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# Divide Whole Numbers

Module by: First Last. E-mail the author

Summary: By the end of this section, you will be able to:

• Use division notation
• Model division of whole numbers
• Divide whole numbers
• Translate word phrases to math notation
• Divide whole numbers in applications

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## Note:

Before you get started, take this readiness quiz.

1. 1) Multiply: 27·3.27·3.
If you missed this problem, review (Reference).
2. 2) Subtract: 4326.4326.
If you missed this problem, review (Reference)
3. 3) Multiply: 62(87).62(87).
If you missed this problem, review (Reference).

## Use Division Notation

So far we have explored addition, subtraction, and multiplication. Now let’s consider division. Suppose you have the 1212 cookies in Figure 1 and want to package them in bags with 44 cookies in each bag. How many bags would we need?

You might put 44 cookies in first bag, 44 in the second bag, and so on until you run out of cookies. Doing it this way, you would fill 33 bags.

In other words, starting with the 1212 cookies, you would take away, or subtract, 44 cookies at a time. Division is a way to represent repeated subtraction just as multiplication represents repeated addition.

Instead of subtracting 44 repeatedly, we can write

12÷412÷4

We read this as twelve divided by four and the result is the quotient of 1212 and 4.4. The quotient is 33 because we can subtract 44 from 1212 exactly 33 times. We call the number being divided the dividend and the number dividing it the divisor. In this case, the dividend is 1212 and the divisor is 4.4.

In the past you may have used the notation 412412, but this division also can be written as 12÷4,12/4,124.12÷4,12/4,124. In each case the 1212 is the dividend and the 44 is the divisor.

### Note: Operation Symbols for Division:

To represent and describe division, we can use symbols and words.

Operation Notation Expression Read as Result
DivisionDivision ÷÷
abab
baba
a/ba/b
12÷412÷4
124124
412412
12/412/4
Twelve divided by fourTwelve divided by four the quotient of 12 and 4the quotient of 12 and 4

Division is performed on two numbers at a time. When translating from math notation to English words, or English words to math notation, look for the words of and and to identify the numbers.

### Example 1

#### Problem 1

Translate from math notation to words.

64÷864÷8 427427 428428

##### Solution: Solution
• We read this as sixty-four divided by eight and the result is the quotient of sixty-four and eight.
• We read this as forty-two divided by seven and the result is the quotient of forty-two and seven.
• We read this as twenty-eight divided by four and the result is the quotient of twenty-eight and four.

### Note:

#### Exercise 1

Translate from math notation to words:

84÷784÷7 186186 824824

##### Solution
• eighty-four divided by seven; the quotient of eighty-four and seven
• eighteen divided by six; the quotient of eighteen and six.
• twenty-four divided by eight; the quotient of twenty-four and eight

### Note:

#### Exercise 2

Translate from math notation to words:

72÷972÷9 213213 654654

##### Solution
• seventy-two divided by nine; the quotient of seventy-two and nine
• twenty-one divided by three; the quotient of twenty-one and three
• fifty-four divided by six; the quotient of fifty-four and six

## Model Division of Whole Numbers

As we did with multiplication, we will model division using counters. The operation of division helps us organize items into equal groups as we start with the number of items in the dividend and subtract the number in the divisor repeatedly.

### Note:

Doing the Manipulative Mathematics activity Model Division of Whole Numbers will help you develop a better understanding of dividing whole numbers.

### Example 2

#### Problem 1

Model the division: 24÷8.24÷8.

##### Solution: Solution

To find the quotient 24÷8,24÷8, we want to know how many groups of 88 are in 24.24.

Model the dividend. Start with 2424 counters.

The divisor tell us the number of counters we want in each group. Form groups of 88 counters.

Count the number of groups. There are 33 groups.

24÷8=324÷8=3

### Note:

#### Exercise 3

Model: 24÷6.24÷6.

### Note:

#### Exercise 4

Model: 42÷7.42÷7.

