Algebra 1 Common Core Student Edition, Grade 8-9

How can you
express decimals
as sim ple sums and
differences?
Think of a decimal as the
sum or difference of its
whole number portion
and its decimal portion.

Y o u c a n u s e th e D is t r ib u t iv e P r o p e r t y to m a k e c a lc u la t io n s e a s ie r t o d o w i t h m e n t a l

m a th. S o m e n u m b e r s c a n b e t h o u g h t o f as s im p le s u m s o r d iffe r e n c e s.

Using the Distributive Property for M ental M ath

Eating Out Deli sandwiches cost $4.95 each. What is the total cost of 8 sandwiches?

Use mental math.

.K n o w ........ ,iMasaa ..

• Sandwiches cost $4.95. Total cost of Express $4.95 as a difference and


• You are buying 8 sandwiches. 8 sandwiches use the Distributive Property.

T h e t o t a l c o s t is t h e p r o d u c t o f th e n u m b e r o f s a n d w ic h e s y o u b u y , 8 , a n d th e c o s t p e r

sandwich, $4.95.

8(4.95) = 8(5 - 0.05) Think of 4.95 as 5 - 0.05.

= 8 ( 5 ) — 8 (0 .0 5 ) Distributive Property

= 40 - 0.4 Multiply mentally.

= 39.6 Subtract mentally.

The total cost fo r 8 s a n d w ic h e s is $39.60.

G o t It? 4. J u lia c o m m u t e s to w o r k o n th e t r a i n 4 t im e s e a c h w e e k. A r o u n d - t r i p t ic k e t

c o s ts $ 7 .2 5. W h a t is h e r w e e k ly c o s t f o r tic k e ts? U s e m e n t a l m a th.

Essent ial Und er st and ing Y o u c a n s i m p li f y a n a lg e b r a ic e x p r e s s io n b y

c o m b in in g t h e p a r ts o f th e e x p r e s s io n t h a t a re a lik e.

In an algebraic expression, a term is a n u m b e r , a v a r ia b le , o r th e p r o d u c t o f a n u m b e r

a n d o n e o r m o r e v a r ia b le s. A constant is a te rm th a t has n o v a ria b le. A coefficient is

a n u m e r ic a l f a c t o r o f a t e r m. R e w r ite e x p re s s io n s as s u m s t o id e n t i f y th e s e p a r t s o f a n

expression.

6a2, - 5ab, 3b, and - 1 2 are terms.

> , '

6 a 2 - 5ab + 3b - 12 = (^6) t a 2 + (-5f ab) + 3> b + (-12)t
coefficientsx constant
In the algebraic expression 6 a 2 - 5ab + 3b- 12, the terms have coefficients of 6 , - 5 ,
and 3. The term —12 is a constant.
Like term s h a v e th e s a m e v a r ia b le fa c to r s. T o i d e n t i f y l ik e te r m s , c o m p a r e th e v a r ia b le
factors o f th e term s, as sh o w n below.
Terms la a n d —3 a 4x 2 and 12 x 2 6 ab a n d —2 a x y 2 and x2y
Variable Factors a a n d a x2 and x2 ab a n d a xy2 and x2y
Like Terms? yes yes no no
48 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