R5-1 Mental Math: Patterns in Division (p. 129)© Scott Foresman, Gr. 5 (130) Use with Chapter 5, Lesson 1. Mental Math: Patterns in Division H 5-1 What has four wheels and flies?

Name _____________________________________________________________________________________________________

© Scott Foresman, Gr. 5 (129) Use with Chapter 5, Lesson 1.

5-1RMental Math: Patterns in Division

Basic facts and patterns with zeros can help you divide larger numbers.

Use the basic fact. 6 ! 2 " 3Look for patterns of zeros. 60 ! 2 " 30

600 ! 2 " 3006,000 ! 2 " 3,000

Find each n.

1. 15 ! 5 " n 2. 24 ! 4 " n 3. 49 ! 7 " n

150 ! 5 " n 240 ! 4 " n 490 ! 7 " n

1,500 ! 5 " n 2,400 ! 4 " n 4,900 ! 7 " n

15,000 ! 5 " n 24,000 ! 4 " n 49,000 ! 7 " n

4. 160 ! 4 5. 280 ! 7 6. 560 ! 7

7. 2,400 ! 6 8. 1,800 ! 3 9. 84,000 ! 7

10. 350 ! 7 11. 1,400 ! 2 12. 240 ! 3 13. 300 ! 6

14. 800 ! 4 15. 540 ! 6 16. 3,500 ! 5 17. 560 ! 8

18. 2,700 ! 3 19. 12,000 ! 2 20. 2,800 ! 7 21. 63,000 ! 9

Find n.150 ! 5 " n

15 ! 5 " 3150 ! 5 " 30

Here’s WHY It Works150 " 15 tens

15 tens ! 5 " 3 tens, or 30

Find n.240 ! 6 " n

24 ! 6 " 4240 ! 6 " 40

Here’s WHY It Works240 " 24 tens

24 tens ! 6 " 4 tens, or 40

Name _____________________________________________________________________________________________________


5-1HMental Math: Patterns in Division

What has four wheels and flies? Use basic facts and patterns to find each quotient. Thenuse the decoder to answer the riddle. The answer blank numbers match the exercisenumbers. Write the letter that matches the quotient for that exercise on the blank.

1. 200 ! 10 " 2. 2,000 ! 10 " 3. 20,000 ! 10 "

4. 25 ! 5 " 5. 250 ! 5 " 6. 2,500 ! 5 "

7. 42 ! 7 " 8. 420 ! 7 " 9. 4,200 ! 7 "

10. 42,000 ! 7 " 11. 810 ! 9 " 12. 8,100 ! 9 "

1 2 4 3 6 1 12 9 11 7 8 5 10

900 2,000 600 60 200 500

G R E U G B

6 50 6,000 5 90 20

R C K A T A

13. Math Reasoning How is the number of zeros in the quotient of 420 ! 7 " 60related to the number of zeros in the dividend?

Test Prep Circle the correct letter for each answer.

14. 350 ! 7 " 15. 5,600 ! 8 "

A 50 F 7,000

B 5 G 70

C 500 H 700

D 5,000 J 7

Name _____________________________________________________________________________________________________


5-2REstimating Quotients

Complete to find each estimated quotient.

1. 58 ! 3 is close to ! 3 "

2. 52 ! 5 is close to ! 5 "

3. 157 ! 4 is close to ! 4 "

Estimate each quotient. Tell which compatible numbers you used.

Quotient Compatible Numbers

4. 6!4"7"7"

5. 4!8"2"

6. 5!5"4"

7. 3!1"6"0"

8. 4!2"1"3"

Estimate

Change the dividend to a numberthat is compatible with the divisor.

Use patterns or mental math tohelp you divide.

Example 178 ! 4

78 ! 4 80 ! 4

80 and 4 arecompatible numbers,since 8 is divisible by 4.

8 ! 4 " 280 ! 4 " 20So, 78 ! 4 is about 20.

Example 2247 ! 5

247 ! 5 250 ! 5

250 and 5 arecompatible numbers,since 250 is divisible by 5.

25 ! 5 " 5250 ! 5 " 50So, 247 ! 5 is about 50.

