012 0.12 0.0120.120

h. 0.31 0.039 0.3100.039

i. 0.4 0.40 0.400.40

j. Write these numbers in order from least to greatest. 0.12, 0.125, 0.015, 0.2

, , ,

least greatest

Teacher Notes:• Review Hint #43, “Tenths and

Hundredths.”

• Overhead base-ten blocks available in the Adaptations Manipulative Kit may be used to show that tenths are greater than hundredths.

0.120.1250.0150.2


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1. Multiples: Think times table.

( ) + ( ) =

third multiple third multiple

of 4 of 5

2. mi

___ ft

1 _____

5280

___

?

3. 29,035 Mt. Everest14,495 Mt. Whitney

4. Mt. Everest 5 miles in feet

5. 5 1 __

3 – w = 4

5 1 __

3 + 40

6. m – 6 4 __

5 = 1

3 __

5

6 4 __

5

+ 1 3 __

5

7. 6.74 + 0.285 + f = 11.025

6.740× 0.285

11.025× 11.025

8. 0.4 – d = 0.33

0.40× 0.33

9. 67 3

__ 4

1 1 __

4

with shoes 10. 8 1

__ 2

1

__ 2

(× 2) (× 2)

÷ =

w = m =

f = d =


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11. thirty-two thousandths 12. is

__ of

___

___

13. a. 0.25 0.125

b. 25% 12.5%

14. standard notation

(6 × 100) + (4 × 1)

15. Multiply by 10: shift decimal point right

Divide by 10: shift decimal point left

10% equals the fraction . Find

of $36 by d $36 by .

shift $36.00


8 s are in 1?

b. How many 5

__ 8

s are in 3?

17. LCM of 2, 3, 4, and 6. 18. (1 ∙ 3)2 =

19. 3 __

4 =

? ___

12 20.

2 __

3 =

? ___

12

0.250.125

.

a.

b.

a.

b.


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21. average

263742

43

22. nearest thousand

364,857

23. boys

_____ girls

___ = 24. a. factors of 100

b. prime numbers

25. fraction and decimal numbers

9%

26. 3 __

4

___

12

2 __

3 +

___

12

27. Nearly half of the r is shaded.

Since 1 _ 2 is equivalent to %, the shaded

part of the r is close to but

l than %.

29. closest to 1

A 0.1 B 0.8 C 1.1 D 1.2

30. What mixed number?

28. 10:30 a.m. to 2:15 p.m.

10:30 a.m. to =

to 2:15 p.m. =


a.

b.

.


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Dividing a Decimal Numberby Whole Number (page 235)

• Decimal numbers divided by a whole number:

Put the first number inside the division box.

Put the second number in front of the box.

Put the decimal straight up on the answer line.

Use zero as a placeholder.

Put a digit above each digit.

Use short division.

Add zeros to the dividend and keep dividing until thereis no remainder.


Teacher Note:• Review Hint #9, “Short Division.”

When dividing by a whole number,decimal goes straight up.

.

Example: 0.3 ÷ 4

4 ) _____

0. 3

0. 4 )

_____ 0. 3

0. 0 7 5

4 ) ________

0. 3 0 0

a. The distance from Margaret’s house to school and back is 3.6 miles. How far does Margaret live from school?

) ________

3. 6000

b. The perimeter of a square is 6.4 meters. How long is each side of the square? How can you check that your answer is reasonable?

sides

_______ meters

4

__ 0

1

__ ?

I can m my answer by .

× = 6.4.

c. 4.5

___ 3

d. 0.6 ÷ 4 e. 2 ) ______

0. 1 4

) _____

4. 5 ) ______

0. 6 0

f. 0.4 ÷ 5 g. 4 ) ________

0. 3 0 0 h. 0.012

______ 6

) ______

0. 4 0 ) ________

0. 0 1 2

i. 10 ) ______

1. 4 0 j. 0.7

___ 5

k. 0.1 ÷ 4

) ______

0. 7 0 ) ________

0. 1 0 0


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1. rule of reciprocals

5 __

3 × ? = 1

2. 1000

_____ 20

=

3. ( is __ of

00

___ 00

00

___ 00

) × 2 = 4. 3 ) _____

4. 5

5. 8 ) ______

0. 2 4 6. Add a zero.

