Algebra 1 Common Core Student Edition, Grade 8-9

The reciprocal o f a n o n z e r o r e a l n u m b e r o f th e f o r m § is §. The product o f a num ber

a n d it s r e c ip r o c a l is 1, so th e r e c ip r o c a l o f a n u m b e r is its m u l t i p l ic a t i v e in v e r s e. T h is

s u g g e s ts a r u le f o r d i v id in g fr a c tio n s.

Here's W hy It W orks Let a, b, c, and d b e n o n z e r o in t e g e r s.

a

| = % = "I" Write the expression as a fraction.

d

— • ^ ri

_ b ' c M u ltip ly the num erator and denom inator by £. Since this is equivalent to

£. d

d c

£ , d

b _ c

1

ci d

b ’ c

m ultiplying by 1, it does n ot change the quotient.

Inverse Property o f M u ltip lica tio n

Simplify.

T h is s h o w s t h a t d i v id in g b y a f r a c t io n is e q u iv a le n t t o m u l t i p l y i n g b y th e r e c ip r o c a l o f
th e fra ctio n.

Pr o b l em 4 Dividing Fractions

Multiple Choice What is the value of f when x = — | and y

*-in k

Rewrite the expression.

Substitute for x and

-f fory. -M -!)

Multiply by the reciprocal

of

Simplify. Since both

factors are negative, the

product is positive.

T h e c o r r e c t a n s w e r is D.

a ‘ W h a t i s f h e v a lu e o f | -t- (— | )?

b. Reasoning Is § = ( - | ) e q u iv a le n t t o - ( f = § )? Explain.

PowerAlgebra.com Lesso n 1-6 Multiplying and Dividing Real Numbers 41