Algebra 1 Common Core Student Edition, Grade 8-9

Properties of

Real Num bers

@ Common Core State Standards

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

product o f tw o rational numbers is rational; that the

sum of a rational number and an irrational number is

irrational...

M P 1, MP 2, MP 3, MP 4, MP 6, MP 7

Objective To id e n tify and use properties o f real num bers

rifff ffffii W.l

Rem em b er t h a t

+ means "is not

equal t o."

, M A T H EM A T I C A L

(pr a c t ic es

ether each

I b y c o m p l e l

or +. Exp la

Lesso n
Vocabulary
eq uiv al ent
expressions
deduct ive
reasoning
count er exam p le

T h e S o lv e I t illu s t r a t e s n u m e r ic a l r e la t io n s h ip s t h a t a re a lw a y s t r u e f o r r e a l n u m b e r s.

Esse n t i a l U n d e r s t a n d i n g R e la t io n s h ip s t h a t a re a lw a y s t r u e f o r r e a l n u m b e r s

are called properties, w h ic h a re r u le s u s e d t o r e w r it e a n d c o m p a r e e x p re s s io n s.

Two algebraic expressions are equivalent expressions i f t h e y h a v e th e s a m e v a lu e

f o r a ll v a lu e s o f th e v a r ia b le ( s ). T h e f o l l o w i n g p r o p e r t ie s s h o w e x p re s s io n s t h a t a re

equivalent for all real numbers.

Pr op ert ies Properties of Real Numbers

Let a, b, and c b e a n y r e a l n u m b e r s.

Commutative Properties of Addition and Multiplication

C h a n g in g t h e o r d e r o f t h e a d d e n d s d o e s n o t c h a n g e th e s u m. C h a n g in g th e o r d e r o f th e

fa cto rs does n o t change th e p ro d u c t.

Algebra Example

Addition a + b = b + a 1 8 + 54 = 54 + 18

Multiplication a • b = b • a 12 • 4 = 1 12

Associative Properties of Addition and M ultiplication

C h a n g in g t h e g r o u p in g o f t h e a d d e n d s d o e s n o t c h a n g e t h e s u m. C h a n g in g th e

grouping of the factors does not change the product.

Addition (a + b) + c = a + [b + c) (23 + 9) + 4 = 23 + (9 + 4)

Multiplication (a • b) • c = a • [b • c ) (7 • 9 ) • 10 = 7 • (9 • 10)

V.

PowerAlgebra.com | L e s s o n 1 - 4 Pr o p er t i es o f Real N u m b er s 23