Name _____________________________________________________________________________________________________


5-2HEstimating Quotients

What did the multiplication problem say to the division problem? To find the answer, use compatible numbers to estimate. Write your answer on the blank. Copy the letter printed next to your answer above each matching estimate below.

1. 5!"2"9"6" H 2. 4!"1"5"0" I 3. 5!"2"4"4" V

4. 9!"7"1"9" S 5. 2!"1"3"8" M 6. 3!"1"0"3" R

7. 3!"8"9"4" N 8. 8!"7"1"8" A 9. 58!6",1"2"0" W

10. 22!7",8"7"8" D 11. 51!9"9"9" E 12. 43!8",1"1"8" O

100 20 60 90 50 20 300 200

!30 20 70 90 40 300 400 20 30 80

13. Math Reasoning Give three different sets of compatible numbers you could use toestimate the quotient of 495 ! 83.


14. 2,095 ! 3 can be best 15. 81!4",9"2"3" can be best estimated using: estimated using:

A 2,000 ! 3 F 81!4",9"0"0"

B 2,100 ! 3 G 80!4",9"0"0"

C 210 ! 3 H 81!4",8"0"0"

D 2,090 ! 3 J 80!4",8"0"0"

Name _____________________________________________________________________________________________________


Dividing by One-Digit Divisors

1. 2. 3. 4.

5. 6. 7. 8.

9. 10. 11. 12. 4!5"6"8!"2"1"6!"3"8"6!"5"8"

3!"7"7"7!"9"2"5!6"0"6!"4"9"

4!"3"9"2!"9"5"5!"5"6"9!"8"3"

5-3R

Find 98 ! 4.Estimate first. 100 ! 4 " 25. Then find the exact quotient.

Step 1Divide the tens.

Step 2Bring down the ones digit.Divide the ones. Write theremainder in the quotient.

Step 3Multiply to check.

24# 4$96

% 2$98

24 R24!"9"8"& 8$$

18& 16$$$

2

24!"9"8"& 8$$

1

Divide: 9 ! 4.Multiply: 2 # 4 " 8.Subtract.Compare: 1 ' 4.

Bring down the 8 ones. Divide: 18 ! 4.Multiply: 4 # 4 " 16.Subtract.The remainder is 2.

Multiply the quotient by the divisor.

Add the remainder: 96 % 2 " 98The sum is the dividend.

Name _____________________________________________________________________________________________________


Dividing by One-Digit Divisors

1. 2. 3. 4.

5. 6. 7. 8.

9. 10. 11. 12.

13. 23 ! 2 14. 135 ! 6 15. 48 ! 5

16. 384 ! 7 17. 79 ! 2 18. 96 ! 8

19. Central Air had 7 flights out of Kansas City on Tuesday, carrying a total of 623 passengers. If each plane carried the same number of passengers, how many passengers were on each flight?

20. On Wednesday Central Air had 8 flights and a total of 744 passengers. Each flightcarried the same number of passengers. Did more passengers fly on Tuesday or Wednesday?


6!"8"2"5!"1"6"5"3!"7"7"4!"2"4"5"

5!"3"7"2"2!"2"2"7"7!"1"8"3"2!"1"9"0"

6!"4"0"5!"7"1"3!"6"5"4!"5"5"

5-3H

21. Boston and Phoenix are 2,300 milesapart. If a plane takes four hours to getfrom Boston to Phoenix and flies at aconstant speed, how fast does it fly?

A 600 miles per hour

B 9,200 miles per hour

C 575 miles per hour

D 757 miles per hour

22. The economy section of a plane holds256 passengers. There are eightseats across in each row. How manyrows are there?

F 2,048 rows

G 248 rows

H 24 rows

J 32 rows

Name _____________________________________________________________________________________________________


5-4R

When you solve a problem using division, sometimes you need to decide whatthe remainder means before you can figure out what to do with it. Depending onthe problem, you might increase the quotient to the next whole number. Youmight use the remainder as your answer. You might drop the remainder. Here areexamples of each situation.

Rudy has 15 juice containers.