5 ) _____

0. 8

7. LCMGo down the 2s, 4s, 6s, and 8s.

Find the first one in common.

8. √___

36 – m = 2 3 ___

10

9. g – 2 2 __

5 = 5

4 __

5

5 4

__ 5

+ 2 2

__ 5

10. m – 1.56 = 1.44

1.56+ 1.44


m =

m =g =


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11. 32 – n = 5.39 12.

4 3 __

8

– 2 1

__ 8

13. 8 __

3 ∙

5 __

2 = 14. estimate

694 412

15. 0.7 × (0.6 × 0.5) = 16. 0.46× 0.17

17. 8 ∙ a = 177.6

miles

_______ gallons

177.6

______ 177.6

? __

1

18. is

__ of

00

___ 00

00

___ 00

19. 25% = is

__ of

00

___ 00

00

___ 00

25% is the fraction .

So I m

times $40.

20. 5 __

6 =

00 ___

12

– 7 ___

12


n =


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21. area 36 ft2

a. each side Think square root.

b. perimeter

22. fraction and decimal numbers

27%

23. Measure length to the nearest eighth of an inch. 24. 75% =

is

__ of

00

___ 00

00

___ 00

25. 1 __

2 ×

2 __

3 =

1 __

3

1 __

3 ÷ =

2 __

3 ×

2 __

3 =

1 __

3

1 __

3 ÷ =

26. Since a little more than h the

circle is shaded, a little more than %

is shaded.

27. nine hundredths

a. fraction

b. decimal

28. 5 × 3 = 00

___ 00

1 __

3 × 3 =

29. students

___________ classrooms

? __

0

24 ___

1

30. 1

__ 2

mi = ft

yd ft

1 __

0

? __

0


Use work area.

b. a.

b.

a.


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Writing Decimal Numbersin Expanded Notation

Mentally MultiplyingDecimal Numbers by 10and by 100 (page 239)

• The values of some decimal places are shown in this table:

• Write 4.025 in expanded notation this way:

(4 × 1) + ( 2 × 1 ___ 100 ) + ( 5 × 1 ____ 1000 ) The zero that acts as a placeholder is not included in expanded notation.

• To multiply by 10: Shift the decimal to the right one place.

• To multiply by 100: Shift the decimal to the right two places.

• To multiply by 1000: Shift the decimal to the right three places.

Examples: Shift right

1.234 × 100 = 123.4 7.8 × 100 = 780


Write these numbers in expanded notation:

a. 2.05 ( × ) + ( × ) b. 20.5 ( × ) + ( × )

c. 0.205 ( × ) + ( × )

Write these numbers in decimal form:

d. (7 × 10) + ( 8 × 1 ___

10 ) e. ( 6 ×

1 ___

10 ) + ( 4 ×

1 ____

100 )

. .

Mentally calculate the product of each multiplication: shift

f. 0.35 × 10 = g. 0.35 × 100 =

h. 2.5 × 10 = i. 2.5 × 100 =

j. 0.125 × 10 = k. 0.125 × 100 =

Teacher Notes:• Review Hint #45, “Multiplying by

10, 100, or 1000.”

• Review “Multiplication and Division of Decimal Numbers by 10, 100, and 1000” on page 6 in the Student Reference Guide.


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Practice Set (continued) (page 241)

For the following statements, answer “true” or “false”:

l. If 0.04 is multiplied by 10, the product is a whole number.

m. If 0.04 is multiplied by 100, the product is a whole number.

Multiply as shown. Then complete the division.

n. 1.5

___ 0.5

× 10

___ 10

= 00

___ 00

= o. 2.5

_____ 0.05

× 100

____ 100

= 00

___ 00

=

1. Convert and reduce.

30

___ 8 =

2. 100.2 – = d

100.2× 098.6

3. Four and twenty is how many dozen? 4. decimal form

(5 × 10) + ( 6 × 1 ___

10 ) + ( 7 ×

1 _____

1000 )

5. fraction and decimal number

21%

6. reduced fraction

20% =

7. 5 ) ______

6. 3 5 8. Add zeros.

4 ) _____

0. 5


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9. Add zeros.

