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Core Mathematics

Katherine Yoshiwara

Appendix A Answers to Odd-Numbered Homework Problems

1 Preliminary Ideas
1.1 Halves and Quarters
1.1.8 Practice 1.1

1.1.8.1.

Answer.
  1. How many things are in the whole.
  2. How many things are in the part.

1.1.8.3.

Answer.
  1. There are 100 cents in a dollar.
  2. 0.5 means \(\dfrac{5}{10}.\)
  3. 50% is half of 100%.

1.1.8.5.

Answer.
  1. 44 inches
  2. 22 inches
  3. 66 inches

1.1.8.7.

Answer.
  1. 32 fluid ounces
  2. 16 fluid ounces
  3. 48 fluid ounces

1.1.8.9.

Answer.

1.1.8.11.

Answer.

1.1.8.13.

Answer.

1.1.8.15.

Answer.

1.1.8.17.

Answer.
450 ml

1.1.8.19.

Answer.
192 pages

1.1.8.21.

Answer.
  1. \(0.5\) cup
  2. \(1.5\) cups

1.1.8.23.

Answer.
  1. \(22.5\) miles
  2. \(67.5\) miles

1.1.8.27.

Answer.
  1. Add them.
  2. Find one-half of one-half and add to one-half.

1.1.8.29.

Answer.
\(36, ~10, ~\dfrac{10}{36}, ~\gt\)

1.1.8.31.

Answer.
\(30, ~8, ~\dfrac{8}{30}, ~\gt\)

1.1.8.33.

Answer.
\(10, ~3, ~\dfrac{3}{10}, ~\gt\)

1.1.8.35.

Answer.
Less

1.1.8.37.

Answer.
Less

1.1.8.39.

Answer.
\(\dfrac{5}{8}\)

1.1.8.41.

Answer.
\(\dfrac{5}{9}\)

1.1.8.43.

Answer.
\(\dfrac{3}{8}\)

1.1.8.45.

Answer.
\(\dfrac{3}{8}\)

1.1.8.47.

Answer.
Many answers are possible.

1.1.8.49.

Answer.
Many answers are possible.

1.1.8.51.

Answer.
Larger

1.1.8.53.

Answer.
Less

1.2 Tenths and Hundredths
1.2.7 Practice 1.2

1.2.7.1.

Answer.

1.2.7.3.

Answer.

1.2.7.5.

Answer.

1.2.7.7.

Answer.

1.2.7.9.

Answer.
  1. \(\displaystyle \dfrac{1}{10} = \dfrac{10}{100}\)
  2. \(\displaystyle \dfrac{10}{10} \not = \dfrac{1}{100}\)

1.2.7.11.

Answer.
  1. \(\dfrac{1}{4}~\) lb
  2. \(0.25~\) lb

1.2.7.13.

Answer.
less

1.2.7.15.

Answer.
less

1.2.7.17.

Answer.
  1. 75 mlb
  2. \(\displaystyle \dfrac{1}{10}\)

1.2.7.19.

Answer.
$950

1.2.7.21.

Answer.
\(\dfrac{1}{2}\)

1.2.7.23.

Answer.
\(\dfrac{1}{4}\)

1.2.7.25.

Answer.
\(\dfrac{1}{2}\)

1.2.7.27.

Answer.
\(\dfrac{2}{5}\)

1.2.7.29.

Answer.
\(\dfrac{31}{50}\)

1.2.7.31.

Answer.
\(\dfrac{2}{3}\)

1.2.7.33.

Answer.
\(\dfrac{4}{5}\)

1.2.7.35.

Answer.
\(\dfrac{5}{9}\)

1.2.7.37.

Answer.
\(\dfrac{9}{10}\)

1.2.7.39.

Answer.
They name the same part of one whole.

1.2.7.41.

Answer.
\(\dfrac{25}{100} = \dfrac{1}{4}\)

1.2.7.43.

Answer.
No. \(\dfrac{9}{12} \not= \dfrac{9}{10}\)

1.2.7.45.

Answer.

1.2.7.47.

Answer.
\(\dfrac{25}{100},~\dfrac{50}{100},~\dfrac{75}{100}\)

1.2.7.49.

Answer.
\(\dfrac{10}{100},~\dfrac{30}{100},~\dfrac{70}{100},~\dfrac{90}{100}\)

1.2.7.51.

Answer.
  2. Fraction in Hundredths \(\dfrac{5}{100}\) \(\dfrac{15}{100}\) \(\dfrac{25}{100}\) \(\dfrac{35}{100}\) \(\dfrac{45}{100}\) \(\dfrac{45}{100}\) \(\dfrac{65}{100}\) \(\dfrac{75}{100}\) \(\dfrac{85}{100}\) \(\dfrac{95}{100}\)
    Reduced Fraction \(\dfrac{1}{20}\) \(\dfrac{3}{20}\) \(\dfrac{1}{4}\) \(\dfrac{7}{20}\) \(\dfrac{9}{20}\) \(\dfrac{11}{20}\) \(\dfrac{13}{20}\) \(\dfrac{3}{4}\) \(\dfrac{17}{20}\) \(\dfrac{19}{20}\)

1.2.7.53.

Answer.
No. They are equal.

1.2.7.55.

Answer.
\(\dfrac{1}{20},~\dfrac{3}{20},~\dfrac{7}{20},~\dfrac{9}{20},~\dfrac{11}{20},~\dfrac{13}{20},~\dfrac{17}{20},~\dfrac{19}{20}\)

1.2.7.57.

Answer.
No. \(\dfrac{1}{2} = \dfrac{2}{4}\)

1.2.7.59.

Answer.
  1. Multiply by 5.
  2. Multiply by 5, then divide by 2.

1.2.7.61.

Answer.
\(\dfrac{3}{4}\)

1.2.7.63.

Answer.
\(\dfrac{3}{20}\)

1.2.7.65.

Answer.
\(\dfrac{2}{25}\)

1.2.7.67.

Answer.
\(\dfrac{5}{8}\)

1.2.7.69.

Answer.
  1. 3.8
  2. 0.38
  3. 0.038

1.2.7.71.

Answer.
  1. 1.82
  2. 0.182
  3. 0.0182

1.3 Whole Numbers
1.3.6 Practice 1.3

1.3.6.1.

Answer.
  1. 1 and 36, 2 and 18, 3 and 12, 4 and 9, 6 and 6
  2. 6

1.3.6.3.

Answer.
  1. 1 and 56, 2 and 28, 4 and 14, 7 and 8
  2. 7

1.3.6.5.

Answer.
  1. 1 2 3 5
    30 15 10 6

1.3.6.7.

Answer.
3 and 8

1.3.6.9.

Answer.
3 and 18

1.3.6.11.

Answer.
210

1.3.6.13.

Answer.
25

1.3.6.15.

Answer.
32, 33, 34, 35, 36

1.3.6.17.

Answer.
\(6 = 2 \times 3\)

1.3.6.19.

Answer.
30, 42, 66, 70

1.3.6.21.

Answer.
64

1.3.6.23.

Answer.
101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199. 21

1.3.6.25.

Answer.
114 to 126

1.3.6.27.

Answer.
First and last

1.3.6.29.

Answer.
It is divisible by 2.

1.3.6.31.

Answer.
\(2 \times 2 \times 3 \times 3\)

1.3.6.33.

Answer.
\(2 \times 2 \times 2 \times 3 \times 3\)

1.3.6.35.

Answer.
\(2 \times 5 \times 5 \times 5\)

1.3.6.37.

Answer.
\(2 \times 3 \times 3 \times 11\)

1.3.6.39.

Answer.
12

1.3.6.41.

Answer.
7

1.3.6.43.

Answer.
2

1.3.6.45.

Answer.
1

1.3.6.47.

Answer.
3

1.3.6.49.

Answer.
72

1.3.6.51.

Answer.
  1. 1, 2, 17
  2. 17

1.3.6.53.

Answer.
  1. 1, 43
  2. 1

1.3.6.55.

Answer.
100

1.3.6.57.

Answer.
42

1.3.6.59.

Answer.
210

1.3.6.61.

Answer.
330

1.3.6.63.

Answer.
  1. 2, 3, 6
  2. 4, 6, 12
  3. 2, 4, 4

1.3.6.65.

Answer.
  1. 23
  2. GCF

1.3.6.67.

Answer.
  1. 60
  2. LCM

1.3.6.69.

Answer.
  1. 5 of daffodils, 8 of tulips
  2. LCM

1.4 Angles and Triangles
1.4.7 Practice 1.4

1.4.7.1.

Answer.
3 o’clock, 6 o’clock

1.4.7.3.

Answer.
No. The sum of the angles would be more than 180°.

1.4.7.5.

Answer.
The point where the two sides of an angle meet, and the angle between the equal sides of an isosocelels triangle.

1.4.7.7.

Answer.

1.4.7.9.

Answer.

1.4.7.11.

Answer.

1.4.7.13.

Answer.
\(80 \degree, ~30 \degree, ~70 \degree\)

1.4.7.15.

Answer.
\(150 \degree\)

1.4.7.17.

Answer.
\(52 \degree\)

1.4.7.19.

Answer.
\(123 \degree\)

1.4.7.21.

Answer.
\(141 \degree, ~39 \degree\)

1.4.7.23.

Answer.
  1. \(\displaystyle 30 \degree\)
  2. \(\displaystyle 60 \degree\)
  3. \(\displaystyle 90 \degree\)
  4. \(\displaystyle 120 \degree\)
  5. \(\displaystyle 150 \degree\)

1.4.7.25.

Answer.
\(109 \degree\)

1.4.7.27.

