Name Dividing by Multiples of 10 R 4-1 - PBworksmskris.pbworks.com/w/file/fetch/45699547/5th Math Chapters 4... · Name Dividing by Multiples of 10 ... You can divide using mental

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Name

Dividing by Multiples of 10You can use basic facts and patterns to divide mentally.

Find each quotient. Use mental math.

1. 280 ! 70 " 2. 320 ! 40 "

3. 360 ! 60 " 4. 7,200 ! 80 "

5. 9,000 ! 30 " 6. 4,800 ! 80 "

7. 2,000 ! 40 " 8. 5,600 ! 70 "

9. Number Sense How is dividing 250 by 50 the same asdividing 2,500 by 500?

10. Writing in Math Explain how you can mentally determinethat 35,000 ! 70 " 500.

R 4-1

Using basic facts

What is 350 ! 70?

Think: 350 ! 70 is the same as 35 tens ! 7 tens.

35 ! 7 " 5

So, 350 ! 70 " 5.

Using patterns

What is 5,400 ! 60?

5,400 ! 60 is the same as 540 ! 6.

54 ! 6 " 9, so 540 ! 60 " 9.

So, 5,400 ! 60 " 90.

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Dividing by Multiples of 10Find each quotient. Use mental math.

1. 480 ! 60 " 2. 8,100 ! 90 "

3. 32,000 ! 40 " 4. 15,000 ! 30 "

5. 4,900 ! 70 " 6. 16,000 ! 40 "

Solve for n.

7. n ! 20 " 60 8. n # (400 ! 20) " 27 9. 420 ! n " 70

The vegetable farm is planning the summer harvest layout.

10. How many plants will be harvested from each section?

11. How many plants will grow in each row?

Test Prep

12. Using the data above, determine how many plants wouldbe harvested in each row if 30,000 plants were harvestedand only 10 sections were used.

A. 10 B. 100 C. 1,000 D. 10,000

13. Writing in Math Explain the steps you took to figure outyour answer for Exercise 12.

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Plants harvested: 60,000

Sections: 20

Rows in each section: 30

Vegetable Farm Layout

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Estimating with Two-Digit DivisorsThere are different ways to estimate quotients.

Estimate each quotient. Tell which method you used.

1. 298 ! 25

2. 5,391 ! 77

3. 24,303 ! 12

4. 43.44 ! 85

5. $63.75 ! 59

6. 397.86 ! 31

At Elmer Elementary School, fifth-grade students are savingmoney for a summer trip to Washington, D.C.

7. About how many times more money has Percy saved than James?

8. About how many times more money has Bertha saved than Emily?

R 4-2

Estimating with decimals and money:

Estimate $78.60 ! 41.

Round $78.60 to $80.

Round 41 to 40.

$80 ! 40 " 2

When estimating with money, it is good to find an overestimate. Round the dividend up and the divisor down.

Estimating using rounding and multiplication:

Estimate 1,750 ! 32.

32 # ? is about 1,750.

Round 32 to 30.

Round 1,750 to 1,800.

30 # 60 " 1,800

So, a good estimate is about 60.

Estimating with compatible numbers:

Estimate 1,750 ! 32.

Substitute 1,800 for 1,750 and 30 for 32.

1,800 ! 30 " 60

So, a good estimate is about 60.

Student Amount SavedPercy $125Emily $80George $202James $41Bertha $159

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Estimating with Two-Digit DivisorsEstimate each quotient. Tell which method you used.

1. 269 ! 33

2. 158 ! 52

3. $910 ! 85

4. $250 ! 48

5. 200 ! 29

6. 1,950 ! 94

The Town Traveling Club has 19 members. Estimate eachmember’s share of each trip expense.

Test Prep

11. Which is a reasonable estimate for 378 ! 87?

A. 1 B. 3 C. 4 D. 7

12. Writing in Math Which quotient is greater? Explain howyou know without finding the answer.

$37.68 ! 15 or $35.25 ! 15

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7. transportation $195

9. food $385

8. jet ski rentals $635

10. Estimate the total expense foreach member of the TownTraveling Club.

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Name PROBLEM SOLVING STRATEGY:

Try, Check, and ReviseHeights David is 10 in. taller than his sister Katie. The sum oftheir heights is 104 in. What is each of their heights?