8 ) _____

1. 0

10. x + 3 5 __

8 = 9

9 5

__ 8

× 3 5

__ 8

11. y – 16 1 __

4 = 4

3 __

4

16 1

__ 4

× 14 3 __

4

12. 1 – q = 0.235

1.000× 0.235

13. 26.9 + 12 + w = 49.25

26.9× 12.9

49.25× 49.25

14. whole area

50% = 1

__ 2

1

__ 2

of whole area?

15. ratio

dime

_______ quarter

000

____ 000

=

16. 0.25× 03.7

17. 3 __

4 =

? ___

12 18. LCM of 3, 4, and 8


19. a. 1 ___

10 0.1

b. 0.1 (0.1)2

20. thousandths place

1,234.5678

x =

y = q =

w =

a.

b.


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21. estimate

3967 48

22. area

each side Think square root.

perimeter

23. 6 – 8 = ? 24. Cancel the 2 and the 4.

1 __

2 ×

4 __

5 =

25. Cancel the 3s.

( 3 __ 4 ) ( 5 __

3 ) =

26. circumference, radius, diameter

least

greatest

27. total cost

$6.95× $6.95

$6.95+ $6.95

28. Measure width to the nearest eighth of an inch.


8 s are in 1?

b. How many 3

__ 8

s are in 3?

30. 1 __

2 = +

1 __

3

1

__ 3

= + 1

__ 3


estimate

8% %

$6.95 $

0000

_____ 0000

Use work area.

a.

b.


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Circumference Pi (π ) (page 244)

Circumference Activity• Part One—How to measure the circumference of a circular object:

1. Cut a string the length of the diameter of the object.

2. Begin wrapping the string around the object.

3. Mark the object at the beginning and the end of the string.

4. Put the beginning of the string on the previous end mark; wrap and mark the object again.

5. Continue wrapping the string andmarking the object until you reachthe starting point.

6. From the marks you made, count how many times the string was used to wrap around the object.

Give a mixed number answer.

• Part Two—Measuring a circular object:

1. Get a circular object: can, plate, pie pan, etc.

2. Use a cloth tape measure to measure the circumference (around the object).

3. Measure the diameter.

4. Divide the circumference by the diameter. Use a calculator.

How many diameters equal a circumference?

5. If a circle has a diameter of 10 inches, estimate the circumference of the circle. inches

• The exact number of diameters in the circumference is a number between 3 and 4 called pi (π ).

• If the radius or diameter of a circle is known, the circumference can be found.

Multiply the diameter by π: C = πd

• Use 3.14 as an approximation for π: C = 3.14d


a. In this lesson two formulas for the circumference of a circle are shown, C = πd and C = 2π r. Why are these two formulas equivalent?

The factors 2 and r in the second equation are equivalent to the d in the first e because

two radii equal one d . So t radii times π is equivalent to the d

times π.

Teacher Notes:• Review “Circle” on page 17 in the

Student Reference Guide.

• Students will need the following items to complete the activity: one or more circular objects (pie pan, plastic lid, trash can); string; scissors; a cloth tape measure; a calculator.

• Students may use this page rather than Activity Master 11.


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Find the circumference of each of these circles. (Use 3.14 for π.) C = πd

b. c.

d. The diameter of a penny is about 3 __

4 of an inch (0.75 inch). Find the circumference of a penny.

Round your answer to two decimal places. Explain why your answer is reasonable.

If the d were one inch, the c would be about 3.14 inches. Since the

diameter is a little than one inch, the circumference should be a little than inches.

e. Roll a penny through one rotation on a piece of paper. Mark the start and the end of the roll. How far

did the penny roll in one rotation? Measure the distance to the nearest eighth of an inch.

f. The radius of the great wheel was 14 7 __

8 ft. Circle the number that is the best rough estimate of the

wheel’s circumference. Explain how you decided on your answer.

A 15 ft B 60 ft C 90 ft D 120 ft

estimate radius ft

estimate π

2 × estimate radius = × estimate π =

g. Use the formula C = 2π r to find the circumference of a circle

with a radius of 5 inches. (Use 3.14 for π.) Shift

1. tenth positive odd number

, , , , ,

, , , ,

4. A = bh

b = 8 h = 4

5. 3 ∙ 7 ∙ 2 ∙ 5 ∙ 2 ∙ 3 ∙ 3 ∙ 5

∙ ∙ ∙ ∙ ∙ ∙ ∙ least greatest


1 3 5

2. 600 × h =

mi

___ hr

600

____ 1

000

____ ?

3. roses

_______ months

2

__ 1

00

___ ?

A = Use work area.