## Divide Whole Numbers

We said that addition and subtraction are inverse operations because one undoes the other. Similarly, division is the inverse operation of multiplication. We know 12÷4=312÷4=3 because 3·4=12.3·4=12. Knowing all the multiplication number facts is very important when doing division.

We check our answer to division by multiplying the quotient by the divisor to determine if it equals the dividend. In Example 2, we know 24÷8=324÷8=3 is correct because 3·8=24.3·8=24.

### Example 3

#### Problem 1

Divide. Then check by multiplying. 42÷642÷6 729729 763763

##### Solution: Solution
•  ⓐ 42÷642÷6 Divide 42 by 6. 77 Check by multiplying. 7·67·6 42✓42✓
•  ⓑ 729729 Divide 72 by 9. 88 Check by multiplying.8·98·9 72✓72✓
•  ⓒ 763763 Divide 63 by 7. 99 Check by multiplying. 9·79·7 63✓63✓

### Note:

#### Exercise 5

Divide. Then check by multiplying:

54÷654÷6 279279

9 3

### Note:

#### Exercise 6

Divide. Then check by multiplying:

369369 840840

##### Solution

4 5

What is the quotient when you divide a number by itself?

1515=1because1·15=151515=1because1·15=15

Dividing any number (except 0)(except 0) by itself produces a quotient of 1.1. Also, any number divided by 11 produces a quotient of the number. These two ideas are stated in the Division Properties of One.

### Note: Division Properties of One:

 Any number (except 0) divided by itself is one. a÷a=1a÷a=1 Any number divided by one is the same number. a÷1=aa÷1=a

### Example 4

#### Problem 1

Divide. Then check by multiplying:

1. 11÷1111÷11
2. 191191
3. 1717
##### Solution: Solution
•  ⓐ 11÷1111÷11 A number divided by itself is 1. 11 Check by multiplying.1·111·11 11✓11✓
•  ⓑ 191191 A number divided by 1 equals itself. 1919 Check by multiplying.19·119·1 19✓19✓
•  ⓒ 1717 A number divided by 1 equals itself. 77 Check by multiplying.7·17·1 7✓7✓

### Note:

#### Exercise 7

Divide. Then check by multiplying:

14÷1414÷14 271271

1. 1
2. 27

### Note:

#### Exercise 8

Divide. Then check by multiplying:

161161 1414

##### Solution
1. 16
2. 4

Suppose we have $0,$0, and want to divide it among 33 people. How much would each person get? Each person would get $0.$0. Zero divided by any number is 0.0.

Now suppose that we want to divide $10$10 by 0.0. That means we would want to find a number that we multiply by 00 to get 10.10. This cannot happen because 00 times any number is 0.0. Division by zero is said to be undefined.

These two ideas make up the Division Properties of Zero.

### Note: Division Properties of Zero:

 Zero divided by any number is 0. 0÷a=00÷a=0 Dividing a number by zero is undefined. a÷0a÷0 undefined

Another way to explain why division by zero is undefined is to remember that division is really repeated subtraction. How many times can we take away 00 from 10?10? Because subtracting 00 will never change the total, we will never get an answer. So we cannot divide a number by 0.0.

### Example 5

#### Problem 1

Divide. Check by multiplying: 0÷30÷3 10/0.10/0.

##### Solution: Solution
•  ⓐ 0÷30÷3 Zero divided by any number is zero. 00 Check by multiplying.0·30·3 0✓0✓
•  ⓑ 10/010/0 Division by zero is undefined. undefined

### Note:

#### Exercise 9

Divide. Then check by multiplying:

0÷20÷2 17/017/0

0 undefined

### Note:

#### Exercise 10

Divide. Then check by multiplying:

0÷60÷6 13/013/0

##### Solution

0 undefined

When the divisor or the dividend has more than one digit, it is usually easier to use the 412412 notation. This process is called long division. Let’s work through the process by dividing 7878 by 3.3.

