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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

Note: You are viewing an old style version of this document. The new style version is available here.

Note:

Before you get started, take this readiness quiz.

  1. Add: 1,683+479.1,683+479.
    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.

Figure 1
An image of 3 horizontal rows of pennies, each row containing 8 pennies.

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.
An image of a horizontal row of 8 counters.

The other factor is 3,3, so we’ll make 33 rows of 88 counters.
An image of 3 horizontal rows of counters, each row containing 8 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.

Solution


No Alt Text

Note:

Exercise 4

Model each multiplication: 5×7.5×7.

Solution


No Alt Text

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

Solution

  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
Solution
  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.

No Alt Text

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.

No Alt Text

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. 45=20.45=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. 41=441=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.

Solution

512512

Note:

Exercise 12

Multiply: 57·6.57·6.

Solution

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. 56=30.56=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. 58=4058=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. 52=10.52=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.

Solution

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. CNX_BMath_Figure_01_04_020_img-02.png
Start by multiplying 7 by 62. Multiply 7 by the digit in the ones place of 62. 72=14.72=14. Write the 4 in the ones place of the product and carry the 1 to the tens place. CNX_BMath_Figure_01_04_020_img-03.png
Multiply 7 by the digit in the tens place of 62. 76=42.76=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. CNX_BMath_Figure_01_04_020_img-04.png
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. 82=16.82=16. Write the 6 in the next place of the product, which is the tens place. Carry the 1 to the tens place. CNX_BMath_Figure_01_04_020_img-05.png
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. CNX_BMath_Figure_01_04_020_img-06.png
The second partial product is 4960. Add the partial products. CNX_BMath_Figure_01_04_020_img-07.png

The product is 5,394.5,394.

Note:

Exercise 15

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

Solution

3,354

Note:

Exercise 16

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

Solution

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.
Solution
  1. 540
  2. 5,400

Note:

Exercise 18

Multiply:

  1. 75·1075·10
  2. 75·100.75·100.

Solution

  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.
An image of the multiplication problem “354 times 438” worked out vertically. 354 is the top number, 438 is the second number. Below 438 is a multiplication bar. Below the bar is the number 2,832. 2832 has the label “Multiply 8 times 354”. Below 2832 is the number 1,062;  1062 has the label “Multiply 3 times 354”.  Below 1062 is the number 1,416; 1416 has the label “Multiply 4 times 354”.  Below this is a bar and below the bar is the number “155,052”, with the label “Add the partial products”.

Note:

Exercise 19

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

Solution

127,995

Note:

Exercise 20

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

Solution

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.
An image of the multiplication problem “896 times 201” worked out vertically. 896 is the top number, the 8 in the hundreds place, the 9 in the tens place, the 6 in the ones place. 201 is the second number,  the 2 in the hundreds place, the 0 in the tens place, the 1 in the ones place. Below 201 is a multiplcation bar. Below the bar is the number 896, the 8 in the hundreds place, the 9 in the tens place, the 6 in the ones place. 896 has the label “Multiply 1 times 896”. Below 896 is the number “000”, the 0 in the thousands place, the 0 in the hundreds place, and the 0 in the tens place. “000” has the label “Multiply 0 times 896”.  Below “000” is the number 1792, the 1 in the hundred thousands place, the 7 in the ten thousands place, the 9 in the thousands place, and the 2 in the hundreds place. 1792 has the label “Multiply 2 times 896”.  Below this is a bar and below the bar is the number “180,096”, with the label “Add the partial products”.

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.

Solution

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 832832
first multiply 8383 242242
then multiply 242242. 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.

Table 12
  the product of 12 and 27
Translate. 12271227
Multiply. 324324

Note:

Exercise 23

Translate and simplify the product of 1313 and 28.28.

Solution

13 · 28; 364

Note:

Exercise 24

Translate and simplify the product of 4747 and 14.14.

Solution

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.

Solution

2(167); 334

Note:

Exercise 26

Translate and simplify: twice two hundred fifty-eight.

Solution

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. 420420
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. 2424
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.

Table 16
Write a phrase. the product of 8 and 14
Translate to math notation. 814814
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.

An image of two squares, one larger than the other. The smaller square is 1 centimeter by 1 centimeter and has the label “1 square centimeter”. The larger square is 1 inch by 1 inch and has the label “1 square inch”.

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.

Figure 3: The area of a rectangle is the product of its length and its width, or 66 square feet.
An image of a rectangle containing 6 blocks, 2 feet tall and 3 feet wide. This image has the label “2 times 3 = 6 feet squared”.

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. 912912
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

Exercise 36

8×68×6

Exercise 37

5·125·12

Solution

five times twelve; the product of five and twelve

Exercise 38

3·93·9

Exercise 39

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

Solution

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

Exercise 40

(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.

