Algebra 1 Common Core Student Edition, Grade 8-9

T w o n u m b e r s t h a t a re th e s a m e d is ta n c e f r o m 0 o n a n u m b e r l in e b u t lie i n o p p o s ite

directions are opposites.

3 units 3 units

H 1 ------ 1 ------h

-3 - 2 - 1

• 3 and 3 are th e same
  distance from 0. So - 3
  and 3 are opposites.

A number and its opposite are called additive inverses. To fin d the sum o f a num ber

a n d its o p p o s ite , y o u c a n u s e th e Inverse Property o f A d d itio n.

P r o p e r t y Inverse Property of Addition

F o r e v e r y r e a l n u m b e r a, th e re is an a d d itiv e inverse -a such th a t

a + ( - a ) = -a + a = 0.

Examples 14 + ( —14) = 0 - 1 4 + 14 = 0

Y o u c a n u s e o p p o s ite s ( a d d it iv e in v e r s e s ) t o s u b t r a c t r e a l n u m b e r s. T o see h o w , lo o k a t

th e n u m b e r lin e b e lo w , w h ic h m o d e ls 3 - 5 a n d 3 + ( - 5 ).

I 1 -

-4 -3

H h

Start at 3 and move

5 u n its le ft.

3 - 5 a n d 3 + ( - 5 ) a re e q u iv a le n t e x p re s s io n s , il lu s t r a t in g t h e r u le b e lo w.

K e y C o n c e p t Subtracting Real Numbers

T o s u b t r a c t a r e a l n u m b e r , a d d its o p p o s ite : a — b = a + (—b).

Examples 3 - 5 = 3 + ( - 5 ) = - 2 3 - ( - 5 ) = 3 + 5 = 8

.'n il
Why rewrite
s u b tra c tio n as
addition?
You can simplify
expressions using the
rules for adding real
numbers that you learned
earlier in this lesson.

Subtracting Real Numbers

What is each difference?

0 - 8 — ( - 1 3 ) = - 8 + 13 The opposite o f - 1 3 is 13. So add 13.

= 5 Use rules fo r addition.

0 3. 5 - 12 .4 = 3 .5 + ( - 1 2. 4 ) The opposite o f 12.4 is - 1 2 .4. So add - 1 2 .4.

= - 8. 9 Use rules for addition.

09-9 = 9 + ( - 9 ) The opposite o f 9 is - 9. So add - 9.

= 0 Inverse Property o f A ddition

© Got It? 3. a. What is 4.8 - (-8.7)?

b. R e a so n in g For w hat values of a a n d b does a — b = b - a?

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