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# Multiply Whole Numbers

Module by: First Last. E-mail the author

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

• Use multiplication notation
• Model multiplication of whole numbers
• Multiply whole numbers
• Translate word phrases to math notation
• Multiply whole numbers in applications

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## Note:

Before you get started, take this readiness quiz.

If you missed this problem, review (Reference).
2. Subtract: 605321.605321.
If you missed this problem, review (Reference).

## Use Multiplication Notation

Suppose you were asked to count all these pennies shown in Figure 1.

Would you count the pennies individually? Or would you count the number of pennies in each row and add that number 33 times.

8+8+88+8+8

Multiplication is a way to represent repeated addition. So instead of adding 88 three times, we could write a multiplication expression.

3×83×8

We call each number being multiplied a factor and the result the product. We read 3×83×8 as three times eight, and the result as the product of three and eight.

There are several symbols that represent multiplication. These include the symbol ×× as well as the dot, ··, and parentheses ().().

### Note: Operation Symbols for Multiplication:

To describe multiplication, we can use symbols and words.

Operation Notation Expression Read as Result
MultiplicationMultiplication ××
··
()()
3×83×8
3·83·8
3(8)3(8)
three times eightthree times eight the product of 3 and 8the product of 3 and 8

### Example 1

#### Problem 1

Translate from math notation to words:

1. 7×67×6
2. 12·1412·14
3. 6(13)6(13)
##### Solution: Solution
• We read this as seven times six and the result is the product of seven and six.
• We read this as twelve times fourteen and the result is the product of twelve and fourteen.
• We read this as six times thirteen and the result is the product of six and thirteen.

### Note:

#### Exercise 1

Translate from math notation to words:

1. 8×78×7
2. 18·1118·11
##### Solution
1. eight times seven ; the product of eight and seven
2. eighteen times eleven ; the product of eighteen and eleven

### Note:

#### Exercise 2

Translate from math notation to words:

1. (13)(7)(13)(7)
2. 5(16)5(16)
##### Solution
1. thirteen times seven ; the product of thirteen and seven
2. five times sixteen; the product of five and sixteen

## Model Multiplication of Whole Numbers

There are many ways to model multiplication. Unlike in the previous sections where we used base-10base-10 blocks, here we will use counters to help us understand the meaning of multiplication. A counter is any object that can be used for counting. We will use round blue counters.

### Example 2

#### Problem 1

Model: 3×8.3×8.

##### Solution: Solution

To model the product 3×8,3×8, we’ll start with a row of 88 counters.

The other factor is 3,3, so we’ll make 33 rows of 88 counters.

Now we can count the result. There are 2424 counters in all.

3×8=243×8=24

If you look at the counters sideways, you’ll see that we could have also made 88 rows of 33 counters. The product would have been the same. We’ll get back to this idea later.

### Note:

#### Exercise 3

Model each multiplication: 4×6.4×6.

### Note:

#### Exercise 4

Model each multiplication: 5×7.5×7.

## Multiply Whole Numbers

In order to multiply without using models, you need to know all the one digit multiplication facts. Make sure you know them fluently before proceeding in this section.

Table 2 shows the multiplication facts. Each box shows the product of the number down the left column and the number across the top row. If you are unsure about a product, model it. It is important that you memorize any number facts you do not already know so you will be ready to multiply larger numbers.

Table 2
× 0 1 2 3 4 5 6 7 8 9
0 0 0 0 0 0 0 0 0 0 0
1 0 1 2 3 4 5 6 7 8 9
2 0 2 4 6 8 10 12 14 16 18
3 0 3 6 9 12 15 18 21 24 27
4 0 4 8 12 16 20 24 28 32 36
5 0 5 10 15 20 25 30 35 40 45
6 0 6 12 18 24 30 36 42 48 54
7 0 7 14 21 28 35 42 49 56 63
8 0 8 16 24 32 40 48 56 64 72
9 0 9 18 27 36 45 54 63 72 81

What happens when you multiply a number by zero? You can see that the product of any number and zero is zero. This is called the Multiplication Property of Zero.