Increase the quotient Rudy can pack the containers in a carrying box. Eachbox can hold 4 containers. What is the fewest number of carrying boxes Rudy canuse to hold the juice? 15 ! 4 " 3 R3. He needs 4 boxes, because he needs anextra box to carry the remaining 3 containers.

Drop the remainder Rudy gives each friend 2 juice containers. To how manyfriends did he give containers? 15 ! 2 " 7 R1. The answer is 7 friends, becausethe remainder is not enough containers to give 2 to an eighth friend.

Use the remainder as the answer How many containers are left over ifRudy gives each friend 2? 15 ! 2 " 7 R1. One container is left.

Problem-Solving Skill

Interpreting Remainders

A national park offers tours of its caves. There must be at least 2 people in a group, andthere cannot be more than 5 people in a group. There are 37 people signed up for tourson Friday morning.

1. What is the answer to 37 ! 5?

2. You want to figure out the number of tour groups that will be sent out that morning.How do you interpret the remainder?

a. Increase the quotient to the next whole number.

b. Drop the remainder.

c. Use the remainder as the answer.

3. How many tour groups will go out on Friday morning?

a. 2 b. 7 c. 8

Name _____________________________________________________________________________________________________


5-4HProblem-Solving Skill

Interpreting Remainders1. For a display page in the company catalog, Ms. Lee drew 4 pictures with the drawing

pencils. It took Ms. Lee 13 hours to draw all the pictures. If she took about the sameamount of time to draw each picture, about how long did it take to draw 1 picture?

2. Phil has 45 photographs of the toys to put in the catalog. Only 6 photographs fit on each

page. How many pages of photographs will be in the catalog?

3. There will be 52 toy makers at the factory’s holiday party. The factory is renting tables that seat 8 people each.

a. How many tables must they rent to give everyone a seat?

b. Will all the tables have the same number of people sitting at them? Explain.

Use the information from the table for Exercises 4–7.

4. Ken has 57 drawing pencils to box. How many full boxes can he pack?

a. 5 boxes b. 6 boxes c. 7 boxes

5. The marble makers have just given Rick 34 marbles to pack. How many full bags of marbles will Rick be able to pack?

a. 4 bags b. 5 bags c. 6 bags

6. Leigh Ann has 12 bubble blowers to pack.

a. How many boxes does Leigh Ann use?

b. Does she have any bubble blowers left over? Explain.

7. Lanny has 80 baseball cards to pack. How many full packs can Lanny make?

Toy Factory Guide for Packers

Type of Toy Number in Each Container

giant multicolor marbles 8 marbles in each bag

bubble blowers 2 bubble blowers in each box

drawing pencils 9 pencils in each box

baseball cards 7 cards in each pack

Name _____________________________________________________________________________________________________


Dividing by Two-Digit Divisors

1. 2. 3.

4. 5. 6.

7. 425 ! 22 8. 691 ! 47 9. 249 ! 78

10. Mr. Kelley ordered 172 granola bars for his 86 students. How many granola bars did each student get?

60!"5"2"3"40!"2"7"5"80!"7"0"5"

30!"1"7"2"40!"9"6"4 R30!"1"3"4"

" 120###

14

5-5R

Find 97 ! 22. Estimate first: 100 ! 20 $ 5

Step 1 Divide using your estimate.

Step 2 Adjust the quotient.

Step 3 Check.

110 % 97, so the estimate istoo high.

Divide.Multiply.Subtract.Compare:9 & 22

Multiply the quotient by the divisor. Remember to add the remainder.

22'4#88(9##97

4R922!9"7""""

"88#9

522!"9"7"

"110#

Name _____________________________________________________________________________________________________


Dividing by Two-Digit Divisors

1. 178 ! 24 2. 211 ! 36

3. 368 !44 4. 456 ! 62

5. 6. 7. 8.

9. 10. 11. 12.

13. 14. 15. 16.


17. Nadir’s school is having an Earth Day celebration. They have received 115 requeststo buy advertising space in a special edition of the school newspaper. They can place12 ads on each page of the newspaper. How many full pages of ads will they have?How many ads will be left over for a partial page?