Answer.
\(29 \degree\)

1.4.7.29.

Answer.
\(77 \degree\)

1.4.7.31.

Answer.
\(120 \degree\)

1.4.7.33.

Answer.
\(88 \degree\)

1.4.7.35.

Answer.
\(60 \degree, ~30 \degree\)

1.4.7.37.

Answer.
The sum of the angles is not 180°.

1.4.7.39.

Answer.
The triangle should be isosceles.

1.4.7.41.

Answer.
\(45 \degree\)

1.4.7.43.

Answer.
It is the largest angle.

1.4.7.45.

Answer.
Central angles: \(45 \degree\text{,}\) all other angles: \(67.5 \degree\)

1.5 Perimeter and Area
1.5.5 Practice 1.5

1.5.5.1.

Answer.
Answers will vary.

1.5.5.3.

Answer.
Answers will vary.

1.5.5.5.

Answer.
Area measures the amount of space inside a closed region; perimeter measures the length of the boundary of the region.

1.5.5.7.

Answer.
Add the length and width and double the sum.

1.5.5.9.

Answer.
Answers will vary.

1.5.5.11.

Answer.
  1. 13 in
  2. 33 cm

1.5.5.13.

Answer.
Answers will vary.

1.5.5.15.

Answer.
  1. Two
  2. One

1.5.5.17.

Answer.
119.2 in

1.5.5.19.

Answer.
  1. 12 ft
  2. 5 sq ft

1.5.5.21.

Answer.
  1. 16 ft
  2. 10 sq ft

1.5.5.23.

Answer.
  1. Closet 5
  2. Closet 1
  3. Closet 3

1.5.5.25.

Answer.
6 sq m

1.5.5.27.

Answer.
46 sq m

1.5.5.29.

Answer.
  1. 20 sq in
  2. 36 sq in
  3. 144 sq ft
  4. 50 ft

1.5.5.31.

Answer.
  1. 49 cm
  2. 120 sq cm

1.5.5.33.

Answer.
  1. 160 ft
  2. 1290 sq ft

1.5.5.35.

Answer.
  1. 80 sq in, 36 in
  2. Answers will vary.
  3. 26 in or 28 in, no, no

1.5.5.37.

Answer.
100 yd

1.5.5.39.

Answer.
8 sq in

1.5.5.41.

Answer.
  1. 22 sq ft
  2. 19 ft

1.5.5.43.

Answer.
Rectangle Width Length Perimeter Area
1 3 ft 6 ft 18 ft 18 sq ft
2 5 ft 8 ft 26 ft 40 sq ft
3 8 ft 9 ft 34 ft 72 sq ft
4 12 ft 20 ft 64 ft 240 sq ft
5 10 ft 15 ft 50 ft 150 sq ft

1.5.5.45.

Answer.
  1. 30
  2. 18
  3. 6
  4. 2.5

1.5.5.47.

Answer.
  1. 4
  2. 12
  3. 10
  4. 10

1.5.5.49.

Answer.
18 sq cm

1.5.5.51.

Answer.
15 sq icm

1.5.5.53.

Answer.
The area of the triangle is half the area of a rectangle with the same base and height.

2 Numbers and Variables
2.1 Decimal Numbers
2.1.7 Practice 2.1

2.1.7.1.

Answer.
  1. \(\displaystyle \dfrac{8}{10}\)
  2. eight tenths

2.1.7.3.

Answer.
  1. \(\displaystyle \dfrac{9}{1000}\)
  2. nine thousandths

2.1.7.5.

Answer.
  1. \(\displaystyle \dfrac{7}{100}\)
  2. seven hundredths

2.1.7.7.

Answer.
  1. \(\displaystyle \dfrac{3}{10,000}\)
  2. three ten-thousandths

2.1.7.9.

Answer.
  1. \(\displaystyle \dfrac{28}{100}\)
  2. twenty-eight hundredths

2.1.7.11.

Answer.
  1. \(\displaystyle \dfrac{452}{1000}\)
  2. four hundred fifty-two thousandths

2.1.7.13.

Answer.
  1. \(\displaystyle \dfrac{64}{100}\)
  2. sixty-four hundredths

2.1.7.15.

Answer.
  1. \(\displaystyle \dfrac{50}{1000}\)
  2. fifty thousandths

2.1.7.17.

Answer.
  1. 3 flats, 1 stick, 7 cubes
  2. \(\displaystyle \dfrac{3}{10} + \dfrac{1}{100} + \dfrac{7}{1000}\)

2.1.7.19.

Answer.
  1. 3 sticks and 4 cubes
  2. \(\displaystyle \dfrac{3}{100} + \dfrac{4}{1000}\)

2.1.7.21.

Answer.
  1. 1 flat and 2 cubes
  2. \(\displaystyle \dfrac{2}{10} + \dfrac{2}{1000}\)

2.1.7.23.

Answer.
  1. 4 flats and 3 sticks
  2. \(\displaystyle \dfrac{4}{10} + \dfrac{3}{100}\)

2.1.7.25.

Answer.

2.1.7.27.

Answer.

2.1.7.29.

Answer.

2.1.7.31.

Answer.

2.1.7.33.

Answer.

2.1.7.35.

Answer.
0.14

2.1.7.37.

Answer.
0.08, 0.200, 0.46, 0.5

2.1.7.39.

Answer.
0.304, 0.316, 0.34, 0.36

2.1.7.41.

Answer.
Units Tenths Hundredths Thousandths
\(8.56\) \(85.6\) \(856\) \(8560\)
\(4.5\) \(45\) \(450\) \(4500\)
\(0.07\) \(0.7\) \(7\) \(70\)

2.1.7.43.

Answer.
0.65 exact

2.1.7.45.

Answer.
0.83 approximate

2.1.7.47.

Answer.
0.68 exact

2.1.7.49.

Answer.
0.57 approximate

2.1.7.51.

Answer.
\(2 \frac{4}{5}\)

2.1.7.53.

Answer.
\(3 \frac{2}{3}\)

2.1.7.55.

Answer.
\(\frac{1}{8}\)

2.1.7.57.

Answer.
\(4 \frac{1}{3}\)

2.1.7.59.

Answer.
  1. 156
  2. 15.6
  3. 15.6
  4. 0.156

2.1.7.61.

Answer.
  1. 21.32
  2. 21.32
  3. 0.2132
  4. 21,320

2.1.7.63.

Answer.
The digits end.

2.1.7.65.

Answer.
No. \(0.3 = \frac{3}{10},\) but \(0.\overline{3} = \frac{1}{3}\)

2.1.7.67.

Answer.
  1. 1.95
  2. 1.995
  3. 1.9995
  4. Add them and divide the sum by 2.

2.2 More Fractions and Percents
2.2.8 Practice 2.2

2.2.8.1.

Answer.
Divide by 10, multiply by 0.1, move the decimal one place to the left.

2.2.8.3.

Answer.
  1. Divide by 2
  2. Add 5% to twice 10%
  3. $190

2.2.8.5.

Answer.
No. Multiply by 0.04

2.2.8.7.

Answer.
Divide by 10

2.2.8.9.

Answer.
Divide by 10, then muliply by 5

2.2.8.11.

Answer.
  1. \(\displaystyle \frac{3}{8}\)
  2. Larger

2.2.8.13.

Answer.
  1. 20%
  2. 4%
  3. 12.5%
  4. \(16.\overline{6}\)%

2.2.8.15.

Answer.
Original Price Discount New Price
$480 $57.60 $422.40
$625 $75 $550
$390 $46.80 $343.20
$238 $28.56 $209.44

2.2.8.17.

Answer.
$646,000

2.2.8.19.

Answer.
30

2.2.8.21.

Answer.
  1. 66,330
  2. 25.6%

2.2.8.23.

Answer.
\(\frac{1}{4}\) off $60

2.2.8.25.

Answer.
\(\frac{1}{3}\) off $6

2.2.8.27.

Answer.
(a), (c), and (d)

2.2.8.29.

Answer.
Food: $34, Decorations: $17, Prizes: $8.50, Cups, etc.: $8.50

2.2.8.31.

Answer.
\(\dfrac{6}{9} = \dfrac{2}{3}\)

2.2.8.33.

Answer.
\(\dfrac{10}{12} = \dfrac{5}{6}\)

2.2.8.35.

Answer.
\(\dfrac{4}{12} = \dfrac{1}{3}\)

2.2.8.37.

Answer.
\(\dfrac{80}{100} = \dfrac{4}{5}\)

2.2.8.39.

Answer.
\(\dfrac{45}{100} = \dfrac{9}{20}\)

2.2.8.41.

Answer.
\(\dfrac{24}{100} = \dfrac{6}{25}\)

2.2.8.43.

Answer.
\(\dfrac{38}{100} = \dfrac{19}{50}\)

2.2.8.45.

Answer.
\(\dfrac{96}{100} = \dfrac{24}{25}\)

2.2.8.47.

Answer.
\(\dfrac{4}{6},~ \dfrac{6}{9},~ \dfrac{8}{12}\)

2.2.8.49.

Answer.
\(\dfrac{2}{12},~ \dfrac{3}{18},~ \dfrac{4}{24}\)

2.2.8.51.

Answer.
\(\dfrac{10}{32},~ \dfrac{15}{48},~ \dfrac{20}{64}\)

2.2.8.53.