Step 3: What strategy will you use? Strategy: Try, Check, and Revise

Try: David ! 50 in., Katie ! 40 in.

Check: 50 " 40 ! 90

Revise: 90 is too low. Their heights must equal 104. Increase each height.

Try: David 57 in., Katie 47 in.

Check: 57 " 47 ! 104

Answer: David is 57 in., Katie is 47 in.

Mr. Caine filled a large container with 129 qt of water. (4 qt ! 1 gal) He wants to pour the water into gallon containers. He does this withoutspilling any water. How many gallon containers will be needed?

1. Identify key facts and details.

2. Solve the problem. Write the answer in a complete sentence.

Plan and Solve

Read and Understand

R 4-3

Step 1: What do you know?

• Tell the problem in your own words.

When you add David’s and Katie’s heights, theytotal 104 in.

• Identify key facts and details.

David is 10 in. taller than Katie.

Step 2: What are you trying to find?

• Tell what the question is asking.

You want to know the height of each person.

• Show the main idea.

David’s height " Katie’s height ! 104 inches

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Try, Check, and ReviseSolve. Write your answer in a sentence.

1. Bryan needs to build a fence around his rectangularvegetable garden. The length will be 2 ft longer than thewidth. If he uses 16 ft of fencing, what will be the lengthand width?

2. Bryan plans on building a larger garden next year. Hewould like to keep the length the same but extend thewidth of his garden so that it is square. If Bryan extends thewidth to make a square, how much fencing will he need tosurround the garden?

3. The school district has 294 basketballs to distribute to 36different teams in the intramural basketball league. If thebasketballs are equally distributed, how many basketballscan each team have for practice? How many basketballswill be remaining?

4. Hannah is 8 in. taller than her brother Quinn. If Quinn stood onHannah’s shoulders they would be 80 in. tall. How tall is Quinn?

5. The area of a rectangle is 50 ft. The length is two times thewidth. What are the length and the width? (Hint: The area of arectangle is l ! w.)

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Dividing Whole Numbers by Two-Digit DivisorsFind 437 ! 39.

Complete.

1. 2. 3.

Find each quotient. Check by multiplying.

4. 18!1"7"9" 5. 94!8"3"5" 6. 67!3"5"6"

R 4-4

437 ! 39 " 11 R8

11437

#3947

#398

39

1437

#394

39

What You Think What You Write

Step 1

Estimate. Decide where to place the first digit in the quotient.$437 ! 39 is about $440 ! 40 or 11.

Step 2

Divide the tens. Multiply and subtract.

Step 3

Divide the ones. Multiply and subtract.

Step 4

Compare and write the answer.

Start dividing tens.

1 group of 39 or

1 $ 39 " 39.

This leaves 4 left over.

1 group of 39 or

1 $ 39 " 39.

This leaves 8 left over.

Since 39 % 8, I do not have to divide again.

R328377

R419749

R1241858

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Dividing Whole Numbers by Two-DigitsComplete. Find each missing remainder or quotient.

1. 2. 3.


4. 25!7"6"8" 5. 34!2"6"4" 6. 19!4"0"1" 7. 62!3"3"8"

8. 599 ! 37 " 9. 9,227 ! 83 "

10. The school student council sponsored a Switch Day where students were able to switch classes every 20 min. The students are in school for 7 hr. If each student switched the same number of times, how many times did each student get to visit another classroom? (Hint: There are 60 min in 1 hr.)

11. 456 students participated in Switch Day. The students raised money for a charity so that the principal would approve of the day. If the total amount of money raised was $912 and each student brought in the same amount of money, how much did each student raise?

Test Prep

12. Which is 458 ! 73?

A. 5 R19 B. 5 R20 C. 6 R19 D. 6 R20

13. Writing in Math If you have a two-digit divisor and athree-digit dividend, does the quotient always have thesame number of digits? Explain.

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R3

12037

R30

34239

R29

41314

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Dividing Larger NumbersFind 899 ! 19.