### Note: Multiplication Property of Zero:

The product of any number and 00 is 0.0.

a·0=00·a=0a·0=00·a=0

### Example 3

#### Problem 1

Multiply:

1. 0·110·11
2. (42)0(42)0

##### Solution: Solution
 ⓐ 0·110·11 The product of any number and zero is zero. 00 ⓑ (42)0(42)0 Multiplying by zero results in zero. 00

### Note:

#### Exercise 5

Find each product:

1. 0·190·19
2. (39)0(39)0

1. 00
2. 00

### Note:

#### Exercise 6

Find each product:

1. 0·240·24
2. (57)0(57)0

##### Solution

1. 00
2. 00

What happens when you multiply a number by one? Multiplying a number by one does not change its value. We call this fact the Identity Property of Multiplication, and 11 is called the multiplicative identity.

### Note: Identity Property of Multiplication:

The product of any number and 11 is the number.

1·a=aa·1=a1·a=aa·1=a

### Example 4

#### Problem 1

Multiply:

1. (11)1(11)1
2. 1·421·42

##### Solution: Solution
 ⓐ (11)1(11)1 The product of any number and one is the number. 1111 ⓑ 1·421·42 Multiplying by one does not change the value. 4242

### Note:

#### Exercise 7

Find each product:

1. (19)1(19)1
2. 1·391·39
1. 1919
2. 3939

### Note:

#### Exercise 8

Find each product:

1. (24)(1)(24)(1)
2. 1×571×57
##### Solution
1. 2424
2. 5757

Earlier in this chapter, we learned that the Commutative Property of Addition states that changing the order of addition does not change the sum. We saw that 8+9=178+9=17 is the same as 9+8=17.9+8=17.

Is this also true for multiplication? Let’s look at a few pairs of factors.

4·7=287·4=284·7=287·4=28
9·7=637·9=639·7=637·9=63
8·9=729·8=728·9=729·8=72

When the order of the factors is reversed, the product does not change. This is called the Commutative Property of Multiplication.

### Note: Commutative Property of Multiplication:

Changing the order of the factors does not change their product.

a·b=b·aa·b=b·a

### Example 5

#### Problem 1

Multiply:

1. 8·78·7
2. 7·87·8

##### Solution: Solution
 ⓐ 8·78·7 Multiply. 5656 ⓑ 7·87·8 Multiply. 5656

Changing the order of the factors does not change the product.

### Note:

#### Exercise 9

Multiply:

1. 9·69·6
2. 6·96·9

##### Solution

54 and 54; both are the same.

### Note:

#### Exercise 10

Multiply:

1. 8·68·6
2. 6·86·8

##### Solution

48 and 48; both are the same.

To multiply numbers with more than one digit, it is usually easier to write the numbers vertically in columns just as we did for addition and subtraction.

27×3___27×3___

We start by multiplying 33 by 7.7.

3×7=213×7=21

We write the 11 in the ones place of the product. We carry the 22 tens by writing 22 above the tens place.

Then we multiply the 33 by the 2,2, and add the 22 above the tens place to the product. So 3×2=6,3×2=6, and 6+2=8.6+2=8. Write the 88 in the tens place of the product.

The product is 81.81.

When we multiply two numbers with a different number of digits, it’s usually easier to write the smaller number on the bottom. You could write it the other way, too, but this way is easier to work with.

### Example 6

#### Problem 1

Multiply: 15·4.15·4.

##### Solution: Solution
 Write the numbers so the digits 55 and 44 line up vertically. 15 ×4_____ 15 ×4_____ Multiply 44 by the digit in the ones place of 15.15. 4⋅5=20.4⋅5=20. Write 00 in the ones place of the product and carry the 22 tens. 125 ×4_____ 0 125 ×4_____ 0 Multiply 44 by the digit in the tens place of 15.15. 4⋅1=44⋅1=4.Add the 22 tens we carried. 4+2=64+2=6. Write the 66 in the tens place of the product. 125 ×4_____ 60 125 ×4_____ 60

### Note:

#### Exercise 11

Multiply: 64·8.64·8.

512512

### Note:

#### Exercise 12

Multiply: 57·6.57·6.

342342

### Example 7

#### Problem 1

Multiply: 286·5.286·5.