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c.

6. s = 1

__ 2

4s =

7. expanded notation

6.25

8. fraction and decimal number

99%

9. Add zeros.

12 ) ______

0. 1 8

10. shift

10 ) ________

1 2. 3 0

11. w ÷ √___

36 = 62

12. 5y = 1.25 13. n + 5 11

___ 12

= 10

10 11

___ 12

× 5 11

___ 12

14. m – 6 2

__ 5 = 3

3 __

5

6 2

__ 5

× 3 3

__ 5

15. 8 3 __

4

+ 5 3 __

4

16. 5

__ 3

× 5

__ 4

= 17. 3

__ 4

= ? ___

20


18. 3__5

= ?___20

19. average closest to which number

18201820

+ 20

A 17 B 18

C 19 D 20

( × ) + ( 1 __ 3 ×

1 __

3 ) + ( 1 __

3 ×

1 __

3 )

w =

y = n = m =


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22. shift

6.25

S the decimal point one p

to the r .

24. 90% =

is

__ of

00

___ 00

? ___

40

25. 687 Mars365 Earth

26. Venus ) ______

Mars

Drop the remainder.

27. Measure length and width.

28. perimeter

29. 2

__ 5 =

00 ___

10

Subtract and reduce.

30. The numbers 1.5 and 1.50 are e . Attaching a

z to a decimal number does not shift place

v . To multiply 1.5 by 10, we may move the

d point one place to the r , which

shifts the place v and makes the product

.

23. shift Then divide.

1.25

_____ 0.5

∙ 10 ___

10 =

000 ____

000 =


20. C = πd

The c of a circle is a

little than

times the diameter. My answer is a little

than × 20.

21. Here are the factors of 20. Cross off the factors that are NOT factors of 30.

1, 2, 4, 5, 10, 20

Use work area.

, , ,

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Subtracting Mixed Numbers with Regrouping, Part 1 (page 250)

• To subtract mixed numbers with regrouping:1. Borrow 1 from the whole number and rename.

2. Combine the top fraction with the renamed 1.

3. Then subtract.

Example: 5 1 __

3

– 2 2 __

3

45

1 __

3 +

3 __

3 = 4

4 __

3

– 2 2

__ 3

2 2 __

3


a. 4 1 __

3

– 1 2 __

3

34

1 __

3 +

3 __

3 = 3

4 __

3

– 1 2 __

3

b. 3 2

__ 5

– 2 3

__ 5

23

2 __

5 +

5 __

5 = 3 4 _ 3

– 2 3

__ 5

c. 5 2

__ 4

– 1 3 __

4

3 4 _ 3

– 1 3 __

4

d. 5 1

__ 8

– 2 4

__ 8

3 4 _ 3

– 2 4

__ 8

e. 7 3 ___

12

– 4 10

___ 12

3 4 _ 3

– 4 10

___ 12

f. 6 1

__ 4

– 2 3

__ 4

3 4 _ 3

– 2 3

__ 4

g. Shade the bottom row of circles to complete the model of exercise a.

4 1

__ 3

– 1 2 __

3

3 4 __

3

– 1 2 __

3

=

=

h. Complete this word problem based on exercise c.

Allan had pot pies. He ate of them at lunch.

How pot pies were left?


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1. ( + ) ÷ 2 = 10

sum

2. shift

$ ___

gal

2.279 ______

x

? ___

10

3. 11:45 a.m. to 12:45 p.m. = hr

12:45 p.m. to 1:20 p.m. = min

4. Which number is NOT equal to the others?

A 1

__ 2 B 0.2

C 0.5 D 10

___ 20

5. least to greatest 6.

7. 0.125 8. 3 2.1 = r

9. estimate

4967 8142 6890

10. 8 ) ________

0. 1 4 4


0.10.20.3

0.4


1.02 0.102 0.12 1.20 0 –1

, , , , ,

3.1 2.1

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11. Add a zero.