Find each quotient. Check your answer by multiplying.

1. 48!3",7"9"6" 2. 41!2",5"8"8" 3. 85!4",3"4"6"

4. 47!7",4"9"2" 5. 94!8",2"0"3" 6. 43!2",3"7"4"

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Step 3

Bring down the ones. Divide the ones. Multiply and subtract.

Multiply:

7 " 19 # 133

Subtract: 139 $ 133 # 6

Compare: 6 % 19

Multiply:

4 " 19 # 76

Subtract: 89 $ 76 # 13

Compare: 13 % 19

Step 4

Check:

So, 899 ! 19 # 47 R6.

Step 2Step 1

Divide the tens. Multiply and subtract.

Estimate. Decide where to place the first digit in the quotient.

899 ! 19 is about 900 ! 20 # 45 or 4 tens, 5 ones.

Start dividing tens.

47899

$76139

$1336

194

899$76

13

19

47"1942347893

& 6899

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Dividing Larger NumbersFind each quotient. Check your answers by multiplying.

1. 53!6",3"2"4" 2. 52!6",3"4"8" 3. 86!3"1",3"0"9" 4. 33!3",4"5"5"

5. 17,496 ! 91 " 6. 25,214 ! 47 "

7. 2,312 ! 26 " 8. 4,895 ! 83 "

The Humphrey family decided to fly from San Francisco,California, to Tokyo, Japan. There were 3 stops along the way.

9. It took the Humphrey family 6 hr to travel from San Francisco to New York. How many kilometers did they travel per hour?

10. During the flight from New Delhi to Tokyo, the childrenplayed some games. If they switched games every 575 km,how many games did they play?

Test Prep

11. Use the data from Exercises 9–10. When the family arrived in NewDelhi from Rome, the youngest son asked the pilot how fast he wasflying the plane. The pilot told him about 847 km per hour. Howmany hours did it take the family to fly from Rome to New Delhi?

A. 5 hr B. 6 hr C. 7 hr D. 8 hr

12. Writing in Math Write a word problem that would requireyou to use 5,621 ! 23.

P 4-5

San Francisco to New York 4,140 km

New York to Rome 6,907 km

Rome to New Delhi 5,929 km

New Delhi to Tokyo 5,857 km

Distances by Plane

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Dividing: Choose a Computation MethodYou can divide using mental math, paper and pencil, or a calculator.

Divide and check. Tell what computation method you used.

1. 25!5"0"0" 2. 100!3",0"0"0" 3. 82!7"3"5"

4. 50!6",4"5"0" 5. 85!8"5"9" 6. 16!3"2",0"0"0"

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93279 37

What You Think

What You Do

Find 50,000 ! 10.

This is easy to do in my head, so I will use mental math.

So, 93,279 ! 37 is a little greater than 2,521.

Find 58,560 ! 80.

Both numbers are multiples of 10, so 58,560 ! 80 is the same as 5,856 ! 8. One digit divisors are easy to do with paper and pencil.

So, 58,560 ! 80 " 732.

Find 93,279 ! 37.

There are no basic facts or zeros, so using a calculator is the easiest way to find the quotient.

50,000 ! 10 is the same as 5,000 ! 1.

Since 50 ! 10 " 5, 5,000 ! 10 must be 500.

So, 50,000 ! 10 " 5,000.

7325,856

#5625

# 2416

8


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Dividing: Choose a Computation MethodDivide and check. Tell which computation method you used.

1. 40!2"4",0"0"0" 2. 40!6",4"4"0" 3. 22!4",8"1"8" 4. 46!9",9"3"6"

5. 37,800 ! 90 " 6. 18,000 ! 30 "

7. 24,000 ! 60 " 8. 350,000 ! 35 "

The summer-sale paper was delivered to everyone in the neighborhood.

9. Toni and Bill saw the sale paper and thought they could share the cost of the speed boat with their 4 brothers and sisters. If they divide the cost equally, how much will each person pay?

Test Prep

10. Use the data from Exercise 9. Four different families decidedto share the cost of the pontoon boat. There would be a totalof 8 people sharing the cost of the boat. How much did eachperson have to pay?

