Algebra 1 Common Core Student Edition, Grade 8-9

\ 3 EESnSBWriting Equivalent Expressions

Simplify each expression.

0 5(3n)

Jf Pf M ........ Need .... Plan

An expression Groups of numbers Use properties to group or reorder

that can be simplified parts of the expression.

5(3n) = (5 • 3)n Associative Property of Multiplication

= 15rc Simplify.

0 (4 + 7b) + 8

(4 + 7b) + 8 = ( 7b + 4) + 8 Commutative Property of Addition

= 7b + (4 + 8 ) Associative Property o f A ddition

= 7b + 12 Simplify.

B6*3'y

6 xy 6 x • y

~T = 1 • y

_6 x y- • y ^ ,u ,c ,u, „ ,u ,u H,y „ iy „ a u , u „ a. £ ' j ~ j^.

Rewrite denominator using Identity Property of Multiplication.

Use rule fo r m ultiplying fractions: f • § - ac

= 6 jc • 1 x-M=xandy- 5 -y = 1.

= 6x Identity Property of Multiplication

G o t It? 3. Simplify eachexpression.

a. 2.1(4.5x) b.6 + ( 4 h + 3 ) c. ^

I n P r o b le m 3, r e a s o n in g a n d p r o p e r t ie s w e r e u s e d t o s h o w t h a t t w o e x p re s s io n s a re

equivalent. This is an example of deductive reasoning. Deductive reasoning is th e

p r o c e s s o f r e a s o n in g l o g ic a lly f r o m g iv e n fa c ts t o a c o n c lu s io n.

To show th a t a statem ent is not tr u e , f i n d a n e x a m p le f o r w h ic h i t is n o t tr u e. A n

e x a m p le s h o w in g t h a t a s ta t e m e n t is fa ls e is a counterexample. Y o u n e e d o n ly o n e

c o u n t e r e x a m p le t o p r o v e t h a t a s ta t e m e n t is fa ls e.

Look for a
counterexample to show
the statement is false. If
you don't find one, try to
use properties to show
that it is true.

Lesson 1-4 Pr o p er t i es o f Real N u m b er s 25

’ ___

_— ---------------—— — i i ... ; --

c

PowerAlgebra.com

Using Deductive Reasoning and Counterexam ples

Is the statem ent true or false? If it is false, give a counterexample.

Q For all real numbers a and b, a • b = b + a.

False. 5*3=A3 + 5 is a counterexam ple.

0 For all real numbers a, b, and c, { a + b) + c = b + [a + c).

T r u e. U s e p r o p e r t ie s o f r e a l n u m b e r s t o s h o w t h a t t h e e x p r e s s io n s a re e q u iv a le n t,

(a + b) + c = {b + a) + c Commutative Property of Addition

= b + [a + c) Associative Property of Addition