 Divide the first digit of the dividend, 7, by the divisor, 3. The divisor 3 can go into 7 two times since 2×3=62×3=6. Write the 2 above the 7 in the quotient. Multiply the 2 in the quotient by 2 and write the product, 6, under the 7. Subtract that product from the first digit in the dividend. Subtract 7−67−6. Write the difference, 1, under the first digit in the dividend. Bring down the next digit of the dividend. Bring down the 8. Divide 18 by the divisor, 3. The divisor 3 goes into 18 six times. Write 6 in the quotient above the 8. Multiply the 6 in the quotient by the divisor and write the product, 18, under the dividend. Subtract 18 from 18.

We would repeat the process until there are no more digits in the dividend to bring down. In this problem, there are no more digits to bring down, so the division is finished.

So78÷3=26.So78÷3=26.

Check by multiplying the quotient times the divisor to get the dividend. Multiply 26×326×3 to make sure that product equals the dividend, 78.78.

216×3___78216×3___78
(4)

It does, so our answer is correct.

### Note: Divide whole numbers.:

1. Step 1. Divide the first digit of the dividend by the divisor.
If the divisor is larger than the first digit of the dividend, divide the first two digits of the dividend by the divisor, and so on.
2. Step 2. Write the quotient above the dividend.
3. Step 3. Multiply the quotient by the divisor and write the product under the dividend.
4. Step 4. Subtract that product from the dividend.
5. Step 5. Bring down the next digit of the dividend.
6. Step 6. Repeat from Step 1 until there are no more digits in the dividend to bring down.
7. Step 7. Check by multiplying the quotient times the divisor.

### Example 6

#### Problem 1

Divide 2,596÷4.2,596÷4. Check by multiplying:

##### Solution: Solution
 Let's rewrite the problem to set it up for long division. Divide the first digit of the dividend, 2, by the divisor, 4. Since 4 does not go into 2, we use the first two digits of the dividend and divide 25 by 4. The divisor 4 goes into 25 six times. We write the 6 in the quotient above the 5. Multiply the 6 in the quotient by the divisor 4 and write the product, 24, under the first two digits in the dividend. Subtract that product from the first two digits in the dividend. Subtract 25−2425−24. Write the difference, 1, under the second digit in the dividend. Now bring down the 9 and repeat these steps. There are 4 fours in 19. Write the 4 over the 9. Multiply the 4 by 4 and subtract this product from 19. Bring down the 6 and repeat these steps. There are 9 fours in 36. Write the 9 over the 6. Multiply the 9 by 4 and subtract this product from 36. So 2,596÷4=6492,596÷4=649. Check by multiplying.

It equals the dividend, so our answer is correct.

### Note:

#### Exercise 11

Divide. Then check by multiplying: 2,636÷42,636÷4

659

### Note:

#### Exercise 12

Divide. Then check by multiplying: 2,716÷42,716÷4

679

### Example 7

#### Problem 1

Divide 4,506÷6.4,506÷6. Check by multiplying:

##### Solution: Solution
 Let's rewrite the problem to set it up for long division. First we try to divide 6 into 4. Since that won't work, we try 6 into 45.There are 7 sixes in 45. We write the 7 over the 5. Multiply the 7 by 6 and subtract this product from 45. Now bring down the 0 and repeat these steps. There are 5 sixes in 30.Write the 5 over the 0. Multiply the 5 by 6 and subtract this product from 30. Now bring down the 6 and repeat these steps. There is 1 six in 6. Write the 1 over the 6. Multiply 1 by 6 and subtract this product from 6. Check by multiplying.

It equals the dividend, so our answer is correct.

### Note:

#### Exercise 13

Divide. Then check by multiplying: 4,305÷5.4,305÷5.

861

### Note:

#### Exercise 14

Divide. Then check by multiplying: 3,906÷6.3,906÷6.

651

### Example 8

#### Problem 1

Divide 7,263÷9.7,263÷9. Check by multiplying.