Answer.
  3. Fraction Inches Percent
    \(\dfrac{1}{8}\) \(4.5\) \(12.5\)
    \(\dfrac{2}{8}\) \(9\) \(25\)
    \(\dfrac{3}{8}\) \(13.5\) \(37.5\)
    \(\dfrac{4}{8}\) \(18\) \(50\)
    \(\dfrac{5}{8}\) \(22.5\) \(62.5\)
    \(\dfrac{6}{8}\) \(27\) \(75\)
    \(\dfrac{7}{8}\) \(31.5\) \(87.5\)
    \(\dfrac{8}{8}\) \(36\) \(100\)

2.2.8.55.

Answer.
  1. \(\displaystyle \dfrac{1}{9}\)
  2. \(\displaystyle \dfrac{2}{9}\)
  3. \(\displaystyle \dfrac{2}{3}\)

2.2.8.57.

Answer.
90

2.2.8.59.

Answer.
  1. \(\displaystyle \dfrac{1}{16}\)
  2. \(\displaystyle 3\dfrac{1}{4}\)
  3. \(\displaystyle \dfrac{5}{4}\)

2.2.8.61.

Answer.
  1. \(\displaystyle 60 \degree\)
  2. \(\displaystyle 240 \degree\)

2.2.8.63.

Answer.
  1. \(\displaystyle 30 \degree\)
  2. \(\displaystyle 300 \degree\)

2.2.8.65.

Answer.
$10,000

2.2.8.67.

Answer.
22 mi, 49.5 lb, 440 yd

2.3 Variables
2.3.5 Practice 2.3

2.3.5.1.

Answer.
Shirley’s laps = Janet’s laps - 8

2.3.5.3.

Answer.
Number of batteries = \(6 \times \) no. of packages

2.3.5.5.

Answer.
Number of pages left = 200 - no. pages read

2.3.5.7.

Answer.
Wages = \(7 \times\) no. hours worked

2.3.5.9.

Answer.
  1. Children born outside marriage
  2. 15%
  3. Ireland
  4. Denmark
  5. Greece

2.3.5.11.

Answer.
  1. Average temperature in Chicago
  2. \(\displaystyle 54 \degree\)
  3. May
  4. April
  5. November

2.3.5.13.

Answer.
  1. Falls: 60, Choking: 125, Suffocation: 350, Drowning: 450, Fires: 750, Motor vehicles: 1000
  2. Motor vehicles
  3. 0.132
  4. Approximately 665

2.3.5.15.

Answer.
  1. US, Mexico
  2. Japan, Mexico
  3. Mexico, 41 years
  4. 8 years

2.3.5.17.

Answer.
A variable can have different values; a constant always has the same value.

2.3.5.19.

Answer.
  1. \(5 \frac{1}{2}\) hr
  2. Subtract \(9 \frac{1}{2}\) from \(t\)
  3. \(t \) 16 20 25 31
    \(t - 9\dfrac{1}{2}\) \(6 \frac{1}{2}\) \(10 \frac{1}{2}\) \(15 \frac{1}{2}\) \(21 \frac{1}{2}\)

2.3.5.21.

Answer.
  1. 1.5 qt
  2. Multiply by 0.10
  3. \(q \) 20 45 260 1250
    \(0.10 \times q\) 2 4.5 26 125

2.3.5.23.

Answer.
  1. 2.45 in
  2. Multiply \(t\) by 0.085
  3. \(t \) 7 60 200 360
    \(0.085\times t\) 0.595 5.1 17 30.6

2.3.5.25.

Answer.
  1. Miles driven 80 150 225 310
    Miles left 320 250 175 90
  2. Subtract miles driven from 400
  3. Miles left = 400 - miles driven
  4. Miles left = \(400 - d\)

2.3.5.27.

Answer.
  1. Total calories 1200 1225 1500 1800
    Fat calories 240 245 300 360
  2. Divide total calories by 5
  3. Calories from fat = total calories \(\div 5\)
  4. Calories from fat = \(c \div 5\)

2.3.5.29.

Answer.
  1. Total bill ($) 32 48 52 60
    Tip ($) 4.80 7.20 7.80 9.00
  2. Multiply the bill by 0.15
  3. Tip = 0.15 \(\times\) Bill
  4. Tip = \(0.15 \times B\)

2.3.5.31.

Answer.
  1. \(\dfrac{1}{5} \times m\) or \(\dfrac{m}{5}\)
  2. $24

2.3.5.33.

Answer.
  1. \(\dfrac{1}{4} \times W\) or \(\dfrac{W}{4}\)
  2. 2.5 in

2.3.5.35.

Answer.
  1. \dfrac{2}{3} \times p
  2. 98

2.4 Algebraic Expressions
2.4.8 Practice 2.4

2.4.8.1.

Answer.
  1. Multiplication
  2. Multiplication
  3. Subtraction
  4. Addition
  5. Addition
  6. Division
  7. Division>

2.4.8.3.

Answer.
\(2 \cdot 3,~ 2(3)\)

2.4.8.5.

Answer.
Terms, sum

2.4.8.7.

Answer.
  1. \(\displaystyle v-8\)
  2. \(\displaystyle \dfrac{c}{4}\)

2.4.8.9.

Answer.
  1. \(\displaystyle \dfrac{t}{5}\)
  2. \(\displaystyle J+20\)

2.4.8.11.

Answer.
  1. \(\displaystyle \dfrac{15}{b}\)
  2. \(\displaystyle 32+f\)

2.4.8.13.

Answer.
  1. \(\displaystyle \dfrac{P}{3}\)
  2. \(\displaystyle Z-\dfrac{3}{2}\)

2.4.8.15.

Answer.
  1. \(\displaystyle r-d\)
  2. \(\displaystyle yz\)

2.4.8.17.

Answer.
\(a\) subtracted from 7.1

2.4.8.19.

Answer.
15 times \(j\)

2.4.8.21.

Answer.
\(A\) divided by \(c\)

2.4.8.23.

Answer.
Sum of \(y\) and \(h\)

2.4.8.25.

Answer.
2.5 subtracted from \(H\)

2.4.8.27.

Answer.
\(\dfrac{3}{5}\) of \(b\)

2.4.8.29.

Answer.
  1. 24 divided by 6, 4
  2. 6 divided by 24, \(\dfrac{1}{4}\)
  3. 6 divided by 24, \(\dfrac{1}{4}\)
  4. 24 divided by 6, 4

2.4.8.31.

Answer.
\(L - 2.5\)

2.4.8.33.

Answer.
\(8A\)

2.4.8.35.

Answer.
\(\dfrac{3}{4} p\)

2.4.8.37.

Answer.
  1. \(\displaystyle m-15\)
  2. \(\displaystyle 15-m\)
  3. \(\displaystyle m+15\)

2.4.8.39.

Answer.
  1. \(\displaystyle 12p\)
  2. \(\displaystyle \dfrac{p}{12}\)
  3. \(\displaystyle \dfrac{p}{12}\)

2.4.8.41.

Answer.
  1. \(\displaystyle \dfrac{c}{36}\)
  2. \(\displaystyle 36-c\)
  3. \(\displaystyle c+36\)

2.4.8.43.

Answer.
\(3c\)

2.4.8.45.

Answer.
\(r-6\)

2.4.8.47.

Answer.
\(\dfrac{2}{5}b\)

2.4.8.49.

Answer.
\(\dfrac{p}{4}\)

2.4.8.51.

Answer.
\(p-15\)

2.4.8.53.

Answer.
  1. c+3
  2. 11 cups

2.4.8.55.

Answer.
  1. \dfrac{T}{600}
  2. 80%

2.4.8.57.

Answer.
  1. \dfrac{1000}{r}
  2. 125 hrs

2.4.8.59.

Answer.
  1. 5
  2. 12
  3. 15.4

2.4.8.61.

Answer.
  1. 48
  2. 288
  3. 1.2

2.4.8.63.

Answer.
  1. \(\displaystyle \dfrac{1}{3}\)
  2. \(\displaystyle \dfrac{3}{4}\)
  3. 0.4

2.5 Equations
2.5.6 Practice 2.5

2.5.6.1.

Answer.
  1. Add 8
  2. Subtract 8
  3. \(\displaystyle r = s + 8\)
  4. Add 8
  5. Subtract 8

2.5.6.3.

Answer.
  1. Add $76
  2. Subtract $76
  3. \(\displaystyle a = b + 76\)
  4. Add $76
  5. Subtract $76

2.5.6.5.

Answer.
  1. \(q\) is 8 less than \(r\text{.}\)
  2. \(\displaystyle q = r - 8\)

2.5.6.7.

Answer.
  1. \(m\) is \(\dfrac{1}{3}\) of \(h\text{.}\)
  2. \(\displaystyle m = \dfrac{h}{3}\)

2.5.6.9.

Answer.
  1. \(k\) is 0.6 more than \(c\text{.}\)
  2. \(\displaystyle k = c + 0.6\)

2.5.6.11.

Answer.
  1. \(d\) is \(\dfrac{3}{4}\) of \(a\text{.}\)
  2. \(\displaystyle d = \dfrac{3}{4}a\)

2.5.6.13.

Answer.
  1. \(\displaystyle 8p=40\)
  2. \(\displaystyle p-8=40\)
  3. \(\displaystyle p-8=40\)
  4. \(\displaystyle p+8=40\)

2.5.6.15.

Answer.
  1. \(\displaystyle b-18=10\)
  2. \(\displaystyle 18-b = 10\)
  3. \(\displaystyle 18-b = 10\)

2.5.6.17.

Answer.
  1. \(\displaystyle \dfrac{16}{t} = 80\)
  2. \(\displaystyle \dfrac{t}{16} = 80\)

2.5.6.19.