##### Solution: Solution
 Write the numbers so the digits 55 and 66 line up vertically. 286 ×5_____ 286 ×5_____ Multiply 55 by the digit in the ones place of 286.286. 5⋅6=30.5⋅6=30. Write the 00 in the ones place of the product and carry the 33 to the tens place.Multiply 55 by the digit in the tens place of 286.286. 5⋅8=405⋅8=40. 2836 ×5_____ 0 2836 ×5_____ 0 Add the 33 tens we carried to get 40+3=4340+3=43.Write the 33 in the tens place of the product and carry the 4 to the hundreds place. 24836 ×5_____ 30 24836 ×5_____ 30 Multiply 55 by the digit in the hundreds place of 286.286. 5⋅2=10.5⋅2=10.Add the 44 hundreds we carried to get 10+4=14.10+4=14.Write the 44 in the hundreds place of the product and the 11 to the thousands place. 24836 ×5_____ 1,430 24836 ×5_____ 1,430

### Note:

#### Exercise 13

Multiply: 347·5.347·5.

1,7351,735

### Note:

#### Exercise 14

Multiply: 462·7.462·7.

##### Solution

3,2343,234

When we multiply by a number with two or more digits, we multiply by each of the digits separately, working from right to left. Each separate product of the digits is called a partial product. When we write partial products, we must make sure to line up the place values.

### Note: Multiply two whole numbers to find the product.:

1. Step 1. Write the numbers so each place value lines up vertically.
2. Step 2. Multiply the digits in each place value.
• Work from right to left, starting with the ones place in the bottom number.
• Multiply the bottom number by the ones digit in the top number, then by the tens digit, and so on.
• If a product in a place value is more than 9,9, carry to the next place value.
• Write the partial products, lining up the digits in the place values with the numbers above.
• Repeat for the tens place in the bottom number, the hundreds place, and so on.
• Insert a zero as a placeholder with each additional partial product.
3. Step 3. Add the partial products.

### Example 8

#### Problem 1

Multiply: 62(87).62(87).

##### Solution: Solution
 Write the numbers so each place lines up vertically. Start by multiplying 7 by 62. Multiply 7 by the digit in the ones place of 62. 7⋅2=14.7⋅2=14. Write the 4 in the ones place of the product and carry the 1 to the tens place. Multiply 7 by the digit in the tens place of 62. 7⋅6=42.7⋅6=42. Add the 1 ten we carried. 42+1=4342+1=43. Write the 3 in the tens place of the product and the 4 in the hundreds place. The first partial product is 434. Now, write a 0 under the 4 in the ones place of the next partial product as a placeholder since we now multiply the digit in the tens place of 87 by 62. Multiply 8 by the digit in the ones place of 62. 8⋅2=16.8⋅2=16. Write the 6 in the next place of the product, which is the tens place. Carry the 1 to the tens place. Multiply 8 by 6, the digit in the tens place of 62, then add the 1 ten we carried to get 49. Write the 9 in the hundreds place of the product and the 4 in the thousands place. The second partial product is 4960. Add the partial products.

The product is 5,394.5,394.

### Note:

#### Exercise 15

Multiply: 43(78).43(78).

3,354

### Note:

#### Exercise 16

Multiply: 64(59).64(59).

3,776

### Example 9

#### Problem 1

Multiply:

1. 47·1047·10
2. 47·100.47·100.

##### Solution: Solution
 ⓐ 47·1047·10. 47×10___00470___47047×10___00470___470 ⓑ 47·10047·100 47×100_____000004700_____4,70047×100_____000004700_____4,700

When we multiplied 4747 times 10,10, the product was 470.470. Notice that 1010 has one zero, and we put one zero after 4747 to get the product. When we multiplied 4747 times 100,100, the product was 4,700.4,700. Notice that 100100 has two zeros and we put two zeros after 4747 to get the product.

Do you see the pattern? If we multiplied 4747 times 10,000,10,000, which has four zeros, we would put four zeros after 4747 to get the product 470,000.470,000.

### Note:

#### Exercise 17

Multiply:

1. 54·1054·10
2. 54·100.54·100.
1. 540
2. 5,400

### Note:

#### Exercise 18

Multiply:

1. 75·1075·10
2. 75·100.75·100.

