62 CHAPTER 1 The Real Number System
Using the Identity PropertiesUse an identity property to complete each statement.
(a)
Identity property of addition- 3 + 0 =- 3
- 3 +? =- 3
EXAMPLE 5
Using the Commutative and Associative PropertiesFind each sum or product.
(a)
= 100
= 50 + 25 + 25
= 141 + 92 + 123 + 22 + 25
23 + 41 + 2 + 9 + 25
EXAMPLE 4
NOW TRY
EXERCISE 5
Use an identity property to
complete each statement.
(a)
(b) 8 + = 8
=
2
5
2
5
(b)
Identity property of multiplication1 #
1
2
=
1
2
? #
1
2
=
1
2
NOW TRYNOW TRY
EXERCISE 3
Is
an example of the associative
property or the commutative
property?
5 + 17 + 62 = 5 + 16 + 72
NOW TRY
EXERCISE 4
Find each sum or product.
(a)
(b) 513721202
8 + 54 + 7 + 6 + 32
(b)
= 6900
= 1001692
= 251421692
251692142
NOW TRYOBJECTIVE 3 Use the identity properties. If
a child wears a costume on Halloween, the child’s
appearance is changed, but his or her identity is
unchanged. The identity of a real number is left
unchanged when identity properties are applied.
The identity propertiessay that the sum of 0
and any number equals that number, and the product
of 1 and any number equals that number.
Use the commutative
and associative
properties.Identity Propertiesand Addition
a# 1 a and 1 #aa Multiplication
a 0 a 0 aa
NOW TRY ANSWERS
- commutative
- (a) 107 (b) 3700
- (a) 1 (b) 0
The number 0 leaves the identity, or value, of any real number unchanged by ad-
dition, so 0 is called the identity element for addition,or the additive identity.Since
multiplication by 1 leaves any real number unchanged, 1 is the identity element for
multiplication,or the multiplicative identity.
(c)
Both the order and the grouping are changed. On the left, the order of the three
numbers is 8, 1, and 7. On the right, it is 8, 7, and 1. On the left, the 8 and 1 are
grouped. On the right, the 7 and 1 are grouped. Therefore, bothproperties are used.
NOW TRY18 + 12 + 7 = 8 + 17 + 12
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