Page 71 - Basic College Mathematics with Early Integers

48 C HAPTE R 1 I THE WHOLE NUMBERS

Multiplication Property of 0

The product of 0 and any number is 0. For example,
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5 0 = 0 and 0 8 = 0

Also notice in Appendix A.2 that when any number is multiplied by 1, the result
is always the original number.We call this result the multiplication property of 1.

Multiplication Property of 1
The product of 1 and any number is that same number. For example,
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1 9 = 9 and 6 1 = 6

PRACTICE 1 Example 1 Multiply.
Multiply.
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a. 6 * 1 b. 0(18) c. 1 45 d. (75)(0)
a. 3 * 0
b. 4(1) Solution:
c. (0)(34) a. 6 * 1 = 6 b. 01182 = 0
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d. 1 76 c. 1 45 = 45 d. 1752102 = 0
Work Practice 1

Like addition, multiplication is commutative and associative. Notice that when
multiplying two numbers, the order of these numbers can be changed without
changing the product. For example,
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3 5 = 15 and 5 3 = 15
This property is the commutative property of multiplication.

Commutative Property of Multiplication
Changing the order of two factors does not change their product. For example,
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9 2 = 18 and 2 9 = 18

Another property that can help us when multiplying is the associative property
of multiplication. This property states that when multiplying numbers, the grouping
of the numbers can be changed without changing the product. For example,

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(2 3) 4=6 4=24
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Also,

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2 (3 4)=2 12=24

Both groupings give a product of 24.
Answers
1. a. 0 b. 4 c. 0 d. 76