1. 750
2. 7,500

### Example 10

#### Problem 1

Multiply: (354)(438).(354)(438).

##### Solution: Solution

There are three digits in the factors so there will be 33 partial products. We do not have to write the 00 as a placeholder as long as we write each partial product in the correct place.

### Note:

#### Exercise 19

Multiply: (265)(483).(265)(483).

127,995

### Note:

#### Exercise 20

Multiply: (823)(794).(823)(794).

653,462

### Example 11

#### Problem 1

Multiply: (896)201.(896)201.

##### Solution: Solution

There should be 33 partial products. The second partial product will be the result of multiplying 896896 by 0.0.

Notice that the second partial product of all zeros doesn’t really affect the result. We can place a zero as a placeholder in the tens place and then proceed directly to multiplying by the 22 in the hundreds place, as shown.

Multiply by 10,10, but insert only one zero as a placeholder in the tens place. Multiply by 200,200, putting the 22 from the 12.12. 2·6=122·6=12 in the hundreds place.

896×201_____89617920__________180,096896×201_____89617920__________180,096
(11)

### Note:

#### Exercise 21

Multiply: (718)509.(718)509.

365,462

### Note:

#### Exercise 22

Multiply: (627)804.(627)804.

##### Solution

504,108

When there are three or more factors, we multiply the first two and then multiply their product by the next factor. For example:

 to multiply 8⋅3⋅28⋅3⋅2 first multiply 8⋅38⋅3 24⋅224⋅2 then multiply 24⋅224⋅2. 4848

## Translate Word Phrases to Math Notation

Earlier in this section, we translated math notation into words. Now we’ll reverse the process and translate word phrases into math notation. Some of the words that indicate multiplication are given in Table 11.

Table 11
Operation Word Phrase Example Expression
Multiplication times
product
twice
33 times 88
the product of 33 and 88
twice 44
3×8,3·8,(3)(8),3×8,3·8,(3)(8),
(3)8,or3(8)(3)8,or3(8)
2·42·4

### Example 12

#### Problem 1

Translate and simplify: the product of 1212 and 27.27.

##### Solution: Solution

The word product tells us to multiply. The words of 1212 and 2727 tell us the two factors.

 the product of 12 and 27 Translate. 12⋅2712⋅27 Multiply. 324324

### Note:

#### Exercise 23

Translate and simplify the product of 1313 and 28.28.

13 · 28; 364

### Note:

#### Exercise 24

Translate and simplify the product of 4747 and 14.14.

47 · 14; 658

### Example 13

#### Problem 1

Translate and simplify: twice two hundred eleven.

##### Solution: Solution

The word twice tells us to multiply by 2.2.

 twice two hundred eleven Translate. 2(211) Multiply. 422

### Note:

#### Exercise 25

Translate and simplify: twice one hundred sixty-seven.

2(167); 334

### Note:

#### Exercise 26

Translate and simplify: twice two hundred fifty-eight.

2(258); 516

## Multiply Whole Numbers in Applications

We will use the same strategy we used previously to solve applications of multiplication. First, we need to 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 to get the answer. Finally, we write a sentence to answer the question.

### Example 14

#### Problem 1

Humberto bought 44 sheets of stamps. Each sheet had 2020 stamps. How many stamps did Humberto buy?

##### Solution: Solution

We are asked to find the total number of stamps.

 Write a phrase for the total. the product of 4 and 20 Translate to math notation. 4⋅204⋅20 Multiply. Write a sentence to answer the question. Humberto bought 80 stamps.

### Note:

#### Exercise 27

Valia donated water for the snack bar at her son’s baseball game. She brought 66 cases of water bottles. Each case had 2424 water bottles. How many water bottles did Valia donate?

##### Solution

Valia donated 144 water bottles.

### Note:

#### Exercise 28

Vanessa brought 88 packs of hot dogs to a family reunion. Each pack has 1010 hot dogs. How many hot dogs did Vanessa bring?

##### Solution

Vanessa bought 80 hot dogs.

