Page 72 - Basic College Mathematics with Early Integers

SE CT I O N 1. 6 I MULTIPLYING WHOLE NUMBERS AND AREA 49

Associative Property of Multiplication

Changing the grouping of factors does not change their product. From the
previous page, we know that for example,
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12 32 4 = 2 13 42

With these properties, along with the distributive property, we can find the
product of any whole numbers. The distributive property says that multiplication
distributes over addition. For example, notice that 312 + 52 simplifies to the same
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number as 3 2 + 3 5.
3(2+5)=3(7)=21

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3 2+3 5=6+15=21
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Since 312 + 52 and 3 2 + 3 5 both simplify to 21, then
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312 + 52 = 3 2 + 3 5
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Notice in 312 + 52 = 3 2 + 3 5 that each number inside the parentheses is multi-
plied by 3.

Distributive Property

Multiplication distributes over addition. For example,

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2(3+4)=2 3+2 4

Example 2 Rewrite each using the distributive property. PRACTICE 2
Rewrite each using the distrib-
a. 314 + 52 b. 1016 + 82 c. 217 + 32
utive property.
Solution: Using the distributive property, we have a. 512 + 32
b. 918 + 72
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a. 3(4+5)=3 4+3 5 c. 316 + 12
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b. 1016 + 82 = 10 6 + 10 8
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c. 217 + 32 = 2 7 + 2 3
Work Practice 2
Objective Multiplying Whole Numbers
Let’s use the distributive property to multiply 7(48).To do so, we begin by writing the
expanded form of 48 (see Section 1.2) and then applying the distributive property.

7(48)=7(40+8) Write 48 in expanded form.
Answers
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=7 40+7 8 Apply the distributive property.
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2. a. 512 + 32 = 5 2 + 5 3
=280+56 Multiply.
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b. 918 + 72 = 9 8 + 9 7
=336 Add. c. 316 + 12 = 3 6 + 3 1
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