A 9 full pages, 7 ads left over C 7 full pages, 9 ads left over

B 127 full pages, 6 ads left over D 103 full pages

18. There are 217 students in the school. The principal wants students to form teams of 24for each special event. Students who are not part of teams will be event announcers.How many full teams can be formed? How many announcers will there be?

F 9 teams H 193 teams, 17 announcers

G 9 teams, 1 announcer J 10 teams

75!"7"3"9"33!"2"0"9"55!"4"0"9"81!"2"9"3"

27!"1"1"8"12!"5"9"36!"2"2"2"39!"3"0"5"

58!"4"9"9"17!"8"6"41!"2"0"6"55!"4"9"7"

5-5H

Name _____________________________________________________________________________________________________


Two-Digit Quotients

1. 2. 21!"3"5"7" 3. 43!"5"6"4"

4. 18!6"9"7" 5. 67!8"0"5" 6. 59!6"5"8"

7. 399 ! 26 8. 101 ! 45 9. 943 ! 71

32!"7"5"3"

5-6R

Find 781 ! 42.

Estimate first: 800 ! 40 " 20, so the quotient is probably a two-digit number.

Step 1 Divide the tens.

Step 2 Divide the ones.

Step 3 Check.

Divide.Multiply.Subtract.Compare: 36 # 42

Bring down the 1.Divide: 361 ! 42 " 8Multiply.Subtract.Compare: 25 # 42.

Multiply. Remember to addthe remainder.

142!7"8"1"$ 42%%%

36

1842!7"8"1"

$ 42%%%

361$ 336%%%

25

42& 18

%%%%336

' 420%%%756

' 25%%%781

13 R33 in the park.13 R37 ay the mall.13 R29 on the roof.

Name _____________________________________________________________________________________________________


5-6H

4. 32!7"6"7"A 23 R31

B 23 R29

C 22 R33

D 22 R16

5. 23!9"5"7"F 40 R1

G 42

H 41 R14

J 40 R37

Two-Digit Quotients

Find the quotient. Then circle the phrase that matches the quotient. Read the sentences formed by the answers.

1. Who? What? When? Where?

27!"7"7"3"48!"8"8"3"47!"9"9"5"38!"9"6"8"

25 R19 The clown

25 R18 The dancer

24 R18 The puppet

21 R8 sang a song11 R9 drove a truck21 R10 went fishing

18 R19 yesterday19 R18 last year18 R18 tomorrow

27 R16 in the park.28 R16 at the mall.28 R17 at the zoo.


55!"7"5"4"37!"9"8"8"72!"8"2"3"48!5"5"0"

11 R33 The seal11 R22 The cat12 R22 The pig

11 R31 screamed12 R33 gurgled11 R13 murmured

26 R22 in the rain26 R26 at noon26 R24 all day

13 R44 in the car.13 R33 in the park.13 R39 on the lake.

16 R21 The batter16 R22 The teacher17 R2 The dogs

16 R8 danced16 R5 laughed16 R7 barked

14 R11 all day14 R14 all night14 R12 Sunday



63!"8"4"8"19!"2"7"7"37!"5"9"9"29!"4"8"5"

Name _____________________________________________________________________________________________________


Dividing Greater Numbers 5-7R

Find 5,888 ! 25.

Estimate first: 6,000 ! 30 " 200, so the quotient is probably a three-digit number.

Step 1 Divide the hundreds.

Step 2 Divide the tens.

Step 3 Divide the ones.

Step 4 Check by multiplying.

Divide.Multiply.Subtract.Compare: 8 # 20

Bring down.

Divide: 84 ! 25 " 3.Multiply.Subtract.Compare: 9 # 25

Bring down.

Divide: 94 ! 25 " 3.Multiply.Subtract.Compare: 19 # 25

23325!5",8"4"4"

$50%%84$75%%94

$75%%19

2325!5",8"4"4"

$50%%84$75%%9

225!5",8"4"4"

$50%%8

!"!

"

R19

1. 2. 26!"9",4"8"5" 3. 33!"3",4"5"5"

4. 42!"6",4"8"7" 5. 51!"8",1"2"9" 6. 22!"6",1"7"7"

7. One of Wacky World’s hottest selling games is Blame It on Maze, which sells for $25. If sales of Blame It on Maze were $8,275 in one week, how many games were sold?