### Example 15

#### Problem 1

When Rena cooks rice, she uses twice as much water as rice. How much water does she need to cook 44 cups of rice?

##### Solution: Solution

We are asked to find how much water Rena needs.

 Write as a phrase. twice as much as 4 cups Translate to math notation. 2⋅42⋅4 Multiply to simplify. 8 Write a sentence to answer the question. Rena needs 8 cups of water for cups of rice.

### Note:

#### Exercise 29

Erin is planning her flower garden. She wants to plant twice as many dahlias as sunflowers. If she plants 14 sunflowers, how many dahlias does she need?

##### Solution

Erin needs 28 dahlias.

### Note:

#### Exercise 30

A college choir has twice as many women as men. There are 18 men in the choir. How many women are in the choir?

##### Solution

There are 36 women in the choir.

### Example 16

#### Problem 1

Van is planning to build a patio. He will have 88 rows of tiles, with 1414 tiles in each row. How many tiles does he need for the patio?

##### Solution: Solution

We are asked to find the total number of tiles.

 Write a phrase. the product of 8 and 14 Translate to math notation. 8⋅148⋅14 Multiply to simplify. 134×8___112134×8___112 Write a sentence to answer the question. Van needs 112 tiles for his patio.

### Note:

#### Exercise 31

Jane is tiling her living room floor. She will need 16 rows of tile, with 20 tiles in each row. How many tiles does she need for the living room floor?

##### Solution

Jane needs 320 tiles.

### Note:

#### Exercise 32

Yousef is putting shingles on his garage roof. He will need 24 rows of shingles, with 45 shingles in each row. How many shingles does he need for the garage roof?

##### Solution

Yousef needs 1,080 tiles.

If we want to know the size of a wall that needs to be painted or a floor that needs to be carpeted, we will need to find its area. The area is a measure of the amount of surface that is covered by the shape. Area is measured in square units. We often use square inches, square feet, square centimeters, or square miles to measure area. A square centimeter is a square that is one centimeter (cm.) on a side. A square inch is a square that is one inch on each side, and so on.

For a rectangular figure, the area is the product of the length and the width. Figure 3 shows a rectangular rug with a length of 22 feet and a width of 33 feet. Each square is 11 foot wide by 11 foot long, or 11 square foot. The rug is made of 66 squares. The area of the rug is 66 square feet.

### Example 17

#### Problem 1

Jen’s kitchen ceiling is a rectangle that measures 9 feet long by 12 feet wide. What is the area of Jen’s kitchen ceiling?

##### Solution: Solution

We are asked to find the area of the kitchen ceiling.

 Write a phrase for the area. the product of 9 and 12 Translate to math notation. 9⋅129⋅12 Multiply. 112×9___108112×9___108 Answer with a sentence. The area of Jen's kitchen ceiling is 108 square feet.

### Note:

#### Exercise 33

Zoila bought a rectangular rug. The rug is 8 feet long by 5 feet wide. What is the area of the rug?

##### Solution

The area of the rug is 40 square feet.

### Note:

#### Exercise 34

Rene’s driveway is a rectangle 45 feet long by 20 feet wide. What is the area of the driveway?

##### Solution

The area of the driveway is 900 square feet

## Key Concepts

Operation Notation Expression Read as Result
MultiplicationMultiplication ××
··
()()
3×83×8
3·83·8
3(8)3(8)
three times eightthree times eight the product of 3 and 8the product of 3 and 8
• Multiplication Property of Zero
• The product of any number and 0 is 0.
a0=0a0=0
0a=00a=0
• Identity Property of Multiplication
• The product of any number and 1 is the number.
1a=a1a=a
a1=aa1=a
• Commutative Property of Multiplication
• Changing the order of the factors does not change their product.
ab=baab=ba
• Multiply two whole numbers to find the product.
1. Step 1. Write the numbers so each place value lines up vertically.
2. Step 2. Multiply the digits in each place value.
3. Step 3. Work from right to left, starting with the ones place in the bottom number.
4. Step 4. Multiply the bottom number by the ones digit in the top number, then by the tens digit, and so on.
5. Step 5. If a product in a place value is more than 9, carry to the next place value.
6. Step 6. Write the partial products, lining up the digits in the place values with the numbers above. Repeat for the tens place in the bottom number, the hundreds place, and so on.
7. Step 7. Insert a zero as a placeholder with each additional partial product.
8. Step 8. Add the partial products.