6 ) ____

0.9

12. Add zeros.

4 ) ____

0.9

13. shift

$0.39

14. standard form

(5 × 10) + ( 6 × 1 ___

10 ) + ( 4 ×

1 ____

100 )

15. LCM of 6 and 8 16. w – 7 7 ___

12 = 5

5 ___

12

7 7 ___

12

+ 5 5 ___

12

17. 12 – m = 5 2 __

3

12 2

__ 3

+ 5 2 __

3

18. n + 2 3

__ 4 = 5

1 __

4

5 1 __

4

+ 2 3 __

4

19. x + 3.21 = 4

4.00+ 3.21

20. 2

__ 3

of 3

__ 4

=



.

w =

m = n =

x =

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21. gains of 3 yd and 5 yd

loss of 12 yd

Use a negative number.

23. length

______ width

xxx

____ xxx

=

24. ft ___

in.

1 ___

xx

4 __

?

25. 1 ft × 1 ft = 1 sq. ft

12 in. × 12 in. = sq. in.

26. d = rt

r = 60 t = 4

27. 75% =

is

__ of

xx

___ x

xxx ____

x

28. 1 __

3 = +

x ___

12

1 __

4 =

+

x ___

12

29. shift Then divide.

3.5

___ 0.7

∙ 10

___ 10

=


22. C = πd

π is a little than ,

so the answer should be about

× = .


30. The server can cut one of the whole p

into 6 _ 6 . Then there will be 2 and pies on the shelf.

The server can remove 1 and pies, and there will

be 1 and pies left on the s .

d =

Use work area.

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Dividing by a Decimal Number (page 254)

• Move the decimal over, over, and up.

• Use zero as a placeholder.

• Put a digit above each digit.

• Use short division.

• Add zeros to the dividend and keep dividing until there is no remainder.

Example: 0.13 ÷ 0.4


a. 1.44

_____ 1.2

What would you multiply 1.2 by to make it 12?

b. 0.12 ) ______

0.144 What would you multiply 0.12 by to make it 12?

Make each divisor a whole number; then divide.

c. 0.4 ) _____

2.24 d. 0.3 ) ___

90 e. 0.05 ) _____

2.50 f. 0.3 ) _____

120

g. 0.24 ÷ 0.8 h. 0.3 ÷ 0.03 i. 0.05 ) ____

0.4 j. 0.2 ÷ 0.4

) _____

0.24 ) _____

0.30 0 ) _____

0.20

k. Find how many nickels are in $3.25 by dividing 3.25 by 0.05.

) _____

3.25

Teacher Note:• Review “Multiplication and Division

of Decimal Numbers by 10, 100, 1000” on page 6 in the Student Reference Guide.

0 0. 3 2 50.4 )

__________ 0. 1 3 0 0

over over

up


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1. ( ) – ( ) = 2. is

__ of

x00

____ 000

____

100

3. area 4. perimeter

5. a. 0.31 0.301 b. 31% 30.1%

0.31 31% 0.301 30.1%

6.

7. 0.25 8. over, over, up

0.07 ) ______

3. 5 0

9. over, over, up

0.5 ) ______

1 2 0

10. Add zeros.

8 ) ______

0. 1 4



2.2 in.

2.6 in.

b. a.

0.670.00

0.00

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11. 12. n – 6 1

__ 8

= 4 3 __

8

6 1

__ 8

+ 4 3 __

8

13. 4 __

5 =

x ____

100 14. 5 – m = 1.37

5.37+ 1.37

15. m + 7 1

__ 4

= 15

15 1

__ 4

+ 7 1 __

4

16. one and twelve thousandths

17. 5 7 ___

10

+ 4 9 ___

10

18. 5 __

2 ∙

5 __

3 =

19. 40% =

is

__ of

xx

___ xx

xx

___ xx

20. xx

___ 24

a. Eight hours is what fraction?

b. sleep

c. not sleep


0.012 001.5


n =

m =

m =

a.

b.

c.

x =

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21. List the factors of 12.

Cross off the factors that are NOT factors of 18.

1 , , , , , 12

22. average

23. 51% %

$49.78 $

24. a. How many 3

__ 4 s are in 1?

b. How many 3 __

4 s are in 4?