34!"7",6"8"5"

233 & 25 = 5,825; then add the remainder;5,825 ' 19 = 5,844.

Name _____________________________________________________________________________________________________


5-7HDividing Greater Numbers

Solve. Write one number in each box.

Across

1. 473 ! 28

4. 2,084 ! 42

6. 363 ! 52

8. 3,464 ! 77

10. 56,241 ! 94

11. 1,872 ! 98

Down

2. 4,411 ! 79

3. 209 ! 42

5. 19,260 ! 31

7. 3,708 ! 62

9. 493 ! 62

1R

32

R4

R5

R76

R

8R

9

RR R10

R11

R


12. 6,845 ! 47 13. 63!8",9"0"4"A 145 F 141 R21

B 145 R63 G 141 R31

C 145 R30 H 144 R30

D 144 R30 J 142 R33

Name _____________________________________________________________________________________________________


Problem-Solving StrategyUse Logical Reasoning

1. Sung-Lee makes jewelry. One necklace uses two stars, two beads, and a diamond. The diamond is between two beads. Each star has a bead between it and the diamond.What is the order of the shapes?

2. Romero is displaying his sculptures, a cat, a turtle, a dog, and a bird, on a table. Theturtle is not last. The cat is neither first nor last. The dog is between the cat and the bird.In what order are the sculptures?

5-8R

Tomas, Dante, Suzanne, and Kate are in the lunch line. Kate is standing betweentwo boys. Tomas is not next to Suzanne. Suzanne is last in line. In what order arethe four friends standing?

Understand You are asked to find the order, from front to back, in which the friends are standing.

Plan You can use logical reasoning to find the friends’ order.

Solve Hint: Begin with the clues that tell you exactly wheresomeone is standing.

Suzanne is last, so put her 1.at the end of the line. 2.

3.4. Suzanne

Kate is between two boys, 1.so she must be second. 2. Kate

3.4. Suzanne

1. Tomas2. Kate3. Dante4. Suzanne

Look Back Check to be sure that the positions of the friends satisfy all the conditions.

Tomas is not next toSuzanne, so he must befirst. That leaves Dante inthird place. Write theirnames in the correct order.

Name _____________________________________________________________________________________________________


2. Farmer Green sent his two children out to count the hens and sheep. His daughtercounted 40 heads, and his son counted 100 legs. How many sheep and how manyhens are in the farm?

3. Nadir’s baby brother made a tower of blocks 10 rows high. There are 19 blocks in thebottom row, 17 blocks in the second row, and so on. How many blocks are there inthe entire tower?

5-8HProblem-Solving StrategyUse Logical Reasoning

Five friends decided to go out for lunch. Each ordered a different dish. The food orderedwas spaghetti, cheese pizza, veggie pizza, a sub sandwich, and a calzone.

1. Use the clues below to figure out what each person ate. Write your answers in thetable. Use ✘ for no and ✔ for yes.

• Jill did not order cheese pizza.

• Ada ordered pizza.

• Doug ordered a sub sandwich or a calzone.

• Bev dislikes pizza.

• Stefan ordered a calzone.

Cheese Veggie SubName Spaghetti Pizza Pizza Sandwich Calzone

Jill

Ada

Bev

Doug

Stefan

Name _____________________________________________________________________________________________________


5-9RUsing Averages

Find the mean for each set of data.

1. 4, 6, 5 2. 10, 12, 14

3. 20 in., 22 in., 24 in. 4. 27 hr, 29 hr, 31 hr

5. $76, $88, $85 6. 72, 74, 81, 73

7. 127 cm, 154 cm, 136 cm 8. 364, 321, 356

9. 78, 79, 125, 76, 77 10. 24 ft, 28 ft, 13 ft, 47 ft

11. 15°, 8°, 10°, 15°, 20°, 10° 12. 69, 75, 68, 52, 89, 67

13. 80, 60, 50, 30, 70, 10 14. 163, 78, 59, 60, 120, 60

15. 30, 50, 74, 31, 50, 27, 116 16. 136, 223, 134, 72, 36, 71

! mean3!"""