### Practice Makes Perfect

Use Multiplication Notation

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

#### Exercise 35

4×74×7

##### Solution

four times seven; the product of four and seven

8×68×6

#### Exercise 37

5·125·12

##### Solution

five times twelve; the product of five and twelve

3·93·9

#### Exercise 39

(10)(25)(10)(25)

##### Solution

ten times twenty-five; the product of ten and twenty-five

(20)(15)(20)(15)

#### Exercise 41

42(33)42(33)

##### Solution

forty-two times thirty-three; the product of forty-two and thirty-three

#### Exercise 42

39(64)39(64)

Model Multiplication of Whole Numbers

In the following exercises, model the multiplication.

3×63×6

4×54×5

5×95×9

#### Exercise 46

3×93×9

Multiply Whole Numbers

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

#### Exercise 54

In the following exercises, multiply.

0·150·15

0

0·410·41

(99)0(99)0

0

(77)0(77)0

1·431·43

43

1·341·34

(28)1(28)1

28

(65)1(65)1

#### Exercise 63

1(240,055)1(240,055)

240,055

#### Exercise 64

1(189,206)1(189,206)

1. 7·67·6
2. 6·76·7
1. 42
2. 42

1. 8×98×9
2. 9×89×8

(79)(5)(79)(5)

395

(58)(4)(58)(4)

275·6275·6

1,650

638·5638·5

3,421×73,421×7

23,947

9,143×39,143×3

52(38)52(38)

1,976

37(45)37(45)

96·7396·73

7,008

89·5689·56

27×8527×85

2,295

53×9853×98

23·1023·10

230

19·1019·10

#### Exercise 81

(100)(36)(100)(36)

360

#### Exercise 82

(100)(25)(100)(25)

#### Exercise 83

1,000(88)1,000(88)

88,000

#### Exercise 84

1,000(46)1,000(46)

#### Exercise 85

50×1,000,00050×1,000,000

50,000,000

#### Exercise 86

30×1,000,00030×1,000,000

247×139247×139

34,333

156×328156×328

586(721)586(721)

422,506

472(855)472(855)

915·879915·879

804,285

968·926968·926

#### Exercise 93

(104)(256)(104)(256)

26,624

#### Exercise 94

(103)(497)(103)(497)

348(705)348(705)

245,340

485(602)485(602)

#### Exercise 97

2,719×5432,719×543

1,476,417

#### Exercise 98

3,581×7243,581×724

Translate Word Phrases to Math Notation

In the following exercises, translate and simplify.

#### Exercise 99

the product of 1818 and 3333

18 · 33; 594

#### Exercise 100

the product of 1515 and 2222

#### Exercise 101

fifty-one times sixty-seven

51(67); 3,417

#### Exercise 102

forty-eight times seventy-one

twice 249249

2(249); 498

twice 589589

#### Exercise 105

ten times three hundred seventy-five

10(375); 3,750

#### Exercise 106

ten times two hundred fifty-five

Mixed Practice

In the following exercises, simplify.

38×3738×37

1,406

86×2986×29

415267415267

148

341285341285

#### Exercise 111

6,251+4,7496,251+4,749

11,000

#### Exercise 112

3,816+8,1843,816+8,184

#### Exercise 113

(56)(204)(56)(204)

11,424

#### Exercise 114

(77)(801)(77)(801)

947·0947·0

0

947+0947+0

15,382+115,382+1

15,383

#### Exercise 118

15,382·115,382·1

In the following exercises, translate and simplify.

#### Exercise 119

the difference of 50 and 18

50 − 18; 32

#### Exercise 120

the difference of 90 and 66

twice 35

2(35); 70

twice 140

20 more than 980

20 + 980; 1,000

65 more than 325

#### Exercise 125

the product of 12 and 875

12(875); 10,500

#### Exercise 126

the product of 15 and 905

#### Exercise 127

subtract 74 from 89

89 − 74; 15

#### Exercise 128

subtract 45 from 99

#### Exercise 129

the sum of 3,075 and 95

##### Solution

3,075 + 950; 4,025

#### Exercise 130

the sum of 6,308 and 724

#### Exercise 131

366 less than 814

814 − 366; 448

#### Exercise 132

388 less than 925

Multiply Whole Numbers in Applications

In the following exercises, solve.