Exercise 43

Exercise 44

4×54×5

Exercise 45

Exercise 46

3×93×9

Multiply Whole Numbers

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

Exercise 48

An image of a table with 11 columns and 11 rows. The cells in the first row and first column are shaded darker than the other cells. The first column has the values “x; 0; 1; 2; 3; 4; 5; 6; 7; 8; 9”. The second column has the values “0; 0; 0; 0 pink; 0; 0; 0; 0; 0; 0; 0”. The third column has the values “1; 0; 1; 2; 3; 4; 5; 6; 7; 8; 9”. The fourth column has the values “2; 0; 2; 4; 6; 8; 10; 12; 14; 16; 18”. The fifth column has the values “3; 0; 3; 6; 9; 12; 15; 18; 21; 24; 27”. The sixth column has the values “4; 0; 4; 8; 12; 16; 20; 24; 28; 32; 36”. The seventh column has the values “5; 0; 5; 10; 15; 20; 25; 30; 35; 40; 45”. The eighth column has the values “6; 0; 6; 12; 18; 24; 30; 36; 42; 48; 54”. The ninth column has the values “7; 0; 7; 14; 21; 28; 35; 42; 49; 56; 63”. The tenth column has the values “8; 0; 8; 16; 24; 32; 40; 48; 56; 64; 72”. The eleventh column has the values “9; 0; 9; 18; 27; 36, 45; 54; 63; 72; 81”.

Exercise 50

PROD: An image of a table with 7 columns and 8 rows. The cells in the first row and first column are shaded darker than the other cells. The cells not in the first row or column are all null.  The first column has the values “x; 3; 4; 5; 6; 7; 8; 9”. The first row has the values “x; 4; 5; 6; 7; 8; 9”.

Exercise 52

An image of a table with 5 columns and 8 rows. The cells in the first row and first column are shaded darker than the other cells. The cells not in the first row or column are all null. The first column has the values “x; 3; 4; 5; 6; 7; 8; 9”. The first row has the values “x; 6; 7; 8; 9”.

Exercise 54

An image of a table with 6 columns and 6 rows. The cells in the first row and first column are shaded darker than the other cells. The cells not in the first row or column are all null.  The first column has the values “x; 5; 6; 7; 8; 9”. The first row has the values “x; 5; 6; 7; 8; 9”.

In the following exercises, multiply.

Exercise 55

Exercise 56

0·410·41

Exercise 57

Exercise 58

(77)0(77)0

Exercise 59

Exercise 60

1·341·34

Exercise 61

Exercise 62

(65)1(65)1

Exercise 63

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

Solution

240,055

Exercise 64

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

Exercise 65

  1. 7·67·6
  2. 6·76·7
Solution
  1. 42
  2. 42

Exercise 66

  1. 8×98×9
  2. 9×89×8

Exercise 67

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

Solution

395

Exercise 68

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

Exercise 69

275·6275·6

Solution

1,650

Exercise 70

638·5638·5

Exercise 71

3,421×73,421×7

Solution

23,947

Exercise 72

9,143×39,143×3

Exercise 73

52(38)52(38)

Solution

1,976

Exercise 74

37(45)37(45)

Exercise 75

96·7396·73

Solution

7,008

Exercise 76

89·5689·56

Exercise 77

27×8527×85

Solution

2,295

Exercise 78

53×9853×98

Exercise 79

23·1023·10

Solution

230

Exercise 80

19·1019·10

Exercise 81

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

Solution

360

Exercise 82

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

Exercise 83

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

Solution

88,000

Exercise 84

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

Exercise 85

50×1,000,00050×1,000,000

Solution

50,000,000

Exercise 86

30×1,000,00030×1,000,000

Exercise 87

247×139247×139

Solution

34,333

Exercise 88

156×328156×328

Exercise 89

586(721)586(721)

Solution

422,506

Exercise 90

472(855)472(855)

Exercise 91

915·879915·879

Solution

804,285

Exercise 92

968·926968·926

Exercise 93

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

Solution

26,624

Exercise 94

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

Exercise 95

348(705)348(705)

Solution

245,340

Exercise 96

485(602)485(602)

Exercise 97

2,719×5432,719×543

Solution

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

Solution

18 · 33; 594

Exercise 100

the product of 1515 and 2222

Exercise 101

fifty-one times sixty-seven

Solution

51(67); 3,417

Exercise 102

forty-eight times seventy-one

Exercise 103

twice 249249

Solution

2(249); 498

Exercise 104

twice 589589

Exercise 105

ten times three hundred seventy-five

Solution

10(375); 3,750

Exercise 106

ten times two hundred fifty-five

Mixed Practice

In the following exercises, simplify.

Exercise 107

38×3738×37

Solution

1,406

Exercise 108

86×2986×29

Exercise 109

415267415267

Solution

148

Exercise 110

341285341285

Exercise 111

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

Solution

11,000

Exercise 112

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

Exercise 113

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

Solution

11,424

Exercise 114

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

Exercise 115

Exercise 116

947+0947+0

Exercise 117

15,382+115,382+1

Solution

15,383

Exercise 118

15,382·115,382·1

In the following exercises, translate and simplify.

Exercise 119

the difference of 50 and 18

Solution

50 − 18; 32

Exercise 120

the difference of 90 and 66

Exercise 121

twice 35

Solution

2(35); 70

Exercise 122

twice 140

Exercise 123

20 more than 980

Solution

20 + 980; 1,000

Exercise 124

65 more than 325

Exercise 125

the product of 12 and 875

Solution

12(875); 10,500

Exercise 126

the product of 15 and 905

Exercise 127

subtract 74 from 89

Solution

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

Solution

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?


Solution

Javier’s portfolio gained $3,600.

Exercise 150

Salary Carlton got a $200$200 raise in each paycheck. He gets paid 24 times a year. How much higher is his new annual salary?

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?

Solution

Answers will vary.

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.

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