Answer.
  1. \(\displaystyle n-5=30\)
  2. \(\displaystyle \dfrac{n}{5} = 30\)
  3. \(\)5n=30
  4. \(\displaystyle n+5=30\)

2.5.6.21.

Answer.
A statement that two expressions are equal.

2.5.6.23.

Answer.
To find a value for the variable that makes the equation true.

2.5.6.25.

Answer.
(1) Identify the operation performed on the variable. (2) Perform the opposite operation on both sides of the equation. (3) Check the solution.

2.5.6.27.

Answer.
(a), (b), and (d) are equations

2.5.6.29.

Answer.
Yes

2.5.6.31.

Answer.
Yes

2.5.6.33.

Answer.
No

2.5.6.35.

Answer.
  1. \(\displaystyle w-4.5\)
  2. \(\displaystyle n=w-4.5\)
  3. \(w\) 20 18 15
    \(n\) 15.5 13.5 10.5

2.5.6.37.

Answer.
  1. \(\displaystyle 1.2p\)
  2. \(\displaystyle d=1.2p\)
  3. \(p\) 5 10 20
    \(d\) 6 12 24

2.5.6.39.

Answer.
7

2.5.6.41.

Answer.
3

2.5.6.43.

Answer.
12

2.5.6.45.

Answer.
30

2.5.6.47.

Answer.
6

2.5.6.49.

Answer.
5

2.5.6.51.

Answer.
28

2.5.6.53.

Answer.
208

2.5.6.55.

Answer.
0

2.5.6.57.

Answer.
0

2.5.6.59.

Answer.
8.3

3 Measurement
3.1 Volume and Surface Area
3.1.5 Practice 3.1

3.1.5.1.

Answer.
The surface area is the sum of the areas of the faces. We measure surface area in square units.

3.1.5.3.

Answer.
6

3.1.5.5.

Answer.
Volume measures the amount of space inside the object. We use cubic units

3.1.5.7.

Answer.
A cubic meter is the amount of space inside a cube 1 meter on each side.

3.1.5.9.

Answer.
Yes, it is 6 units on each side.

3.1.5.11.

Answer.
Volume

3.1.5.13.

Answer.
Surface area

3.1.5.15.

Answer.
Perimeter

3.1.5.17.

Answer.
Surface area

3.1.5.19.

Answer.
Area

3.1.5.21.

Answer.
  1. box 3 by 8 by 6
  2. 180 sq in
  3. 144 cu in

3.1.5.23.

Answer.
No

3.1.5.25.

Answer.
No

3.1.5.27.

Answer.
  1. 80 cu ft
  2. 112 sq ft

3.1.5.29.

Answer.
  1. 512 cu in
  2. 384 sq in

3.1.5.31.

Answer.
  1. 2560 cu cm
  2. 1216 sq cm

3.1.5.33.

Answer.
  1. 44 cu m
  2. 94 sq m

3.1.5.35.

Answer.
  1. 3 cu yd
  2. 14 sq yd

3.1.5.37.

Answer.
  1. 4000 cu in
  2. 1300 sq in

3.1.5.39.

Answer.
396 sq in

3.1.5.41.

Answer.
24 cu ft, 179.52 gal

3.1.5.43.

Answer.
6 ft

3.1.5.45.

Answer.
10 ft

3.1.5.47.

Answer.
192

3.1.5.49.

Answer.
100

3.1.5.51.

Answer.
Count the grids to find length, width, and height

3.1.5.53.

Answer.
Many answers are possible.

3.1.5.55.

Answer.
  1. 4 cu in, 18 sq in
  2. 16 sq in, 18 sq in

3.2 Exponents
3.2.6 Practice 3.2

3.2.6.1.

Answer.
\(8^5\)

3.2.6.3.

Answer.
\(16^2\)

3.2.6.5.

Answer.
\(4^8\)

3.2.6.7.

Answer.
\(0.5^3\)

3.2.6.9.

Answer.
\(3^4 \cdot 5^3 \cdot 10^2\)

3.2.6.11.

Answer.
\(2^3 \cdot 5^2 \cdot 3^3\)

3.2.6.13.

Answer.
\(2^3 \cdot 5\)

3.2.6.15.

Answer.
\(3^4\)

3.2.6.17.

Answer.
  1. 64 sq in
  2. 512 cu in

3.2.6.19.

Answer.
  1. 4000 sq cm
  2. 6 faces, 2400 sq cm
  3. 8000 cu cm

3.2.6.21.

Answer.
  1. \(\displaystyle 2\times 2 \times 2 = 8\)
  2. \(\displaystyle 5 \times 5 = 25\)
  3. \(\displaystyle 7 \times 7 = 49\)
  4. \(\displaystyle 6\)

3.2.6.23.

Answer.
  1. \(\displaystyle 2 \times 2 \times 2 \times 2 = 16\)
  2. \(\displaystyle 2\)
  3. \(\displaystyle 4 \times 4 \times 4 = 64\)
  4. \(\displaystyle 1 \times 1 \times 1 = 1\)

3.2.6.25.

Answer.
  1. \(\displaystyle 9 \times 9 = 81\)
  2. \(\displaystyle 6 \times 6 \times 6 = 216\)
  3. \(\displaystyle 10\)
  4. \(\displaystyle 12 \times 12 = 144\)

3.2.6.27.

Answer.
To multiply the number by copies of itself

3.2.6.29.

Answer.
  1. 10; 100; 1000; 10,000; 100,000
  2. 1 followed by 24 zeroes

3.2.6.31.

Answer.
  1. 6.76
  2. 10.24
  3. 117.649
  4. 0.02

3.2.6.33.

Answer.
  1. \(\displaystyle \dfrac{1}{4}\)
  2. \(\displaystyle \dfrac{1}{8}\)
  3. \(\displaystyle \dfrac{1}{16}\)
  4. \(\displaystyle \dfrac{1}{32}\)

3.2.6.35.

Answer.
  1. 0.01
  2. 0.001
  3. 0.0001
  4. 0.00001

3.2.6.37.

Answer.
  1. \(\displaystyle \dfrac{8}{27}\)
  2. \(\displaystyle \dfrac{27}{8}\)
  3. 0.64
  4. 1.44

3.2.6.39.

Answer.
No. \((\frac{1}{2})^2 = \frac{1}{4} \lt \frac{1}{2}\)

3.2.6.41.

Answer.
No

3.2.6.43.

Answer.
Yes

3.2.6.45.

Answer.
Yes

3.2.6.47.

Answer.
  1. 3-4-5 triangle with square on each side
  2. 9 sq cm, 16 sq cm, 25 sq cm

3.2.6.49.

Answer.
  1. 8-15-17 triangle with square on each side
  2. \(\displaystyle 8^2 + 15^2 = 64 + 225 = 289 = 17^2\)

3.2.6.51.

Answer.
  1. \(\displaystyle 12^7\)
  2. \(\displaystyle 19^8\)

3.2.6.53.

Answer.
  1. \(\displaystyle 7^3\)
  2. \(\displaystyle 15^6\)

3.2.6.55.

Answer.
We add the number of factors.

3.2.6.57.

Answer.
\(1 + 36\)

3.2.6.59.

Answer.
\(16 + 36\)

3.2.6.61.

Answer.
\(25 + 49\)

3.2.6.63.

Answer.
\(16 + 64\)

3.2.6.65.

Answer.
False

3.2.6.67.

Answer.
False

3.2.6.69.

Answer.
True

3.2.6.71.

Answer.
True

3.2.6.73.

Answer.
False

3.2.6.75.

Answer.
False

3.3 Units of Measure
3.3.6 Practice 3.3

3.3.6.1.

Answer.
A conversion factor is a fraction that is equal to 1. It is used to convert from one type of units to another.

3.3.6.3.

Answer.
A yard

3.3.6.4.

Answer.
An inch

3.3.6.7.

Answer.

3.3.6.9.

Answer.
A quart

3.3.6.11.

Answer.
  1. 2
  2. 8
  3. 5.5
  4. \(\displaystyle 5\frac{1}{3}\)
  5. \(\displaystyle \frac{1}{2}\)
  6. \(\displaystyle \frac{2}{3}\)

3.3.6.13.

Answer.
  1. 4
  2. 8
  3. 2.5
  4. 2.5
  5. 2.5
  6. 5

3.3.6.15.

Answer.
  1. 80 in
  2. \(6\frac{2}{3}\) ft
  3. \(2 \frac{2}{9}\) yd

3.3.6.17.

Answer.
114.3 cm

3.3.6.19.

Answer.
164.042 ft

3.3.6.21.

Answer.
  1. 30.48 cm
  2. 182.88 cm

3.3.6.23.

Answer.
Necklace cm in
Collar 32 12.5
Choker 38 15
Princess 45 17.75
Matinee 56 22
Opera 78 30.75
Lariat 120 47.25

3.3.6.25.

Answer.
30 ft, 10 yd, 54 sq ft, 6 sq yd

3.3.6.27.

Answer.
36 ft, 12 yd, 72 sq ft, 8 sq yd

3.3.6.29.

Answer.
Divide by 9

3.3.6.31.

Answer.
Lakeview Centre

3.3.6.33.

Answer.
  1. 1296
  2. \(\displaystyle \frac{1}{16}\)

3.3.6.35.

Answer.
  1. 1.196 sq yd, 10.764 sq ft
  2. 2368.06 sq ft

3.3.6.37.

Answer.
121.5

3.3.6.39.

Answer.

3.3.6.41.

Answer.
Country sq m sq ft Fraction
USA 214 2303.5 1.00
Australia 206 2217.4 0.96
Denmark 137 1474.7 0.64
France 113 1216.3 0.53
Spain 97 1044.1 0.45
Ireland 88 947.2 0.41
UK 76 818.1 0.36

3.3.6.43.