1012

" 14##

! mean3!"4

6" 5#15

To find the average, or mean, of a set of data, follow these steps:

Step 1 Find the sum of the numbers.

Thereare 4numbers.

214736

" 32##136

Step 2 Divide the sum by thenumber of addends.

This is theaverage, or mean.

344!"1"3"6"$ 12##

16$ 16##

0

Name _____________________________________________________________________________________________________


Using Averages

Find the mean for each set of data.

1. 27 in., 54 in., 36 in. 2. 64 ft, 21 ft, 56 ft

3. 7, 9, 5, 3 4. $18, $27, $42, $61

5. 262 cm, 264 cm, 269 cm 6. 15°, 19°, 23°, 28°, 35°

7. 1,056; 2,138 8. 714, 283, 540, 629, 304

9. 1,564; 2,193; 1,607 10. 181, 260, 276

11. The Garcias drove 128 miles the first day of their trip. Then they drove 146 miles, 62 miles, and 212 miles on days 2–4. What is the average distance they drove each day?

12. At the end of the trip, their odometer showed that they had traveled 1,035 miles. If they were gone for nine days, how many miles did they average per day?


13. Green Bus lines has five bus drivers. They are 28 years old, 37 years old, 54 yearsold, 45 years old, and 31 years old. What is the average age of the drivers?

A 24 years old B 32 years old C 37 years old D 39 years old

14. The bus to Springfield makes four round trips per day. On the first trip the driver counted 23 passengers. On the second trip he counted 41. There were 16 passengers for each of the remaining trips. What is the average number of people who rode the bus?

F 26 G 24 H 20 J 30

5-9H

Name _____________________________________________________________________________________________________


Problem-Solving ApplicationAnalyzing Data

Use the data in the table above for Exercises 1–3.

1. Find the mean of Sam’s scores.

2. What is the mode of Sam’s scores?

3. What is the median of Sam’s scores?

5-10R

Claridon Elementary School is having its February Fitness Day. Here are the scoresof 2 students. What are the mode, median, and mean for Jeanette’s scores?

Understand You know Jeanette’sscores in 5 events. Youneed to find the mode,median, and mean forJeanette’s scores.

Plan You can solve themean by finding thesum of the scores anddividing by 5. You canfind the mode byfinding the numberwhich occurs mostoften. You can find themedian by arranging the numbers from least to greatest and identifying the middle number.

Solve 7 ! 10 ! 10 ! 9 ! 4 " 4040 # 5 " 8, Jeanette’s mean score is 8. 10 occurs most often, so the mode of Jeanette’s score is 10.The scores from least to greatest are 4, 7, 9, 10, 10. Themiddle number is 9, so the median of Jeanette’s scores is 9.

Look Back Did you add all of Jeanette’s scores? Did you divide by 5?

February Fitness Scores

Jeanette Sam

Running 7 6

Hopping 10 7

Jump-Rope 10 5

Push-Ups 9 10

Sit-Ups 4 7

Name _____________________________________________________________________________________________________


5-10HProblem-Solving ApplicationAnalyzing Data

Christie’s school is having their

annual Laugh Olympics.

The table shows some scores.

1. Find the mean of each student’s scores. Write it at the bottom of the column.

Who is the winner?

2. Find the median of Christie’s scores. How does it compare to her mean?

3. Find the mode of Jerry’s scores. How does it compare to his mean?

4. Suppose Kate’s score of 2 in the Egg Roll were changed to 7. Would that make her the winner? Explain.

5. Find the mean, mode, and median of 40, 42, 38, 40, 35, and 45.

6. Math Reasoning The mean for a set of five numbers is 24. Four of the numbers are 18, 30, 24, and 27. The fifth number is

Laugh Olympics Scores

Christie Ben Kate Jerry

Juggling 5 10 5 2

Belly Flops 10 9 10 5

Hula Hoop 4 6 7 10

Egg Roll 8 6 2 4

Yodeling 8 9 6 4

Mean Score

Name _____________________________________________________________________________________________________


5-11RRelating Multiplication and Division

Multiplication and division are inverse operations. Division can undo multiplication and multiplication can undo division.

