Algebra 1 Common Core Student Edition, Grade 8-9

1 - 3 R e a l N u m b e r s a n d t h e N u m b e r L i n e

Quick Review

T h e r a t io n a l n u m b e r s a n d i r r a t i o n a l n u m b e r s f o r m th e set

of real num bers.

A rational num ber is a n y n u m b e r t h a t y o u c a n w r it e

as | , w h e re a a n d b a re in te g e r s a n d b + 0. T h e r a t i o n a l

n u m b e r s in c lu d e a ll p o s it iv e a n d n e g a tiv e in te g e r s , as w e ll

as fr a c tio n s , m ix e d n u m b e r s , a n d t e r m i n a t i n g a n d r e p e a t in g

decimals.

Irratio nal num bers c a n n o t b e r e p r e s e n te d as t h e q u o t ie n t

o f t w o in te g e r s. T h e y in c lu d e th e s q u a re r o o ts o f a ll p o s it iv e

in te g e rs th a t are n o t p e rfe c t squares.

Example

Is the number rational or irrational?

Q—5.422 rational

0V 7 irrational

Exercises

Tell whether each number is rational or irrational.

33. 2


34. 0.57


35. 77


36. 
    

    Estimate each square root. Round to the nearest integer.

    
    


37. V99 37. V48 38. V30
    Name the subset(s) of the real numbers to which each
    number belongs.


38. -1 7


39. VlOO


40. 6213


41. 4.288


42. V94


43. l|
    Order the numbers in each exercise from least to greatest.


44. -l|, 1.6, - if 46. |, -0 .8 , V 3

1 - 4 P r o p e r t i e s o f R e a l N u m b e r s

Quick Review Exercises

Y o u c a n u s e p r o p e r t ie s s u c h as t h e o n e s b e lo w to s im p lif y Simplify each expression. Justify each step.

and evaluate expressions.

47. -8 + 9w+ (-2 3 )
    Commutative Properties -2 + 7 = 7 + (-2 )
    3 X 4 = 4 X 3 48. | • (-10 • (a \^8 )
    Associative Properties 2 X (1 4 X 3) = (2 X 14) X 3 49. • OJ • ( - 2 0 )
    3 + (12 + 2) = (3 + 12) + 2 50. 53 +(-12) + (-4 1 )
    Identity Properties -6 + 0 = -6
    51- S P
    21 X 1 = 21 Tell whether the expressions in each pair are equivalent.
    Zero Property of M ultiplication -7X 0 = 0


48. (5 - 2)c and c • 3
    Multiplication Property of - 1 6 • (-1 ) = -6


49. 41 + z + 9 a n d 41 • z • 9
    Example 54. 81xyand 9xy
    Use an identity property to simplify — 55. t----------------r and t
    —M = — 7b. f = — 7b. i = — 7b (5 + 7 - 1 1 )

70 Ch ap t er 1 Ch ap t er Review