##### Solution: Solution
 Let's rewrite the problem to set it up for long division. First we try to divide 9 into 7. Since that won't work, we try 9 into 72. There are 8 nines in 72. We write the 8 over the 2. Multiply the 8 by 9 and subtract this product from 72. Now bring down the 6 and repeat these steps. There are 0 nines in 6. Write the 0 over the 6. Multiply the 0 by 9 and subtract this product from 6. Now bring down the 3 and repeat these steps. There are 7 nines in 63. Write the 7 over the 3. Multiply the 7 by 9 and subtract this product from 63. Check by multiplying.

It equals the dividend, so our answer is correct.

### Note:

#### Exercise 15

Divide. Then check by multiplying: 4,928÷7.4,928÷7.

704

### Note:

#### Exercise 16

Divide. Then check by multiplying: 5,663÷7.5,663÷7.

##### Solution

809

So far all the division problems have worked out evenly. For example, if we had 2424 cookies and wanted to make bags of 88 cookies, we would have 33 bags. But what if there were 2828 cookies and we wanted to make bags of 8?8? Start with the 2828 cookies as shown in Figure 2.

Try to put the cookies in groups of eight as in Figure 3.

There are 33 groups of eight cookies, and 44 cookies left over. We call the 44 cookies that are left over the remainder and show it by writing R4 next to the 3.3. (The R stands for remainder.)

To check this division we multiply 33 times 88 to get 24,24, and then add the remainder of 4.4.

3×8___24+4___283×8___24+4___28

### Example 9

#### Problem 1

Divide 1,439÷4.1,439÷4. Check by multiplying.

##### Solution: Solution
 Let's rewrite the problem to set it up for long division. First we try to divide 4 into 1. Since that won't work, we try 4 into 14. There are 3 fours in 14. We write the 3 over the 4. Multiply the 3 by 4 and subtract this product from 14. Now bring down the 3 and repeat these steps. There are 5 fours in 23. Write the 5 over the 3. Multiply the 5 by 4 and subtract this product from 23. Now bring down the 9 and repeat these steps. There are 9 fours in 39. Write the 9 over the 9. Multiply the 9 by 4 and subtract this product from 39. There are no more numbers to bring down, so we are done. The remainder is 3. Check by multiplying.

So 1,439÷41,439÷4 is 359359 with a remainder of 3.3. Our answer is correct.

### Note:

#### Exercise 17

Divide. Then check by multiplying: 3,812÷8.3,812÷8.

##### Solution

476 with a remainder of 4

### Note:

#### Exercise 18

Divide. Then check by multiplying: 4,319÷8.4,319÷8.

##### Solution

539 with a remainder of 7

### Example 10

#### Problem 1

Divide and then check by multiplying: 1,461÷13.1,461÷13.

##### Solution: Solution
 Let's rewrite the problem to set it up for long division. 131,461131,461 First we try to divide 13 into 1. Since that won't work, we try 13 into 14. There is 1 thirteen in 14. We write the 1 over the 4. Multiply the 1 by 13 and subtract this product from 14. Now bring down the 6 and repeat these steps. There is 1 thirteen in 16. Write the 1 over the 6. Multiply the 1 by 13 and subtract this product from 16. Now bring down the 1 and repeat these steps. There are 2 thirteens in 31. Write the 2 over the 1. Multiply the 2 by 13 and subtract this product from 31. There are no more numbers to bring down, so we are done. The remainder is 5. 1,462÷131,462÷13 is 112 with a remainder of 5. Check by multiplying.

Our answer is correct.

### Note:

#### Exercise 19

Divide. Then check by multiplying: 1,493÷13.1,493÷13.

114 R11

### Note:

#### Exercise 20

Divide. Then check by multiplying: 1,461÷12.1,461÷12.

121 R9

### Example 11

#### Problem 1

Divide and check by multiplying: 74,521÷241.74,521÷241.