A. $2,418.00 B. $1,209.00 C. $806.00 D. $604.50

11. Writing in Math Describe when it is helpful to use a calculatorin dividing. When is it better to use another method?

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Speed boat $18,000

Pontoon boat $9,672

Jet ski $2,100

Summer

Sale

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Dividing with Zeros in the QuotientSometimes when you bring down the next digit in dividing, youget a number less than the divisor. You need to place a zero inthe quotient and bring down the next digit.

Find each quotient. Check your answer by multiplying.

1. 59!6"4"1" 2. 32!3",3"5"4" 3. 53!5",7"7"7"

4. 58!6",3"2"6" 5. 79!8",2"9"9" 6. 49!5",3"5"8"

7. Number Sense Is 5,309 ! 26 greater than 20, less than20, greater than 200, or less than 200?

R 4-7

Step 3

Continue to divide.

So, 9,286 ! 89 " 104 R30.

Step 2Step 1

Divide hundreds. Multiply, subtract, and bring down.

Find 9,286 ! 89.

Estimate. Decide where to place the first digit in the quotient.

Think: 9,000 ! 90 " 100.

Start dividing hundreds.

Since 38 # 89, you cannot divide. Write a zero in the quotient. Bring down the next digit.

1049,286

$8938

$ 0386

$ 35630

89109,286

$8938

89

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Dividing with Zeros in the QuotientFind each quotient. Check your answers by multiplying.

1. 60!6",3"6"0" 2. 84!8",7"5"0" 3. 14!9",8"2"8" 4. 57!3"6",4"8"5"

5. 12,925 ! 19 " 6. 22,348 ! 37 "

7. 9,523 ! 28 " 8. 16,451 ! 81 "

9. If 75 players hit 7,950 baseballs at the batting cages, how many hits were there for each player?

Find each quotient.

10. 3,030 ! 30 " 11. 4,242 ! 42 12. 5,050 ! 50 "

13. Number Sense Explain the reason for the pattern in thequotients in Exercises 10–12.

Test Prep

14. Which is 17,889 ! 88?

A. 203 B. 203 R25 C. 204 R1 D. 205

15. Writing in Math Write a problem with a two-digit divisor, a five-digit dividend, and a quotient of 308. Explain how you did it.

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Name PROBLEM-SOLVING SKILL

Multiple-Step ProblemsLaw Firm Mr. Barnett earned about $98,000 last year at his law firm.He had to pay about $19,000 in taxes. He also had to pay about$6,000 for office supplies. About how much did he make each month?

To solve problems that involve multiple steps, ask yourself what hidden questions are in the problem.

• Hidden question 1: What were Mr. Barnett’s total expenses?

$19,000 ! $6,000 " $25,000

• Hidden question 2: How much did he earn after expenses?

$98,000 # $25,000 " $73,000

$73,000 $ 12 is about $6,000. So, Mr. Barnett made about $6,000 each month.

Write and answer the hidden question or questions and then solve the problem.

1. Leslie bought 3 posters that were priced at $9.98 each,including tax. The store had a special sale that day. For each3 posters you buy, you get the third one for half price. Lesliegave the cashier $30.00. How much change did she receive?

Plan and Solve

Read and Understand

R 4-8

Step 1: What do you know?

$98,000 was Mr. Barnett’s income. He had to pay$19,000 and $6,000.

Step 2: What are you trying to find?

How much money he earned each month

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Multiple-Step ProblemsWrite and answer the hidden question or questions in each problem and then solve the problem. Write your answer in a complete sentence.

1. Sue bought 2 pairs of jeans and a belt that cost $6.95. The tax on the items was $5.85. Sue paid the cashier $70.00. How much money did Sue receive in change?

2. A recreation department purchased 12 T-shirts for daycamp. The department does not have to pay sales tax. Itpaid with a $100.00 bill. How much change did it receive?

3. When Mrs. Johnson saw the sale, she decided to getclothes for each child in her family. She bought each of her6 children a pair of jeans and a T-shirt. She paid $14.35 insales tax. How much was Mrs. Johnson’s total bill?

