SECTION 1.4 Properties of Real Numbers 37
Concept Check Complete each statement so that the indicated property is illustrated.
Simplify each answer if possible.Complete solution available
on the Video Resources on DVD
1.4 EXERCISES
Concept Check Choose the correct response in Exercises 1–4.
1.The identity element for addition isA. B. 0 C. 1 D..2.The identity element for multiplication isA. B. 0 C. 1 D..1
a- a
1
a- a
3.The additive inverse of aisA. B. 0 C. 1 D..4.The multiplicative inverse of a, where
, isA. B. 0 C. 1 D..1
a- a
1 aZ^0
a- a
Concept Check Complete each statement.
5.The multiplication property of 0 says that the of 0 and any real number is.
6.The commutative property is used to change the of two terms or factors.
7.The associative property is used to change the of three terms or factors.
8.Like terms are terms with the variables raised to the powers.
9.When simplifying an expression, only terms can be combined.
10.The numerical coefficient in the term is.Simplify each expression. See Examples 1 and 2.Simplify each expression. See Examples 1– 4.
- 2 + 312 z- 52 - 314 z+ 62 - 8 40.- 4 + 414 k- 32 - 612 k+ 82 + 7
- 12 p+ 52 + 312 p+ 42 - 2 p - 17 m- 122 - 214 m+ 72 - 8 m
0.25 18 + 4 p 2 - 0.5 16 + 2 p 2 0.4 110 - 5 x 2 - 0.8 15 + 10 x 2- 21 m+ 12 - 1 m- 42 61 a- 52 - 1 a+ 62
31 k+ 22 - 5 k+ 6 + 3 51 r- 32 + 6 r- 2 r+ 4- 6 p+ 5 - 4 p+ 6 + 11 p - 8 x- 12 + 3 x- 5 x+ 9
- 12 y+ 4 y+ 3 + 2 y - 5 r- 9 r+ 8 r- 5
- 12 d-ƒ 2 - 13 m-n 2 - 1 - x-y 2 - 1 - 3 x- 4 y 2
- 8 z+ 4 w - 12 k+ 3 r a+ 7 a s+ 9 s
5 k+ 3 k 6 a+ 5 a 7 r- 9 r 4 n- 6 n21 m+p 2 31 a+b 2 - 121 x-y 2 - 101 p-q 2- 7 yz^2
41.
(distributive property)42.
(distributive property)5 x+ 8 x= 9 y- 6 y=43.
(associative property)44.
(associative property)519 r 2 = - 4 + 112 + 82 =45.
(commutative property)46.
(commutative property)5 x+ 9 y= - 5 # 7 =