##### Solution: Solution
 Let's rewrite the problem to set it up for long division. 24174,52124174,521 First we try to divide 241 into 7. Since that won’t work, we try 241 into 74. That still won’t work, so we try 241 into 745. Since 2 divides into 7 three times, we try 3. Since 3×241=7233×241=723, we write the 3 over the 5 in 745. Note that 4 would be too large because 4×241=9644×241=964, which is greater than 745. Multiply the 3 by 241 and subtract this product from 745. Now bring down the 2 and repeat these steps. 241 does not divide into 222. We write a 0 over the 2 as a placeholder and then continue. Now bring down the 1 and repeat these steps. Try 9. Since 9×241=2,1699×241=2,169, we write the 9 over the 1. Multiply the 9 by 241 and subtract this product from 2,221. There are no more numbers to bring down, so we are finished. The remainder is 52. So 74,521÷24174,521÷241is 309 with a remainder of 52. Check by multiplying.

Sometimes it might not be obvious how many times the divisor goes into digits of the dividend. We will have to guess and check numbers to find the greatest number that goes into the digits without exceeding them.

### Note:

#### Exercise 21

Divide. Then check by multiplying: 78,641÷256.78,641÷256.

307 R49

### Note:

#### Exercise 22

Divide. Then check by multiplying: 76,461÷248.76,461÷248.

308 R77

## Translate Word Phrases to Math Notation

Earlier in this section, we translated math notation for division into words. Now we’ll translate word phrases into math notation. Some of the words that indicate division are given in Table 19.

Table 19
Operation Word Phrase Example Expression
Division divided by
quotient of
divided into
1212 divided by 44
the quotient of 1212 and 44
44 divided into 1212
12÷412÷4
124124
12/412/4
412412

### Example 12

#### Problem 1

Translate and simplify: the quotient of 5151 and 17.17.

##### Solution: Solution

The word quotient tells us to divide.

the quotient of 51 and 17Translate.51÷17Divide.3the quotient of 51 and 17Translate.51÷17Divide.3

We could just as correctly have translated the quotient of 5151 and 1717 using the notation

1751or5117.1751or5117.

### Note:

#### Exercise 23

Translate and simplify: the quotient of 9191 and 13.13.

91 ÷ 13; 7

### Note:

#### Exercise 24

Translate and simplify: the quotient of 5252 and 13.13.

52 ÷ 13; 4

## Divide Whole Numbers in Applications

We will use the same strategy we used in previous sections to solve applications. First, we determine what we are looking for. Then we write a phrase that gives the information to find it. We then translate the phrase into math notation and simplify it to get the answer. Finally, we write a sentence to answer the question.

### Example 13

#### Problem 1

Cecelia bought a 160-ounce160-ounce box of oatmeal at the big box store. She wants to divide the 160160 ounces of oatmeal into 8-ounce8-ounce servings. She will put each serving into a plastic bag so she can take one bag to work each day. How many servings will she get from the big box?

##### Solution: Solution

We are asked to find the how many servings she will get from the big box.

 Write a phrase. 160 ounces divided by 8 ounces Translate to math notation. 160÷8160÷8 Simplify by dividing. 2020 Write a sentence to answer the question. Cecelia will get 20 servings from the big box.

### Note:

#### Exercise 25

Marcus is setting out animal crackers for snacks at the preschool. He wants to put 99 crackers in each cup. One box of animal crackers contains 135135 crackers. How many cups can he fill from one box of crackers?

##### Solution

Marcus can fill 15 cups.

### Note:

#### Exercise 26

Andrea is making bows for the girls in her dance class to wear at the recital. Each bow takes 44 feet of ribbon, and 3636 feet of ribbon are on one spool. How many bows can Andrea make from one spool of ribbon?

##### Solution

Andrea can make 9 bows.

