Prealgebra (2nd Edition, 2011) – Solutions Manual – by Rusczyk

ALL 15 CHAPTERS COVERED

, CONTENTS




1
Contents




1 Properties of Arithmetic 1


2 Exponents 12



3 Number Theory 26


4 Fractions 46



5 Equations and Inequalities 68



6 Decimals 85


7 Ratios, Conversions, and Rates 101



8 Percents 117

,CONTENTS




9 Square Roots 127




1 0 Angles 140



1 1 Perimeter and Area 149



1 2 Right Triangles and Quadrilaterals 159



1 3 Data and Statistics 174



1 4 Counting 187



1 5 Problem-Solving Strategies 205

, CHAPTER 1 I


Properties of Arithmetic

24® Cards

First Card (7 + 1 — 4) x 6.

Second Card (5 + 1) x (8 — 4) or (5 — 1) x 4 + 8.
Third Card (1 + 1) x 23 — 22.
Fourth Card 5 x 7 — 10 — 1.


Exercises for Section 1.2

1.2.1 We can group each 99 with a 101:
99 + 99 + 99 +101 +101 + 101 = (99 +101)+(99 + 101) + (99 +101): 200 + 200 + 200 = - .
1.2.2 We can group the numbers into pairs without moving them:
1999 + 2001 + 1999 + 2001 + 1999 + 2001 + 1999 + 2001
= (1999 + 2001) + (1999 + 2001) + (1999 + 2001) + (1999 + 2001)
= 4000 + 4000 + 4000 + 4000 = 16,000 .

1.2.3 We can pair each number in the first group with a number in the second group:
(3+13+23+33+43)+(7+17+27+37+47)
=(3+47)+(13+37)+(23+27)+(33+17)+(43+7) = 5 0 + 5 0 + 5 0 + 5 0 + 5 0 = - .

1.2.4 Again let’s match each number in the first group with a number in the second:
(1 + 2 + 3 + ~ ~ + 4 9 + 5 0 ) + ( 9 9 + 9 8 + 9 7 + - ~ + 5 1 +50)
= (1 + 9 9 ) + ( 2 + 9 8 ) + ( 3 + 9 7 ) + - - . + ( 4 9 + 5 1 ) + ( 5 0 + 5 0 )
=300+100+100+m+100+1og=soo1oo=-.
50 numbers