Algebra 1 Common Core Student Edition, Grade 8-9

Essent ial Und er st and ing R u le s f o r d i v id in g r e a l n u m b e r s a re r e la t e d t o th e

r u le s f o r m u l t i p l y i n g r e a l n u m b e r s.

Think
H o w is d iv id in g
similar to
multiplying?
You fin d th e sign o f a
q u o tie n t using th e signs
o f th e num bers y o u 're
d iv id in g , ju s t as you fin d
th e sign o f a p ro d u ct
using th e signs o f th e
factors.

For any real num bers a, b, and c w h e r e a # 0, if a • b = c, then b = c + a.

F o r in s ta n c e , — 8 (—2) = 16, so — 2 = 16 -t- (— 8 ). S im ila rly —8 (2 ) = —16, so

2 = —16 -e ( - 8 ). T h e s e e x a m p le s i llu s t r a t e th e f o l l o w i n g r u le s.

Key Concept Dividing Real Numbers

Words T h e q u o t ie n t o f t w o r e a l n u m b e r s w i t h different s i g n s i s negative.

Examples -2 0 -t- 5 = - 4 20 -t- (-5 ) = -4

Words T h e q u o t ie n t o f t w o r e a l n u m b e r s w i t h t h e same s ig n is positive.

Examples 20^-5 = 4 -20 -t- (-5 ) = 4

Division Involving 0

Words T h e q u o t ie n t o f 0 a n d a n y n o n z e r o r e a l n u m b e r is 0. T h e q u o t ie n t o f a n y r e a l

num ber and 0 is u n d e fin e d.

Examples 0 8 = 0 8 -^ 0 is undefined.

Dividing Real Numbers

Sky Diving A sky diver's elevation changes by - 3600 ft in 4 min after the parachute

opens. What is the average change in the sky diver's elevation each minute?

-3 6 0 0 -e- 4 = -9 0 0 The n u m b e rs h a v e d if fe r e n t signs, so th e q u o tie n t is n e g a tiv e.

T h e s k y d iv e r 's a v e ra g e c h a n g e i n e le v a t io n is - 9 0 0 f t p e r m in u t e.

G o t It? 3. Y o u m a k e fiv e w it h d r a w a ls o f e q u a l a m o u n t s f r o m y o u r b a n k a c c o u n t. T h e

t o t a l a m o u n t y o u w it h d r a w is $ 3 6 0. W h a t is th e c h a n g e i n y o u r a c c o u n t

b a la n c e e a c h t im e y o u m a k e a w it h d r a w a l?

T h e In v e r s e P r o p e r t y o f M u l t i p l ic a t i o n d e s c r ib e s th e r e la t io n s h ip b e tw e e n a n u m b e r

and its m ultiplicative inverse.

Pr o p er t y Inverse Property of Multiplication

Words For every nonzero real num ber a, there is a multiplicative inverse \ s u c h t h a t

a(a) = 1 -

Examples The m ultip lica tive inverse o f —4 is — \ because —4(—| ) = 1.

40 Ch ap t er 1 Fo u n d a t i o n s f o r A l g e b r a