## Key Concepts

Operation Notation Expression Read as Result
DivisionDivision ÷÷
abab
baba
a/ba/b
12÷412÷4
124124
412412
12/412/4
Twelve divided by fourTwelve divided by four the quotient of 12 and 4the quotient of 12 and 4
• Division Properties of One
• Any number (except 0) divided by itself is one. a÷a=1a÷a=1
• Any number divided by one is the same number. a÷1=aa÷1=a
• Division Properties of Zero
• Zero divided by any number is 0. 0÷a=00÷a=0
• Dividing a number by zero is undefined. a÷0a÷0 undefined
• Divide whole numbers.
1. Step 1. Divide the first digit of the dividend by the divisor.
If the divisor is larger than the first digit of the dividend, divide the first two digits of the dividend by the divisor, and so on.
2. Step 2. Write the quotient above the dividend.
3. Step 3. Multiply the quotient by the divisor and write the product under the dividend.
4. Step 4. Subtract that product from the dividend.
5. Step 5. Bring down the next digit of the dividend.
6. Step 6. Repeat from Step 1 until there are no more digits in the dividend to bring down.
7. Step 7. Check by multiplying the quotient times the divisor.

### Practice Makes Perfect

Use Division Notation

In the following exercises, translate from math notation to words.

#### Exercise 27

54÷954÷9

##### Solution

fifty-four divided by nine; the quotient of fifty-four and nine

567567

#### Exercise 29

328328

##### Solution

thirty-two divided by eight; the quotient of thirty-two and eight

642642

#### Exercise 31

48÷648÷6

##### Solution

forty-eight divided by six; the quotient of forty-eight and six

639639

#### Exercise 33

763763

##### Solution

sixty-three divided by seven; the quotient of sixty-three and seven

#### Exercise 34

72÷872÷8

Model Division of Whole Numbers

In the following exercises, model the division.

15÷515÷5

10÷510÷5

147147

186186

420420

315315

24÷624÷6

#### Exercise 42

16÷416÷4

Divide Whole Numbers

In the following exercises, divide. Then check by multiplying.

18÷218÷2

9

14÷214÷2

273273

9

303303

428428

7

436436

455455

9

355355

72/872/8

9

864864

357357

5

42÷742÷7

15151515

1

12121212

43÷4343÷43

1

37÷3737÷37

231231

23

291291

19÷119÷1

19

17÷117÷1

0÷40÷4

0

0÷80÷8

5050

undefined

9090

260260

undefined

320320

120120

0

160160

72÷372÷3

24

57÷357÷3

968968

12

786786

54655465

93

45284528

924÷7924÷7

132

861÷7861÷7

5,22665,2266

871

3,77683,7768

431,324431,324

7,831

546,855546,855

7,209÷37,209÷3

2,403

4,806÷34,806÷3

5,406÷65,406÷6

901

3,208÷43,208÷4

42,81642,816

704

63,62463,624

91,881991,8819

10,209

83,256883,2568

2,470÷72,470÷7

352 R6

3,741÷73,741÷7

855,305855,305

6,913 R1

951,492951,492

431,1745431,1745

86,234 R4

297,2774297,2774

#### Exercise 97

130,016÷3130,016÷3

43,338 R2

#### Exercise 98

105,609÷2105,609÷2

155,735155,735

382 R5

4,933214,93321

#### Exercise 101

56,883÷6756,883÷67

849

#### Exercise 102

43,725/7543,725/75

#### Exercise 103

30,14431430,144314

96

#### Exercise 104

26,145÷41526,145÷415

#### Exercise 105

273542,195273542,195

1,986 R17

#### Exercise 106

816,243÷462816,243÷462

Mixed Practice

In the following exercises, simplify.

15(204)15(204)

3,060

74·39174·391

256184256184

72

305262305262

719+341719+341

1,060

647+528647+528

2587525875

35

#### Exercise 114

1104÷231104÷23

Translate Word Phrases to Algebraic Expressions

In the following exercises, translate and simplify.

#### Exercise 115

the quotient of 4545 and 1515

45 ÷ 15; 3

#### Exercise 116

the quotient of 6464 and 1616

#### Exercise 117

the quotient of 288288 and 2424

288 ÷ 24; 12

#### Exercise 118

the quotient of 256256 and 3232

Divide Whole Numbers in Applications

In the following exercises, solve.

#### Exercise 119

Trail mix Ric bought 6464 ounces of trail mix. He wants to divide it into small bags, with 22 ounces of trail mix in each bag. How many bags can Ric fill?