25.

a. halfway between 1 and 2

b. closer to 1 than 2

c. closer to 2 than 1

27. over, over, up

0.25 ) _____

3.00

28. Measure a side to the nearest eighth of an inch. Then find the perimeter.

29. C = πd


26. Cancel the matching factors.

2 ∙ 3 ∙ 2 ∙ 5 ∙ 7

______________ 2 ∙ 5 ∙ 7

=


30. Answer: Yes or No

Both 10

___ 10

and 100

____ 100

are e to 1. When we multiply a number

by different f names for one, the numbers may look

d , but they are e . So 2.5

___ 0.5

and 25

___ 5

and 250

____ 50

are three e problems with the s quotient.

, , ,

1.21.3

1.7

a.

b.

a.

b.

c.

Use work area.

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Decimal Number Line (Tenths) Dividing by a Fraction (page 259)

• We can locate decimal numbers on the number line.

• On a decimal number line, each tick mark is one tenth from the next.

Example:

y = 7 4 ___

10 y = 7.4

• To divide by a fraction, use two steps:

Original problem: How many 3 _ 4 s are in 6? 6 ÷ 3

__ 4

Step 1: Find the number of 3 _ 4 s in 1. 1 ÷ 3

__ 4

= 4

__ 3

(reciprocal)

Step 2: Use the number of 3 _ 4 s in 1 to 6 × 4

__ 3

= 24

___ 3

find the number of 3 _ 4 s in 6. Then simplify the answer.

24 ___

3 = 8


To which decimal number is each arrow pointing?

g. Write and solve a fraction division problem to find the number of quarters

in four dollars. Use 1 __

4 instead of 0.25 for a quarter.

Follow this pattern.

Original problem: 4 ÷ 1 __

4

Step 1: 1 ÷ =

Step 2: 4 × =

h. Write and solve a fraction division problem for this question:

Pads of writing paper were stacked 12 inches high on a shelf. The thickness

of each pad was 3 __

8 of an inch. How many pads were in a 12-inch stack?

Original problem: 12 ÷

Step 1: 1 ÷ =

Step 2: 12 × =


0.1

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1. 1 + 3 + 5 = 9 1 + 3 + 5 + 7 + 9 = 25

32 = 9 52 = 25

102 =

I found a pattern.

2. 6 ÷ 3 __

8

reciprocal of 3 __

8

6 __

1 ×

xx ___

x =

3. (3 × ) + = 4. a. 3.4 3.389 b. 0.60 0.600

3.4 0.60 3.389 0.600

5. 7.25 + 2 + w = √_____

100

7.25+ 2.25

6. 6w = 0.144

7. w + 5 ___

12 = 12 8. 6

1 __

8 – x = 1

7 __

8

6 1

__ 8

+ 1 7

__ 8

9. total cost

$20.00$020.00

$20.00$020.00

10.


b. a.

w = w =

w = x =

1.00 1.00

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11. over, over, up

0.12 ) _____

7.20

12. over, over, up

0.4 ) ___

70

13. 6 ) ______

0.138 14.

15. 3 __

4 =

? ___

24 16. 4.637

85.21

17. 1 m × 1 m = 1 sq. m100 cm × 100 cm = sq. cm

18. LCM of 6 and 9

19. 6 5 __

8

+ 4 5 __

8

20. 8

__ 3

∙ 3 __

1 =


3.75+ 02.4

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21. 2

__ 3 ∙

3 __

4 =

23. average

2.46.3

5.7

24. over, over, up

) _____

8.75

25. What decimal number? 26. Cancel the matching factors.

2 ∙ 3 ∙ 5 ∙ 7

__________ 2 ∙ 5

=

27. 0.375 × 100 = 28. 1

__ 3

= xx

___ 6

Subtract and reduce.

29.

a. halfway between 6 and 7

b. 6 7 ___

10

c. closest to 6

30. Which is divisible by both 2 and 5?Use tests for divisibility.

A 552 B 255 C 250 D 525


22. C = πd

π is a little

than , so my

answer should be about

× = .

quarters

a.

b.

c.

Documents

41 Finding a Percent of Name - LearningTOPSlearningtops.yolasite.com/resources/Crs1_Lessons041-050.pdf† To find a percent of a number: 1. Change the percent to a fraction or decimal