Answer.
  1. 36
  2. 9

3.3.6.45.

Answer.
  1. 10,000
  2. 1,000,000

3.3.6.47.

Answer.
24 cu yd

3.3.6.49.

Answer.
1000 liters

3.3.6.51.

Answer.
  1. 147 sq yd
  2. 98 cu yd

3.3.6.53.

Answer.
  1. 640
  2. 247.105
  3. 4840

3.3.6.55.

Answer.
  1. 100
  2. 258.999
  3. 2.47105

3.3.6.57.

Answer.
It uses a common conversion factor of 2 (instead of 10).

3.3.6.59.

Answer.
  1. \(1 \frac{9}{16}\) sq yd
  2. \(1 \frac{16}{64}\) cu yd

3.4 Circles and Spheres
3.4.7 Practice 3.4

3.4.7.1.

Answer.
The distance around the circle.

3.4.7.3.

Answer.
By dividing the circumference of a circle by its diameter.

3.4.7.5.

Answer.
More than \(\pi\)

3.4.7.7.

Answer.
\(C = \pi d\)

3.4.7.9.

Answer.
\(A = \pi r^2\)

3.4.7.11.

Answer.
50.27 in

3.4.7.13.

Answer.
3.77 m

3.4.7.15.

Answer.
9.55 yd

3.4.7.17.

Answer.
6.76 in

3.4.7.19.

Answer.
0.13 sq cm

3.4.7.21.

Answer.
1963.50 sq yd

3.4.7.23.

Answer.
33.5 cu m

3.4.7.25.

Answer.
0.004 cu cm

3.4.7.27.

Answer.
588.98 cu ft

3.4.7.29.

Answer.
201.06 sq ft

3.4.7.31.

Answer.
23 in

3.4.7.33.

Answer.
111,409.34 cu ft

3.4.7.35.

Answer.
452.39 sq ft

3.4.7.37.

Answer.
  1. 1237.8 ft
  2. 41.26 ft per min
  3. 0.47 mph

3.4.7.39.

Answer.
Area: 55.86 sq cm, perimeter: 37.42 cm

3.4.7.41.

Answer.
Area: 76.27 sq ft, perimeter: 34.85 ft

3.4.7.43.

Answer.
Area: 30.90 sq m, perimeter: 85.70 m

3.4.7.45.

Answer.
4.51 ft

3.4.7.47.

Answer.
530.14 sq ft

3.5 Large Numbers
3.5.7 Practice 3.5

3.5.7.1.

Answer.
60,000

3.5.7.3.

Answer.
275,000

3.5.7.5.

Answer.
4862.3

3.5.7.7.

Answer.
7,280,000,000,000

3.5.7.11.

Answer.
0.6

3.5.7.13.

Answer.
\(10^3\)

3.5.7.15.

Answer.
\(10^5\)

3.5.7.17.

Answer.
\(10^3\)

3.5.7.19.

Answer.
\(10^{17}\)

3.5.7.21.

Answer.
\(3.5 \times 10^6\)

3.5.7.23.

Answer.
\(2.76 \times 10^1\)

3.5.7.25.

Answer.
\(6.752 \times 10^4\)

3.5.7.27.

Answer.
\(7.92 \times 10^{24}\)

3.5.7.29.

Answer.
\(4.39 \times 10^{18}\)

3.5.7.31.

Answer.
\(3.92 \times 10^{24}\)

3.5.7.33.

Answer.
\(12,000\)

3.5.7.35.

Answer.
\(125\)

3.5.7.37.

Answer.
\(5.12 \times 10^{38}\)

3.5.7.39.

Answer.
\(1.33 \times 10^8\) sec, 1543.21 days

3.5.7.41.

Answer.
  1. \(\displaystyle 1.32 \times 10^{25}, ~3.825 \times 10^{22}\)
  2. 345 lb per cu ft

3.5.7.43.

Answer.
  1. \(\displaystyle 3.2 \times 10^4\)
  2. 104.8576; 32,000

3.5.7.45.

Answer.
  1. \(\displaystyle 5.28 \times 10^3\)
  2. \(\displaystyle 3.65 \times 10^2\)
  3. \(\displaystyle 6.048 \times 10^5\)
  4. \(\displaystyle 2.788 \times 10^7\)

3.5.7.47.

Answer.

3.5.7.49.

Answer.

3.5.7.51.

Answer.

3.5.7.53.

Answer.

3.5.7.55.

Answer.

3.5.7.57.

Answer.

3.5.7.59.

Answer.
  1. 695,700 km
  2. \(1.41 \times 10^{18}\) cu km; 1,410,000,000,000,000,000 cu km

4 Calculation
4.1 Adding and Subtracting Fractions
4.1.7 Practice 4.1

4.1.7.1.

Answer.
\(\dfrac{1}{6}\) More slices must be smaller.

4.1.7.3.

Answer.
Their pieces aren’t the same size.

4.1.7.5.

Answer.
\(\dfrac{6}{8},~\dfrac{9}{12},~\dfrac{12}{16}\)

4.1.7.7.

Answer.
\(\dfrac{14}{10},~\dfrac{21}{15},~\dfrac{28}{20}\)

4.1.7.9.

Answer.
larger than

4.1.7.11.

Answer.
smaller than

4.1.7.13.

Answer.
\(1\)

4.1.7.15.

Answer.
\(\dfrac{2}{5}\)

4.1.7.17.

Answer.
\(\dfrac{4}{3}\)

4.1.7.19.

Answer.
\(\dfrac{3}{8}\)

4.1.7.21.

Answer.
Fractions with different denominators

4.1.7.23.

Answer.
\(\dfrac{1}{4} + \dfrac{1}{4} = \dfrac{2}{4} = \dfrac{1}{2}\)

4.1.7.25.

Answer.
24

4.1.7.27.

Answer.
36

4.1.7.29.

Answer.
  1. 8
  2. \(\dfrac{6}{8}\) and \(\dfrac{3}{8}\)

4.1.7.31.

Answer.
  1. 12
  2. \(\dfrac{2}{12}\) and \(\dfrac{3}{12}\)

4.1.7.33.

Answer.
  1. 12
  2. \(\dfrac{8}{12}\) and \(\dfrac{5}{12}\)

4.1.7.35.

Answer.
  1. 10
  2. \(\dfrac{6}{10}\) and \(\dfrac{5}{10}\)

4.1.7.37.

Answer.
  1. 24
  2. \(\dfrac{20}{24}\) and \(\dfrac{9}{24}\)

4.1.7.39.

Answer.
  1. 30
  2. \(\dfrac{9}{30}\) and \(\dfrac{4}{30}\)

4.1.7.41.

Answer.
\(\dfrac{11}{8}\)

4.1.7.43.

Answer.
\(\dfrac{1}{2}\)

4.1.7.45.

Answer.
\(\dfrac{7}{6}\)

4.1.7.47.

Answer.
\(\dfrac{1}{12}\)

4.1.7.49.

Answer.
\(\dfrac{19}{18}\)

4.1.7.51.

Answer.
\(\dfrac{8}{15}\)

4.1.7.53.

Answer.
\(3 \frac{5}{12}\) hr = 3 hr 25 min

4.1.7.55.

Answer.
\(\dfrac{13}{40}\)

4.1.7.57.

Answer.
\(\dfrac{1}{2}\) is larger than \(\dfrac{5}{12}\)

4.1.7.59.

Answer.
False

4.1.7.62.

Answer.
True

4.1.7.63.

Answer.
\(\dfrac{11}{4}\)

4.1.7.65.

Answer.
\(\dfrac{32}{5}\)

4.1.7.67.

Answer.
\(\dfrac{2}{5},~\dfrac{3}{5} \lt \dfrac{3}{2}\)

4.1.7.69.

Answer.
\(\dfrac{7}{9},~\dfrac{2}{9} \lt \dfrac{2}{7}\)

4.2 Multiplying and Dividing Fractions
4.2.6 Practice 4.2

4.2.6.1.

Answer.
\(\dfrac{1}{4} \times \dfrac{8}{1} = \dfrac{1 \times 8}{4 \times 1} = \dfrac{8}{4}\)

4.2.6.3.

Answer.
Dividing by 7 finds \(\dfrac{1}{7}\) of the number; multiplying by 3 finds \(\dfrac{3}{7}\text{.}\)

4.2.6.5.

Answer.
\(2\frac{1}{4}\) acres

4.2.6.7.

Answer.

4.2.6.9.

Answer.

4.2.6.11.

Answer.
\(\dfrac{2}{27}\)

4.2.6.13.

Answer.
\(\dfrac{1}{3}\)

4.2.6.15.

Answer.
\(35\dfrac{1}{2}\) in

4.2.6.17.

Answer.
\(50\dfrac{15}{16}\) in

4.2.6.19.

Answer.
  1. greater, \(\dfrac{10}{9} \gt 1\)
  2. less, \(\dfrac{7}{8} \lt 1\)

4.2.6.21.

Answer.
\(\dfrac{7}{8} \div \dfrac{1}{3}\)

4.2.6.23.

Answer.
There are five fifths in each whole.
How many fifths in 4

4.2.6.25.

Answer.
24

4.2.6.27.

Answer.
15

4.2.6.29.

Answer.
\(\dfrac{4}{3}\)

4.2.6.31.

Answer.
\(10\)

4.2.6.33.

Answer.
\(\dfrac{1}{6}\)

4.2.6.35.

Answer.
\(\dfrac{2}{9}\)

4.2.6.37.