##### Solution

Ric can fill 32 bags.

#### Exercise 120

Crackers Evie bought a 4242 ounce box of crackers. She wants to divide it into bags with 33 ounces of crackers in each bag. How many bags can Evie fill?

#### Exercise 121

Astronomy class There are 125125 students in an astronomy class. The professor assigns them into groups of 5.5. How many groups of students are there?

##### Solution

There are 25 groups.

#### Exercise 122

Flower shop Melissa’s flower shop got a shipment of 152152 roses. She wants to make bouquets of 88 roses each. How many bouquets can Melissa make?

#### Exercise 123

Baking One roll of plastic wrap is 4848 feet long. Marta uses 33 feet of plastic wrap to wrap each cake she bakes. How many cakes can she wrap from one roll?

##### Solution

Marta can wrap 16 cakes from 1 roll.

#### Exercise 124

Dental floss One package of dental floss is 5454 feet long. Brian uses 22 feet of dental floss every day. How many days will one package of dental floss last Brian?

Mixed Practice

In the following exercises, solve.

#### Exercise 125

Miles per gallon Susana’s hybrid car gets 4545 miles per gallon. Her son’s truck gets 1717 miles per gallon. What is the difference in miles per gallon between Susana’s car and her son’s truck?

##### Solution

The difference is 28 miles per gallon.

#### Exercise 126

Distance Mayra lives 5353 miles from her mother’s house and 7171 miles from her mother-in-law’s house. How much farther is Mayra from her mother-in-law’s house than from her mother’s house?

#### Exercise 127

Field trip The 4545 students in a Geology class will go on a field trip, using the college’s vans. Each van can hold 99 students. How many vans will they need for the field trip?

##### Solution

They will need 5 vans for the field trip

#### Exercise 128

Potting soil Aki bought a 128128 ounce bag of potting soil. How many 44 ounce pots can he fill from the bag?

#### Exercise 129

Hiking Bill hiked 88 miles on the first day of his backpacking trip, 1414 miles the second day, 1111 miles the third day, and 1717 miles the fourth day. What is the total number of miles Bill hiked?

##### Solution

Bill hiked 50 miles

#### Exercise 130

Reading Last night Emily read 66 pages in her Business textbook, 2626 pages in her History text, 1515 pages in her Psychology text, and 99 pages in her math text. What is the total number of pages Emily read?

#### Exercise 131

Patients LaVonne treats 1212 patients each day in her dental office. Last week she worked 44 days. How many patients did she treat last week?

##### Solution

LaVonne treated 48 patients last week.

#### Exercise 132

Scouts There are 1414 boys in Dave’s scout troop. At summer camp, each boy earned 55 merit badges. What was the total number of merit badges earned by Dave’s scout troop at summer camp?

### Writing Exercises

#### Exercise 133

Explain how you use the multiplication facts to help with division.

#### Exercise 134

Oswaldo divided 300300 by 88 and said his answer was 3737 with a remainder of 4.4. How can you check to make sure he is correct?

### Everyday Math

#### Exercise 135

Contact lenses Jenna puts in a new pair of contact lenses every 1414 days. How many pairs of contact lenses does she need for 365365 days?

##### Solution

Jenna uses 26 pairs of contact lenses, but there is 1 day left over, so she needs 27 pairs for 365 days.

#### Exercise 136

Cat food One bag of cat food feeds Lara’s cat for 2525 days. How many bags of cat food does Lara need for 365365 days?

### Self Check

After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

Overall, after looking at the checklist, do you think you are well-prepared for the next Chapter? Why or why not?

## Chapter Review Exercises

### Introduction to Whole Numbers

Identify Counting Numbers and Whole Numbers

In the following exercises, determine which of the following are (a) counting numbers (b) whole numbers.

0,2,990,2,99

1. 2, 99
2. 0, 2, 99

0,3,250,3,25

0,4,900,4,90

1. 4, 90
2. 0, 4, 90

#### Exercise 140

0,1,750,1,75

Model Whole Numbers

In the following exercises, model each number using base-10base-10 blocks and then show its value using place value notation.

