36 CHAPTER 1 Review of the Real Number System
Using the Properties of Real NumbersSimplify each expression.
(a)
Distributive property
Combine like terms.(b)
Distributive propertyCommutative property=- 2 x- 9 Combine like terms.
= 3 x- 5 x+ 4 - 5 - 8
= 3 x+ 4 - 5 x- 5 - 8
3 x+ 4 - 51 x+ 12 - 8
= 2 y
= 15 - 8 - 6 + 112 y
5 y- 8 y- 6 y+ 11 y
EXAMPLE 4
(c)
Identity property
Distributive property
Combine like terms.(d)
Order of operations
Associative property
Commutative property
Associative property
Multiply.
Associative propertyAs previously mentioned, many of these steps are not usually written out.
NOW TRY= 15 xy
= 151 xy 2
= 115 x 2 y
= 313 # 52 x 4 y
= 3315 x 24 y
= 331 x# 524 y
= 33 x 1524 y
3 x 1521 y 2
= 6 - 3 m
= 8 - 3 m- 2
= 8 - 113 m+ 22
8 - 13 m+ 22
NOW TRY
EXERCISE 4
Simplify each expression.
(a)
(b) 5 x 16 y 2
- 31 t- 42 - t+ 15
NOW TRY ANSWERS
- (a)- 4 t+ 27 (b) 30 xy
CAUTION Be careful. The distributive property does not apply in Exam-
ple 4(d),because there is no addition involved.
13 x 21521 y 2 Z 13 x 2152 # 13 x 21 y 2
OBJECTIVE 5 Use the multiplication property of 0. The additive identity
property gives a special property of 0, namely, that
, for any real number a.
The multiplication property of 0gives another special property of 0, namely that
the product of any real number and 0 is 0.
a+ 0 = 0 + a= a
Multiplication Property of 0For any real number a, the following are true.
a# 0 0 and 0 #a 0
Be careful with signs.