You can also use the idea of inverse operations with algebraic expressions to get thevariable alone.

Tell what you would do to get each variable alone.

1. !8n! 2. n ! 7 3. 15f

4. 5 " b 5. 48d 6. !1x0!

For each table, tell what you would do to get n alone. Then find n.

7. 8. 9.

5 " 3 means 5 is multiplied by 3.Division can undo multiplication.

(5 " 3) # 3$ 5

14 " n, or 14n, means n is multiplied by 14.

Division can undo multiplication.

14n # 14 $ n

32 # 8, or !382!, means 32 is divided

by 8. Multiplication can undo division.

!382! " 8 $ 32

!6n! means n is divided by 6.

Multiplication can undo division.

!6n! " 6 $ n

Rule: Multiply by 7.

12 84

6 42

n 49

Rule: Divide by 15.

30 2

n 6

75 5

Rule: Multiply by 3.

n 51

10 30

16 48

Rule: Multiply by 11

4

77

n 165

Rule: Divide by 8

32

7

n 12


45

105

n 600

Name _____________________________________________________________________________________________________


5-11H

Rule: Multiply by 7

4

n 35

49

Rule: Divide by 6

n

8

396 66


1

225

n 600

Relating Multiplication and Division

Tell what you would do to get each variable alone.

1. 5n 2. !6a! 3. 6 " b 4. c # 15

5. !9n! 6. d # 21 7. 16t 8. 12 " n

For each table, tell what you would do to get n alone. Then find n.

9. 10. 11.

12. 13. 14.


15. A large balloon basket holds twice as many people as a small one. If the large basket holds 16 people, how many does the small one hold?

A 16 B 18 C 32 D 8

16. We are two numbers that are less than 10. Our product is 48. Who are we?

F 4 and 12 G 6 and 8 H 8 and 4 J 24 and 2

Name _____________________________________________________________________________________________________


Solving Multiplication and Division Equations

Solve each equation.

1. 9m ! 72 2. "m7" ! 4

9m 72 "m7" # ! 4 # !

3. 5x ! 30 4. 12p ! 72 5. "1p2" ! 7

6. "1x1" ! 5 7. "1

w5" ! 6 8. 12s ! 132

You can multiply or divide both sides of an equation by the same nonzeronumber without changing the equality.

5-12R

Solve 4x = 32.

To get x by itself, divide by 4. To keepthe sides equal, divide both sides ofthe equation by 4.

Check:

Solve "8x

" ! 6.

To get x by itself, multiply by 8. Tokeep the sides equal, multiply bothsides of the equation by 8.

"8x

" ! 6

"8x

" # 8 ! 6 # 8

x ! 48

Check: "8x

" ! 6

"488" ! 6

6 ! 6

4x ! 32

4 # 8 ! 32

32 ! 32

4x ! 32

"44x" ! "

342"

x ! 8

Name _____________________________________________________________________________________________________


Solving Multiplication and Division Equations

1. !1m1! " 3 2. 8x " 56 3. 6n " 72

4. 4p " 256 5. !2z1! " 2 6. 16n " 48

7. 20x " 100 8. !1d7! " 2 9. 5m " 225

10. 5w " 625 11. !1c6! " 16 12. !1

p2! " 4

13. 24x " 408 14. 17b " 204 15. !2x2! " 11

16. !1w2! " 8 17. 12s " 144 18. !3

k! " 13


19. Ahmed purchased 3,456 widgets. They were shipped in 24 boxes. Which equation below could you use to find the number, n, packed in each box?

A 24n " 3,456 B 3,456 " !2n4! C n # 24 " 3,456 D 3,456n " 24

20. Kristy planted several shrubs equally in the gardens of 4 homeowners. Eachhomeowner received 7 shrubs. If x is the total number of shrubs, which equation can be used to find x?

F 7x " 4 G 4x " 7 H !4x! " 7 J !4x! " 7

5-12H

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R5-1 Mental Math: Patterns in Division (p. 129)© Scott Foresman, Gr. 5 (130) Use with Chapter 5, Lesson 1. Mental Math: Patterns in Division H 5-1 What has four wheels and flies?