4. Writing in Math Write a two-step problem about buying somethingat the mall that has a hidden question. Tell what the hiddenquestion is and solve your problem. Use $8.95 somewhere in your equation. Write your answer in a complete sentence.

P 4-8

Jeans $29.95 for 1 pairOR 2 pairs for $55.00

T-shirts $9.95 for 1OR 3 T-shirts for $25.00

Storewide Sale

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Dividing Decimals by 10, 100, and 1,000Understanding place value makes it easy to divide decimals by10, 100, and 1,000.

Dividing a number by 10 moves the decimal point one place to the left.

Example: 317 ! 10 " 31.7

Dividing a number by 100 moves the decimal point two places to the left.

Example: 317 ! 100 " 3.17

Dividing a number by 1,000 moves the decimal point three places to the left.

Example: 317 ! 1,000 " 0.317


1. 87.3 ! 10 " 2. 56.2 ! 100 "

3. 77.78 ! 100 " 4. 275 ! 100 "

5. 38.93 ! 1,000 " 6. 128.75 ! 10 "

7. 66.28 ! 1,000 " 8. 1.85 ! 1,000 "

9. Writing in Math 87.5 divided by 100 is the same as 87.5multiplied by what decimal? Explain your answer.

Algebra Write 10, 100, or 1,000 for each n.

10. 14.7 ! n " 0.147

11. 6.4 ! n " 0.64

12. 325.67 ! n " 0.32567

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Dividing Decimals by 10, 100, and 1,000Find each quotient. Use mental math.

1. 86.6 ! 10 " 2. 192.5 ! 100 "

3. 1.99 ! 100 " 4. 0.87 ! 10 "

5. 228.55 ! 1,000 " 6. 0.834 ! 100 "

7. 943.35 ! 1,000 " 8. 1.25 ! 10 "

Algebra Write 10, 100, or 1,000 for each n.

9. 78.34 ! n " 0.7834 10. 0.32 ! n " 0.032 11. (75.34 #25.34) !n"5

12. There are 145 children taking swimming lessons at the pool. If 10 children will be assigned to each instructor, how many instructors need to be hired?

13. The instructors must pass a test before getting the job. The instructors must swim 2 mi. If it takes Jane 5 min every half mile, how long should it take her to finish?

Test Prep

14. Ronald ran 534.3 mi in 100 days. If he ran an equaldistance each day, how many miles did he run per day?

A. 5 B. 5.13 C. 5.343 D. 6.201

15. Writing in Math Carlos says that 17.43 ! 100 is the sameas 174.3 $ 0.01. Is he correct? Explain.

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Dividing Money by Two-Digit DivisorsYou buy a 22 oz box of granola for $2.86. How much do youpay per ounce?

Find each quotient. Check your answers by multiplying.

1. 13!$"8".7"1" 2. 59!$"3"6".5"8" 3. 87!$"1"6"7".9"1"

Decide if each quotient is greater than or less than $1.00.

4. 7!$"1"1".5"5" 5. 11!$"8".2"5" 6. 16!$"1"7".9"5"

7. Writing in Math Suppose 2.1 lb of ham costs $6.30. Is itreasonable to state that the price per pound of ham is$3.00? Why or why not?

R 4-10

Step 1 Step 3

Write the decimal point in the quotient directly above the decimal point in the dividend.

Bring down the hundredths. Continue dividing.

You paid $0.13 for 1 oz of granola.

0.13$2.86

! 2 266

! 660

22

0.1$2.86

! 2 26

22

Step 2

22 is greater than 2, so place a zero above the 2.

Start dividing tenths.

0.$2.8622.

$2.8622

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Dividing Money by Two-Digit DivisorsFind each quotient. Check your answers by multiplying. (Roundto the nearest cent, if necessary.)

1. 11!$"8".9"1" 2. 61!$"4"3".9"2" 3. 12!$"8"4".2"4" 4. 28!$"4".2"0"

5. $87.08 ! 82 " 6. $93.49 ! 59 "

7. $17.83 ! 5 " 8. $114.38 ! 19 "

Number Sense Decide if each quotient is greater than or lessthan $1.00.