Answer.
We can only add two fractions if they have the same denominator.

4.2.6.39.

Answer.
To add two like fractions, we add their numerators and keep the same denominator.

4.2.6.41.

Answer.
\(1500, ~\dfrac{5}{6}\)

4.2.6.43.

Answer.
12

4.2.6.45.

Answer.
More, \(\dfrac{1}{8}\)

4.2.6.47.

Answer.
Area: \(1\frac{31}{32}\) sq cm, Perimeter: \(7\frac{1}{4}\) cm

4.2.6.49.

Answer.
Area: \(40\frac{11}{16}\) sq in, Perimeter: \(26\) in

4.2.6.51.

Answer.
  1. \(\displaystyle \dfrac{8}{7}\)
  2. \(\displaystyle \dfrac{16}{7}\)

4.2.6.53.

Answer.
  1. \(\displaystyle \dfrac{4}{15}\)
  2. \(\displaystyle \dfrac{19}{15}\)

4.2.6.55.

Answer.
\(2\frac{3}{5}\)

4.2.6.57.

Answer.
\(7\frac{1}{6}\)

4.2.6.59.

Answer.
\(0.1 = \dfrac{1}{10}\)

4.2.6.61.

Answer.
  1. 60
  2. 60
  3. \(\displaystyle \dfrac{15}{16} = 1 - \dfrac{1}{16}\)

4.2.6.63.

Answer.
15% \(= \dfrac{10}{100} + \dfrac{5}{100} = \dfrac{1}{10} + \dfrac{1}{2} \left(\dfrac{1}{10}\right)\)

4.2.6.65.

Answer.
6 in

4.2.6.67.

Answer.
\(42 \frac{2}{3}\) m

4.2.6.69.

Answer.
\(\dfrac{5}{4}\) cm

4.2.6.71.

Answer.
\(10 \frac{1}{3}\) ft

4.3 Roots and Radicals
4.3.6 Practice 4.3

4.3.6.1.

Answer.
  1. 6
  2. 7
  3. 1

4.3.6.3.

Answer.
  1. 8
  2. 9
  3. 12

4.3.6.5.

Answer.
To square q number, we multiply it by itself. The square root of a number is a number that, when squared, gives the original number. \(9^2 = 81; \sqrt{9} = 3\)

4.3.6.7.

Answer.
A radical sign indicates the square root of the number inside.

4.3.6.9.

Answer.
  1. 7
  2. 13

4.3.6.11.

Answer.
  1. 11
  2. 12

4.3.6.13.

Answer.
  1. \(\displaystyle \dfrac{1}{4}\)
  2. \(\displaystyle \dfrac{1}{5}\)

4.3.6.15.

Answer.
  1. \(\displaystyle \dfrac{14}{5}\)
  2. \(\displaystyle \dfrac{2}{17}\)

4.3.6.17.

Answer.
\(N\) 1 2 3 4 5 6 7 8 9 10
\(\sqrt{N}\) 1 1.414 1.732 2 2.236 2.449 2.646 2.828 3 3.162

4.3.6.19.

Answer.
  1. 6.971
  2. 5.413

4.3.6.21.

Answer.
  1. 1.183
  2. 1.342

4.3.6.23.

Answer.
  1. 20.479
  2. 28.914

4.3.6.25.

Answer.
193.8 mi

4.3.6.27.

Answer.
9.61 sec

4.3.6.29.

Answer.
\(\dfrac{5}{4}, ~~ 2, ~~ 2.3, ~~ \sqrt{8}\)

4.3.6.31.

Answer.
\(\sqrt{6}, ~~ 3, ~~2\sqrt{3}, ~~ \dfrac{23}{6}\)

4.3.6.33.

Answer.
85

4.3.6.35.

Answer.
168

4.3.6.37.

Answer.
4082

4.3.6.39.

Answer.
The original number. \(\sqrt{4^2} = 4\)

4.3.6.41.

Answer.
  1. 144
  2. 9

4.3.6.43.

Answer.
  1. 81
  2. 16

4.3.6.45.

Answer.
  1. 17
  2. 39

4.3.6.47.

Answer.
  1. 453
  2. 208

4.3.6.49.

Answer.
\(100\)

4.3.6.51.

Answer.
\(\dfrac{1}{7}\)

4.3.6.53.

Answer.
\(0.5\)

4.3.6.55.

Answer.
15 in

4.3.6.57.

Answer.
24 cm

4.3.6.59.

Answer.
14.422

4.3.6.61.

Answer.
42.650

4.3.6.63.

Answer.
26 ft

4.3.6.65.

Answer.
13.86 ft

4.3.6.67.

Answer.
4 ft

4.4 Negative Numbers
4.4.7 Practice 4.4

4.4.7.1.

Answer.
\(-100\)

4.4.7.3.

Answer.
\(2\)

4.4.7.5.

Answer.
\(-450\)

4.4.7.7.

Answer.
\(-3,000,000\)

4.4.7.9.

Answer.
\(-384\)

4.4.7.11.

Answer.

4.4.7.13.

Answer.

4.4.7.15.

Answer.

4.4.7.17.

Answer.

4.4.7.19.

Answer.
\(-4\)

4.4.7.21.

Answer.
\(15\)

4.4.7.23.

Answer.
\(2\)

4.4.7.25.

Answer.
\(-7\)

4.4.7.27.

Answer.
  2. 3

4.4.7.29.

Answer.
  2. \(\displaystyle -8\)

4.4.7.31.

Answer.
  1. \(\displaystyle -3 \degree\)
  2. January, \(-11 \degree\text{;}\) July, \(17\degree\)
  3. \(22 \degree\)>

4.4.7.33.

Answer.

4.4.7.35.

Answer.

4.4.7.37.

Answer.

4.4.7.39.

Answer.
\(6.5 \gt 6.07, 6.07 \lt 6.5\)

4.4.7.41.

Answer.
\(-12 \lt -2, -2 \gt -12\)

4.4.7.43.

Answer.
\(\dfrac{-3}{4} \lt \dfrac{-1}{2}, \dfrac{-1}{2} \gt \dfrac{-3}{4}\)

4.4.7.45.

Answer.
True

4.4.7.47.

Answer.
False

4.4.7.49.

Answer.
True

4.4.7.51.

Answer.
False

4.4.7.53.

Answer.
True

4.4.7.55.

Answer.
  1. Country 1900 2000 Change
    United States \(193\) \(149\) \(-44\)
    Russia \(33\) \(54\) \(21\)
    India \(26\) \(38\) \(12\)
    France \(24\) \(21\) \(-3\)
    Britain \(19\) \(11\) \(-8\)
  2. Subtraction
  3. Whether the number increased or decreased

4.5 Order of Operations
4.5.8 Practice 4.5

4.5.8.1.

Answer.
5

4.5.8.3.

Answer.
14

4.5.8.5.

Answer.
5.8

4.5.8.7.

Answer.
6

4.5.8.9.

Answer.
73

4.5.8.11.

Answer.
24

4.5.8.13.

Answer.
  1. \(\displaystyle 18\)
  2. \(\displaystyle 50\)

4.5.8.15.

Answer.
  1. \(\displaystyle 3\)
  2. \(\displaystyle 18\)

4.5.8.17.

Answer.
  1. \(\displaystyle 2\)
  2. \(\displaystyle 8\)

4.5.8.19.

Answer.
  1. \(\displaystyle 42\)
  2. \(\displaystyle 12\)

4.5.8.21.

Answer.
  1. \(\displaystyle 2\)
  2. \(\displaystyle 18\)

4.5.8.23.

Answer.
  1. \(\displaystyle 3(5 + 8)\)
  2. \(\displaystyle 3 \cdot 5 + 8\)

4.5.8.25.

Answer.
  1. \(\displaystyle 25 - (12 - 8)\)
  2. \(\displaystyle (25 - 12) - 8\)

4.5.8.27.

Answer.
27

4.5.8.29.

Answer.
24

4.5.8.31.

Answer.
54

4.5.8.33.

Answer.
12

4.5.8.35.

Answer.
23

4.5.8.37.

Answer.
8

4.5.8.39.

Answer.
13

4.5.8.41.

Answer.
4

4.5.8.43.

Answer.
52

4.5.8.45.

Answer.
2

4.5.8.47.

Answer.
7

4.5.8.49.

Answer.
28

4.5.8.51.

Answer.
48

4.5.8.53.

Answer.
5

4.5.8.55.

Answer.
12

4.5.8.57.

Answer.
6

4.5.8.59.

Answer.
  1. \(\displaystyle 5\)
  2. \(\displaystyle 7\)

4.5.8.61.

Answer.
  1. \(\displaystyle 18\)
  2. \(\displaystyle 18\)

4.5.8.63.

Answer.
  1. \(\displaystyle \dfrac{4}{7}\)
  2. \(\displaystyle \dfrac{4}{7}\)

4.5.8.65.

Answer.
  1. \(\displaystyle \dfrac{9}{4}\)
  2. \(\displaystyle \dfrac{9}{2}\)

4.5.8.67.

Answer.
  1. \(\displaystyle 6\)
  2. \(\displaystyle 18\)

4.5.8.69.

Answer.
10.69

4.5.8.71.

Answer.
0.69

4.5.8.73.

Answer.
5.76

5 Using Variables
5.1 Working with Variables
5.1.8 Practice 5.1

5.1.8.1.

Answer.
Terms in which the variable parts are the same. \(2x,~ 3x; ~~ 2x,~ 3y\)

5.1.8.3.

Answer.
Check to see if they both simplify to the same expression.

5.1.8.5.

Answer.
It does not change the result.