#### Exercise 133

Party supplies Tim brought 9 six-packs of soda to a club party. How many cans of soda did Tim bring?

##### Solution

Tim brought 54 cans of soda to the party.

#### Exercise 134

Sewing Kanisha is making a quilt. She bought 6 cards of buttons. Each card had four buttons on it. How many buttons did Kanisha buy?

#### Exercise 135

Field trip Seven school busses let off their students in front of a museum in Washington, DC. Each school bus had 44 students. How many students were there?

##### Solution

There were 308 students.

#### Exercise 136

Gardening Kathryn bought 8 flats of impatiens for her flower bed. Each flat has 24 flowers. How many flowers did Kathryn buy?

#### Exercise 137

Charity Rey donated 15 twelve-packs of t-shirts to a homeless shelter. How many t-shirts did he donate?

##### Solution

Rey donated 180 t-shirts.

#### Exercise 138

School There are 28 classrooms at Anna C. Scott elementary school. Each classroom has 26 student desks. What is the total number of student desks?

#### Exercise 139

Recipe Stephanie is making punch for a party. The recipe calls for twice as much fruit juice as club soda. If she uses 10 cups of club soda, how much fruit juice should she use?

##### Solution

Stephanie should use 20 cups of fruit juice.

#### Exercise 140

Gardening Hiroko is putting in a vegetable garden. He wants to have twice as many lettuce plants as tomato plants. If he buys 12 tomato plants, how many lettuce plants should he get?

#### Exercise 141

Government The United States Senate has twice as many senators as there are states in the United States. There are 50 states. How many senators are there in the United States Senate?

##### Solution

There are 100 senators in the U.S. senate.

#### Exercise 142

Recipe Andrea is making potato salad for a buffet luncheon. The recipe says the number of servings of potato salad will be twice the number of pounds of potatoes. If she buys 30 pounds of potatoes, how many servings of potato salad will there be?

#### Exercise 143

Painting Jane is painting one wall of her living room. The wall is rectangular, 13 feet wide by 9 feet high. What is the area of the wall?

##### Solution

The area of the wall is 117 square feet.

#### Exercise 144

Home décor Shawnte bought a rug for the hall of her apartment. The rug is 3 feet wide by 18 feet long. What is the area of the rug?

#### Exercise 145

Room size The meeting room in a senior center is rectangular, with length 42 feet and width 34 feet. What is the area of the meeting room?

##### Solution

The area of the room is 1,428 square feet.

#### Exercise 146

Gardening June has a vegetable garden in her yard. The garden is rectangular, with length 23 feet and width 28 feet. What is the area of the garden?

#### Exercise 147

NCAA basketball According to NCAA regulations, the dimensions of a rectangular basketball court must be 94 feet by 50 feet. What is the area of the basketball court?

##### Solution

The area of the court is 4,700 square feet.

#### Exercise 148

NCAA football According to NCAA regulations, the dimensions of a rectangular football field must be 360 feet by 160 feet. What is the area of the football field?

### Everyday Math

#### Exercise 149

Stock market Javier owns 300 shares of stock in one company. On Tuesday, the stock price rose $12$12 per share. How much money did Javier’s portfolio gain?

### Writing Exercises

#### Exercise 151

How confident do you feel about your knowledge of the multiplication facts? If you are not fully confident, what will you do to improve your skills?

#### Exercise 152

How have you used models to help you learn the multiplication facts?

### Self Check

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

On a scale of 1–10, how would you rate your mastery of this section in light of your responses on the checklist? How can you improve this?

## Glossary

product:
The product is the result of multiplying two or more numbers.

## Content actions

### Give feedback:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

#### Definition of a lens

##### Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

##### What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

##### Who can create a lens?

Any individual member, a community, or a respected organization.

##### What are tags?

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks