1 - 5 a n d 1 - 6 Op er at i ons Wit h Reai Numbers
Quick Review
To add n u m b e rs w ith d iffe re n t signs, fin d th e d iffe re n ce o f
th e ir absolute values. Then use the sign of the addend
with the greater absolute value.
3 + ( —4 ) = —( 4 — 3 ) = —1
To subtract, add the opposite.
9 - ( - 5 ) = 9 + 5 = 14
T h e p r o d u c t o r q u o t ie n t o f t w o n u m b e r s w i t h th e s a m e s ig n
is p o s itiv e : 5 • 5 = 25 (—5) • (—5) = 25
T h e p r o d u c t o r q u o t ie n t o f t w o n u m b e r s w i t h d i f f e r e n t s ig n s
is ne g a tive : 6 • ( - 6 ) = - 3 6 —36 + 6 = — 6Ex a m p l e
C a ve e x p lo r e r s d e s c e n d t o a s ite t h a t h a s a n e le v a t io n o f
— 1.3 k m. ( N e g a tiv e e le v a t io n m e a n s b e lo w s ea le v e l.) T h e
explorers descend another 0.6 k m b e fo r e t h e y s to p t o re s t.
W h a t is th e e le v a t io n a t t h e i r r e s t in g p o in t?
-1 .3 +(-0.6)= -1.9T h e e le v a tio n a t t h e i r r e s t in g p o i n t is - 1. 9 k m.1 - 7 The Distributive Propert y
Ex e r c i s e s
Find each sum. Use a number line.- 1 + 4 57. 3 + (- 8 ) 58. -2+ (-7 )
Simplify each expression.- -5 .6 + 7.4 60. — 122
- —5(— 8 ) 62. 4.5+ (-1 .5 )
- -1 3 + ( - 6 ) 64. -9 - (-12)
- (—2)(— 2 )(— 2 ) 66. -5 4 + (-0 .9 )
Evaluate each expression forp = 5 and q = — 3.
-3q + (^768). - ( 4q)
q — 8 70. 5p - 6
—(2 p)2 72. 7q - 7p
{pq)2 74. 2 q + (4p)
Quick Review
T e rm s w i t h e x a c tly th e s a m e v a r ia b le fa c to r s a re like term s.
You can com bine like term s and use the D istributive
Property to sim plify expressions.
Distributive Property a{b + c) = ab + ac
a(b — c) = ab — acEx a m p l e
Simplify 7t + (3 — 4 f).
It + (3 - At) = 7t + {—At + 3 ) C ommutative Property
= ( 7 t + ( —4 f) ) + 3 Associative Property
= (7 + ( —4 ) ) f + 3 Distributive Property
= 3 t + 3 Simplify.Ex e r c i s e s
Simplify each expression.- 5(2x — 3)
- ( - ; + 8 )|
- 2(3y - 3)
- (2 4 -2 4 y )|
- |y + 6 - |y
76. -2 (7 - a)
78. 31 /2 - 2v2 - ( 6 y-l)±
- 6 y - 3 - 5y
- -ab2 - ab2
- Music All 95 members of the jazz club pay $30 each
to go see a jazz p e rfo rm a n ce. W h a t is th e to ta l cost o f
ticke ts? U se m e n ta l m a th. - R e a s o n i n g Are 8 x2y a n d —5yx2 like term s? Explain.
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