5.1.8.7.

Answer.
False

5.1.8.9.

Answer.
True

5.1.8.11.

Answer.
True

5.1.8.13.

Answer.
Many answers are possible.

5.1.8.15.

Answer.
Many answers are possible.

5.1.8.17.

Answer.
In \(2x\) we multiply the variable by 2; in \(x^2\) we multiply the variable by itself.

5.1.8.19.

Answer.
  1. In \(4x + 7x\) we add terms, and in \(4(7x)\) we multiply coefficients.
  2. \(\displaystyle 33; ~84\)

5.1.8.21.

Answer.
  1. \(\displaystyle 6y\)
  2. \(\displaystyle 4x\)

5.1.8.23.

Answer.
  1. \(\displaystyle 16b\)
  2. \(\displaystyle 0\)

5.1.8.25.

Answer.
  1. \(\displaystyle 48W\)
  2. \(\displaystyle K\)

5.1.8.27.

Answer.
  1. \(\displaystyle 3x\)
  2. \(\displaystyle 7z\)

5.1.8.29.

Answer.
\(2t+3\)

5.1.8.31.

Answer.
\(4y+6\)

5.1.8.33.

Answer.
\(16st+s\)

5.1.8.35.

Answer.
\(30d\)

5.1.8.37.

Answer.
\(4a\)

5.1.8.39.

Answer.
\(10m\)

5.1.8.41.

Answer.
\(3w^3\)

5.1.8.43.

Answer.
\(13bc\)

5.1.8.45.

Answer.
\(0\)

5.1.8.47.

Answer.
  1. \(\displaystyle 2z\)
  2. \(\displaystyle x^2\)

5.1.8.49.

Answer.
  1. cannot be simplified
  2. \(\displaystyle x^3\)

5.1.8.51.

Answer.
  1. cannot be simplified
  2. \(\displaystyle x^5\)

5.1.8.53.

Answer.
  1. cannot be simplified
  2. \(\displaystyle x^2y\)

5.1.8.55.

Answer.
  1. cannot be simplified
  2. \(\displaystyle 6xy\)

5.1.8.57.

Answer.
In \(2x^3\) only \(x\) is cubed; in \((2x)^3\text{,}\) \(2x\) is cubed. For \(x=10,~ 2x^3 = 2000\) and \((2x)^3= 8000\text{.}\)

5.1.8.59.

Answer.
  1. \(\displaystyle 18\)
  2. \(\displaystyle 18\)
  3. \(\displaystyle 81\)
\(a^2+a^2\) and \(2a^2\) are equivalent.

5.1.8.61.

Answer.
  1. \(\displaystyle 150\)
  2. \(\displaystyle 30\)
  3. \(\displaystyle 150\)
\(2v(3v)\) and \(6v^2\) are equivalent.

5.1.8.63.

Answer.
  1. \(\displaystyle 160\)
  2. \(\displaystyle 40\)
  3. \(\displaystyle 160\)
\(5w^2(2w^2)\) and \(10w^4\) are equivalent.

5.1.8.65.

Answer.
  1. \(\displaystyle 6\)
  2. \(\displaystyle 42\)

5.1.8.67.

Answer.
  1. \(\displaystyle 65\)
  2. \(\displaystyle 58\)

5.2 More Algebraic Expressions
5.2.5 Practice 5.2

5.2.5.1.

Answer.
A formula is an equation that relates two or more variables.

5.2.5.3.

Answer.
Divide by 100.

5.2.5.5.

Answer.
\(A=\dfrac{S}{n}\text{;}\) \(S\) is the sum of values, \(n\) is the number of values

5.2.5.7.

Answer.
\(I=Prt\text{;}\) \(P\) is the principal, \(r\) is the interest rate, \(t\) is the time

5.2.5.9.

Answer.
\(P=rW\text{;}\) \(r\) is the percentage rate, \(W\) is the whole

5.2.5.11.

Answer.
$1365

5.2.5.13.

Answer.
84 miles

5.2.5.15.

Answer.
0.75 lbs per wk

5.2.5.17.

Answer.
$12.50

5.2.5.19.

Answer.
$525

5.2.5.21.

Answer.
4, 19, 54

5.2.5.23.

Answer.
18, 14, 8

5.2.5.25.

Answer.
0.5, 2, 4.75

5.2.5.27.

Answer.
9.6, 32, 60

5.2.5.29.

Answer.
0.14, 0.5, 0.8

5.2.5.31.

Answer.
  1. Add 30 times the nuber of minutes elapsed to 75.
  2. \(\displaystyle 75 + 30m\)

5.2.5.33.

Answer.
  1. Add half of luisa’s expenses to 800.
  2. \(\displaystyle 800 + 0.5a\)

5.2.5.35.

Answer.
  1. Subtract Mildred’s pints from 80 and divide the result by 4.
  2. \(\displaystyle \dfrac{80-M}{4}\)

5.2.5.37.

Answer.
\(12-2t\)

5.2.5.39.

Answer.
\(2t-12\)

5.2.5.41.

Answer.
\(\dfrac{12}{m-3}\)

5.2.5.43.

Answer.
\(\dfrac{m-3}{12}\)

5.2.5.45.

Answer.
\(400 + 30u\)

5.2.5.47.

Answer.
\(\dfrac{R-560}{4}\)

5.2.5.49.

Answer.
\(2000-60p\)

5.2.5.51.

Answer.
\(L+W\)

5.2.5.53.

Answer.
\(bh\)

5.2.5.55.

Answer.
\(\dfrac{c}{w}\)

5.2.5.57.

Answer.
\(\dfrac{d}{t}\)

5.2.5.59.

Answer.
\(7w+5\)

5.2.5.61.

Answer.
\(r+u-60\)

5.2.5.63.

Answer.
\(\dfrac{1}{2}(r+3)\)

5.2.5.65.

Answer.
24.4 ft

5.2.5.67.

Answer.
37°

5.2.5.69.

Answer.
525 sq ft

5.2.5.71.

Answer.
$65,000

5.2.5.73.

Answer.
5

5.2.5.75.

Answer.
280

5.2.5.77.

Answer.
26

5.2.5.79.

Answer.
5

5.2.5.81.

Answer.
1.2

5.3 Problem Solving
5.3.4 Practice 5.3

5.3.4.1.

Answer.
  1. \(\displaystyle 1500 = R - 215\)
  2. $1715

5.3.4.3.

Answer.
  1. \(\displaystyle 0.36W = 162\)
  2. 450

5.3.4.5.

Answer.
  1. \(\displaystyle 98.80 = 1300r\)
  2. 7.6%

5.3.4.7.

Answer.
  1. \(\displaystyle 98.80 = 1300r\)
  2. 7.6%

5.3.4.9.

Answer.
  1. \(\displaystyle 171=0.095P\)
  2. $1800

5.3.4.11.

Answer.
  1. \(\displaystyle 10 = 2.6t\)
  2. 3,85 min

5.3.4.13.

Answer.
\(6n = 162\)

5.3.4.15.

Answer.
\(n-24 = 38\)

5.3.4.17.

Answer.
\(\dfrac{n}{2.5} = 6.6\)

5.3.4.19.

Answer.
\(n+15.3 = 20\)

5.3.4.21.

Answer.
  1. money before the Fair: \(m\)
  2. \(\displaystyle m-24.50 = 39.75\)
  3. $64.75

5.3.4.23.

Answer.
  1. hourly wage: \(w\)
  2. \(\displaystyle 22w = 149.60\)
  3. $6.50

5.3.4.25.

Answer.
  1. profit: \(P\)
  2. \(\displaystyle \dfrac{P}{8} = 64.35\)
  3. $514.80

5.3.4.27.

Answer.
  1. calories in a cheeseburger: \(c\)
  2. \(\displaystyle c+342 = 1070\)

5.3.4.29.

Answer.
  1. fortune: \(M\)
  2. \(\displaystyle \dfrac{M}{4} = 350,000\)

5.3.4.31.

Answer.
  1. account balance: \(b\)
  2. \(\displaystyle b - 2378 = 1978\)

5.3.4.33.

Answer.
  1. percent on rent: \(p\)
  2. \(\displaystyle 1800p = 576\)

5.3.4.35.

Answer.
  1. total acres: \(A\)
  2. \(\displaystyle \dfrac{A}{50} = 222,960\)

5.3.4.37.

Answer.
\(d = 150t\)

5.3.4.39.

Answer.
\(I = 64t\)

5.3.4.41.

Answer.
\(I = 1800r\)

5.3.4.43.

Answer.
\(G = 0.20W\)

5.3.4.45.

Answer.
\(A = \dfrac{S}{12}\)

5.3.4.47.

Answer.
  1. Danny’s weight: \(D\text{,}\) Brenda’s weight: \(B\)
  2. \(\displaystyle D = B + 32\)

5.3.4.49.

Answer.
  1. Trinh’s age: \(T\text{,}\) Loc’s age: \(L\)
  2. \(\displaystyle T = L - 14\)

5.3.4.51.

Answer.
  1. number of coats: \(c\text{,}\) number of buttons: \(b\)
  2. \(\displaystyle b = 3c\)

5.3.4.53.

Answer.
  1. rates now: \(r\text{,}\) rates five years ago: \(p\)
  2. \(\displaystyle r = 2p\)

5.3.4.55.

Answer.
  1. \(\displaystyle w = t - 15\)
  2. 75; 110

5.3.4.57.

Answer.
  1. \(\displaystyle H = 4D\)
  2. 44; 16

5.4 More Equations
5.4.6 Practice 5.4

5.4.6.1.

Answer.
11

5.4.6.3.