258

#### Exercise 142

104

Identify the Place Value of a Digit

In the following exercises, find the place value of the given digits.

#### Exercise 143

472,981472,981

1. 88
2. 44
3. 11
4. 77
5. 22
##### Solution
1. tens
2. hundred thousands
3. ones
4. thousands
5. ten thousands

#### Exercise 144

12,403,29512,403,295

1. 44
2. 00
3. 11
4. 99
5. 33

Use Place Value to Name Whole Numbers

In the following exercises, name each number in words.

#### Exercise 145

5,2805,280

##### Solution

Five thousand two hundred eighty

204,614204,614

#### Exercise 147

5,012,5825,012,582

##### Solution

Five million twelve thousand five hundred eighty-two

#### Exercise 148

31,640,97631,640,976

Use Place Value to Write Whole Numbers

In the following exercises, write as a whole number using digits.

six hundred two

#### Exercise 150

fifteen thousand, two hundred fifty-three

15,253

#### Exercise 151

three hundred forty million, nine hundred twelve thousand, sixty-one

340,912,061

#### Exercise 152

two billion, four hundred ninety-two million, seven hundred eleven thousand, two

Round Whole Numbers

In the following exercises, round to the nearest ten.

412412

410

648648

3,5563,556

3,560

#### Exercise 156

2,7342,734

In the following exercises, round to the nearest hundred.

38,97538,975

39,000

26,84926,849

81,48681,486

81,500

75,99275,992

### Add Whole Numbers

In the following exercises, translate the following from math notation to words.

#### Exercise 161

4+34+3

##### Solution

four plus three; the sum of four and three

25+1825+18

#### Exercise 163

571+629571+629

##### Solution

five hundred seventy-one plus six hundred twenty-nine; the sum of five hundred seventy-one and six hundred twenty-nine

#### Exercise 164

10,085+3,49210,085+3,492

Model Addition of Whole Numbers

In the following exercises, model the addition.

6+76+7

#### Exercise 166

38+1438+14

In the following exercises, fill in the missing values in each chart.

#### Exercise 168

In the following exercises, add.

#### Exercise 169

0+190+19 19+019+0

1. 19
2. 19

#### Exercise 170

0+4800+480 480+0480+0

7+67+6 6+76+7

1. 13
2. 13

#### Exercise 172

23+1823+18 18+2318+23

44+3544+35

82

63+2963+29

96+5896+58

154

375+591375+591

#### Exercise 177

7,281+12,5467,281+12,546

19,827

#### Exercise 178

5,280+16,324+9,7315,280+16,324+9,731

Translate Word Phrases to Math Notation

In the following exercises, translate each phrase into math notation and then simplify.

#### Exercise 179

the sum of 3030 and 1212

30 + 12; 42

#### Exercise 180

1111 increased by 88

#### Exercise 181

2525 more than 3939

39 + 25; 64

#### Exercise 182

total of 1515 and 5050

Add Whole Numbers in Applications

In the following exercises, solve.

#### Exercise 183

Shopping for an interview Nathan bought a new shirt, tie, and slacks to wear to a job interview. The shirt cost $24,$24, the tie cost $14,$14, and the slacks cost $38.$38. What was Nathan’s total cost?

### Exercise 296

Each class at Greenville School has 2222 children enrolled. The school has 2424 classes. How many children are enrolled at Greenville School?

### Exercise 297

Clayton walked 1212 blocks to his mother’s house, 66 blocks to the gym, and 99 blocks to the grocery store before walking the last 33 blocks home. What was the total number of blocks that Clayton walked?

#### Solution

Clayton walked 30 blocks.

## Glossary

dividend:
When dividing two numbers, the dividend is the number being divided.
divisor:
When dividing two numbers, the divisor is the number dividing the dividend.
quotient:
The quotient is the result of dividing two numbers.

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##### Lenses

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##### What is in a lens?

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