Algebra 1 Common Core Student Edition, Grade 8-9

Multiplying and

Dividing Real Numbers

Common Core State Standards

Prepares fo r N-RN.B.3 Explain why the sum or

product of tw o rational numbers is rational; that the

sum o f a rational number and an irrational number is

irrational...

MP 1, MP 3, MP 4, M P 6, MP 7

Objective To fin d products and quotients o f real num bers

' Getting Ready!

You may not know

the answer, but

you can make a

co nject ur e.

Use p at t erns t o complete t he t ab le and answer t he questions below.

Explain your reasoning.

• W h at is t he sign o f t he product o f a posit ive number and a
  negative number?


• W hat is t he sign o f t he product o f two negat ive numbers?

MATHEMATICAL

PRACTI CES

Lesson '
Vocabulary
multiplicative
inverse
reciprocal

........2-3= 6...._ ...../.J

............. '

[ —2 - 3 = —6

..... ..

2-2= 4 —2 - 2 = —4

2-1= 2 —2- 1 = - 2

2-0= -2-0= 1

2-(—1 )= —2 - ( — 1 ) =

2-( 2)-1 ;-2-(—2)= a :

T h e p a t t e r n s i n th e S o lv e I t s u g g e s t 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.

Esse n t i a l U n d e r st a n d i n g T h 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 a re r e la t e d to

th e p r o p e r t ie s o f r e a l n u m b e r s a n d t h e d e f i n it io n s o f o p e r a t io n s.

You know that the product o f tw o positive num bers is positive. For example,

3 ( 5 ) = 15. Y o u c a n t h i n k a b o u t t h e p r o d u c t o f a p o s it iv e n u m b e r a n d a n e g a tiv e

n u m b e r i n t e r m s o f g r o u p s o f n u m b e r s. F o r e x a m p le , 3 ( —5 ) m e a n s 3 g r o u p s o f - 5. So,

3(—5) = (-5 ) + (-5 ) + (-5 ), or 3 (-5) = -15.

You can also derive the product of two negative num bers, such as -3 (-5 ).

3 ( —5 ) = — 15 Start w ith the product 3 ( - 5 ) = - 1 5.

— [ 3 ( —5 )] = - ( - 1 5 ) The opposites o f tw o equal numbers are equal.

Multiplication Property of -1

Associative Property o f M ultiplication

M ultiplication Property o f —1

The opposite o f - 1 5 is 15.

—1 [3 (—5)] = - ( - 1 5 )

[ —1 ( 3 ) ] ( —5 ) = —( —15)

—3 ( —5 ) = —( —15)

—3 ( —5 ) = 15

T h e s e d is c u s s io n s i llu s t r a t e th e f o l l o w i n g 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.

Chapter 1 Fo u n d at i o n s f o r A l g e b r a

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