9. $76.65 ! 73

10. $9.30 ! 62

11. Estimation Is the quotient you get when you divide $550.81 by 70 closer to $0.80, $8.00, or $80.00?

Test Prep

12. If 6 people split a dinner bill of $180.30, how much willeach person pay?

A. $30.05 B. $30.15 C. $30.50 D. $30.55

13. Writing in Math Explain why $46.50 ! 30 could not be $15.00.

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Dividing Decimals by Whole Numbers


1. 14!6".3" 2. 77!2".3"1" 3. 89!2".4"9"2"

Choose the best estimate for each.

4. 34.61 ! 16

A. 2.2 B. 0.22 C. 20.2

5. 16.3 ! 17

A. 1 B. 0.1 C. 0.01

6. 59.4 ! 65

A. 0.9 B. 9.1 C. 0.09

7. Reasonableness Is 61.5 ! 15 a little less than 4, a littlemore than 4, a little less than 40, or a little more than 40?

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Dividing decimals by multiples of 10, 100, and 1,000

Notice the pattern. When you move the decimal one place to the left and then divide by the same number, you move the decimal point in the previous answer one more place to the left. To do this, you often have to add zeros as decimal place holders.

Dividing decimals by whole numbers

Find 1.64 ! 4.

Step 1: Place the decimal point in the quotient above the decimal point in the dividend.

Step 2: Divide the same way you would with whole numbers.

36

3.6

0.36

! 90 " 0.4

! 90 " 0.04

! 90 " 0.004

Answer: 0.41

Check: 0.41 # 4 " 1.64

0.411.64

$1 604

$ 40

4

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Dividing Decimals by Whole NumbersFind each quotient. Check by multiplying.

1. 13!6"8".9" 2. 35!4"1"2".3" 3. 90!1"4".4" 4. 60!5"3".4"

5. 123.08 ! 34 " 6. 0.57 ! 30 "

7. 562.86 ! 59 " 8. 24.4 ! 80 "

9. If a package of granola bars with 12 bars costs $3.48, how much does each granola bar cost?

10. John paid $7.99 for 3 boxes of cereal. The tax was $1.69. Excluding tax, how much did John pay for each box of cereal if they all were the same price?

Test Prep

11. 64.82 ! 11 is

A. a little more than 6. B. a little less than 6.

C. a little more than 60. D. a little less than 60.

12. Writing in Math Explain how to divide 0.12 by 8.

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Cable TVIn the year 2000, the number of American homes that had cabletelevision was 68,544,000. What is 68,544,000 ! 10?

Remember, to divide a number by 10, you can move the decimal point one place to the left.

Cable Television There were 10,929 cable television systemsin the United States in the year 2000.


1. 10,929 ! 10 " 2. 10,929 ! 100 " 3. 10,929 ! 1,000 "

4. The Jameson Cable Television Company is housed in a building that takes up 9,400 sq yd. Suppose the building is divided into 25 separate departments. How big is each department?

5. The company sold a total of 15 cable TV systems for $9,285. How much does each system cost?

R 4-12

68,544,000.

So, 68,544,000 ! 10 " 6,854,400.

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Listen to ThisThe Federal Communications Commission (FCC) reported thatthere were 12,615 radio stations in the United States in 1999.

1. The FCC reported that there were 4,783 AM radio stations inthe United States in 1999. Round 4,783 to the nearest hundred.

2. Use that number to determine the average number of AMradio stations per state in the United States. (Hint: Thereare 50 states in the United States.)

3. There were 5,766 FM radio stations in the United States in1999. Find the average number of FM radio stations perstate in the United States. Round your answer to thenearest one.

4. In a 30-year period between 1970 and 2000, 6,108 newradio stations were started in the United States. If thenumber of radio stations started was the same each year,about how many radio stations were started per year?

5. During a 20 hr broadcast day, the average United Statesradio station broadcasts about 280 min of commercials.About how many minutes of commercials are broadcasteach hour? (Remember: There are 60 min in 1 hr.)

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Name Dividing by Multiples of 10 R 4-1 - PBworksmskris.pbworks.com/w/file/fetch/45699547/5th Math Chapters 4... · Name Dividing by Multiples of 10 ... You can divide using mental