Answer.
5

5.4.6.5.

Answer.
3

5.4.6.7.

Answer.
5

5.4.6.9.

Answer.
28

5.4.6.11.

Answer.
6

5.4.6.13.

Answer.
10

5.4.6.15.

Answer.
3

5.4.6.17.

Answer.
11

5.4.6.19.

Answer.
0.55

5.4.6.21.

Answer.
100

5.4.6.23.

Answer.
13.608

5.4.6.25.

Answer.
\(e + 0.15p\)

5.4.6.27.

Answer.
\(0.62(t + h)\)

5.4.6.29.

Answer.
  1. \(x\) 2 4 6 8 10 12
    \(3x-6\) 0 6 12 18 24 30
  2. 6

5.4.6.31.

Answer.
  1. \(x\) 4 6 8 10 12 14 16
    \(\dfrac{4+2x}{3}\) 4 \dfrac{16}{3} \dfrac{20}{3} 8 \dfrac{28}{3} \dfrac{32}{3} 12
  2. 16

5.4.6.33.

Answer.
\(3n-12=30\)

5.4.6.35.

Answer.
\(\dfrac{n}{3} - 12 = 30\)

5.4.6.37.

Answer.
\(4x+20 = 80\)

5.4.6.39.

Answer.
\(\dfrac{x}{4} +20 = 80\)

5.4.6.41.

Answer.
25 m

5.4.6.43.

Answer.
300 mi

5.4.6.45.

Answer.
6%

5.4.6.47.

Answer.
10 in

5.4.6.49.

Answer.
  1. \(\displaystyle 72+6h\)
  2. In 4 hours

5.4.6.51.

Answer.
  1. \(\displaystyle 50+\dfrac{P}{12}\)
  2. $216

5.4.6.53.

Answer.
  1. \(\displaystyle \dfrac{S-60}{15}\)
  2. $405

5.4.6.55.

Answer.
  1. \(\displaystyle 20+0.02B\)
  2. $16,000

5.4.6.57.

Answer.
  1. number of DVD’s: \(n\)
  2. \(\displaystyle 7n+2=30\)
  3. He bought 4 DVD’s.

5.4.6.59.

Answer.
  1. hours to work: \(h\)
  2. \(\displaystyle 30 + 8h = 86\)
  3. She must work for 7 hours.

5.4.6.61.

Answer.
  1. cost of tripod: \(c\)
  2. \(\displaystyle 4c+9 = 269\)
  3. The tripod costs $65.

5.4.6.63.

Answer.
  1. adjusted income: \(I\)
  2. \(\displaystyle 600 + 0.07I = 2840\)
  3. Her adjusted income was $32,000.

5.4.6.65.

Answer.
28

5.4.6.67.

Answer.
20

5.4.6.69.

Answer.
29.36

5.4.6.71.

Answer.
14

5.4.6.73.

Answer.
8

5.4.6.75.

Answer.
8

5.4.6.77.

Answer.
3

5.5 Graphs
5.5.6 Practice 5.5

5.5.6.1.

Answer.
  1. $1000
  2. March, July, November
  3. June, $1500
  4. July

5.5.6.3.

Answer.
  1. 1,200,000
  2. 1973
  3. 5,900,000
  4. 800,000

5.5.6.5.

Answer.
  2. What feature of the original bar graph could be considered misleading?

5.5.6.7.

Answer.
  2. 1982, 1989
  3. 1981, 1986
  4. 8.5%

5.5.6.9.

Answer.
  2. The number of people who agree with the statement is decreasing.
  3. Some people are undecided.

5.5.6.11.

Answer.
By the height of the bar.

5.5.6.13.

Answer.
\(H\)

5.5.6.15.

Answer.
The values of two related variables

5.5.6.17.

Answer.
1) Make a table of values, 2) Scale the axes, 3) Plot points and connect them

5.5.6.19.

Answer.
\(h=4, W=16.\) A chocolate bunny that is 4 inches tall weighs 16 ounces.

5.5.6.21.

Answer.
  1. \(x\) 0 20 40 60
    \(y\) 70 50 30 10
  2. \(\displaystyle y = 70 - x\)

5.5.6.23.

Answer.
  1. \(p\) 20 50 80 120
    \(k\) 0 30 60 100
  2. \(\displaystyle y = p - 20\)

5.5.6.24.

Answer.

5.5.6.25.

Answer.
  1. \(r\) 2 3 5 6
    \(p\) 3 4.50 7.50 9
  2. \(\displaystyle p = 1.50r\)

5.5.6.27.

Answer.
  1. \(r\) 20 36 42 50
    \(p\) 3 5.40 6.30 7.20
  2. \(t = 0.15b\text{.}\)

5.5.6.29.

Answer.
\(v\) \(t\)
30 20
50 12
60 10
100 6
120 5
150 4
200 3
300 2
  1. 12 hr
  2. 200 mph

5.5.6.31.

Answer.
\(h\) \(d\)
5000 86.3
10,000 122
15,000 149.4
20,000 172.5
25,000 192.9
30,000 211.3
  1. 122 mi
  2. 6719 ft

5.5.6.33.

Answer.
  1. Month Sales
    April \(m=0\) 40
    May \(m=1\) 20
    June \(m=2\) 10
    July \(m=3\) 5
    August \(m=4\) 2.5
    September \(m=5\) 1.25
    October \(m=6\) 0.625

6 Core Concepts
6.1 Ratios
6.1.6 Practice 6-1

6.1.6.1.

Answer.
  1. Subtraction
  2. Division?

6.1.6.3.

Answer.
The length should be \(\frac{3}{2}\) of the width.

6.1.6.5.

Answer.
The deep end is 9 feet deeper than the shallow end.

6.1.6.7.

Answer.
  1. The ratio of \(a\) to \(b\)
  2. Divide \(a\) by \(b\)

6.1.6.9.

Answer.
10 and 16, 15 and 24, 20 and 32

6.1.6.11.

Answer.
It is greater than 1.

6.1.6.13.

Answer.
  1. \(\displaystyle \dfrac{3}{4}\)
  2. \(\displaystyle \dfrac{4}{3}\)
  3. \(\displaystyle \dfrac{3}{7}, ~\dfrac{4}{7}\)
  4. 48
  5. 45

6.1.6.15.

Answer.
\(\dfrac{4}{3}\)

6.1.6.17.

Answer.
  1. \(\displaystyle \dfrac{2}{7}\)
  2. \(\displaystyle \dfrac{6}{23}\)

6.1.6.19.

Answer.
\(\dfrac{2}{3}\)

6.1.6.21.

Answer.
  1. \(\displaystyle \dfrac{3}{250}\)
  2. \(\displaystyle \dfrac{247}{3}\)
  3. 1.2%

6.1.6.23.

Answer.
  1. Divide the numerator by the denominator
  2. Multiply by 100

6.1.6.25.

Answer.
0.262

6.1.6.27.

Answer.
0.625

6.1.6.29.

Answer.
0.6

6.1.6.31.

Answer.
Harriet

6.1.6.33.

Answer.
1.618

6.1.6.35.

Answer.
  1. 48 mpg
  2. 720 mi

6.1.6.37.

Answer.
  1. 8 min per mile
  2. \(\frac{1}{8}~\) mile per min

6.1.6.39.

Answer.
72 sq ft per hr

6.1.6.41.

Answer.
  1. 6.5 cents per dollar
  2. 6.5%
  3. $13

6.1.6.43.

Answer.
  1. \(\displaystyle \dfrac{192}{15} = \dfrac{84}{5}\)
  2. $12.80 per hour

6.2 Proportion
6.2.6 Practice 6-2

6.2.6.1.

Answer.
A quantity that takes on different values in different situations.

6.2.6.3.

Answer.
Build-up strategy and unit rate strategy

6.2.6.5.

Answer.
  1. \(\vphantom{\dfrac{1}{2}}\)Carbonated water (oz) 32 64 96
    \(\vphantom{\dfrac{1}{2}}\)Secret Syrup (oz) 3 6 9
  2. Yes

6.2.6.7.

Answer.
  1. \(\vphantom{\dfrac{1}{2}}\)Pages 25 50 75
    \(\vphantom{\dfrac{1}{2}}\)Thickness (mm) 7 8> 9
  2. No

6.2.6.9.

Answer.
20 oz

6.2.6.11.

Answer.
32 in

6.2.6.13.

Answer.
6.5 mi

6.2.6.15.

Answer.
63\(\frac{1}{3}\) ft

6.2.6.17.

Answer.
86

6.2.6.19.

Answer.
21 gal

6.2.6.21.

Answer.
He will not run at the same rate for the whole hour.

6.2.6.23.

Answer.
Her rate of growth will decrease.

6.2.6.25.

Answer.
20 hrs

6.2.6.27.

Answer.
$17.60

6.2.6.29.

Answer.
  1. \(\vphantom{\dfrac{1}{2}}\)Side length (cm) 2 5 8 11
    \(\vphantom{\dfrac{1}{2}}\)Perimeter (cm) 8 20 32 44
  3. Yes

6.2.6.31.

Answer.
  1. \(\vphantom{\dfrac{1}{2}}\)Side length (m) 2 5 6 8
    \(\vphantom{\dfrac{1}{2}}\)Area (sq cm) 4 25 36 64
  3. No

6.3 Slope
6.3.8 Practice 6-3

6.3.8.1.

Answer.
\(k=3h\)

6.3.8.3.

Answer.
No

6.3.8.5.

Answer.
No

6.3.8.7.

Answer.
No

6.3.8.9.

Answer.
No

6.3.8.11.

Answer.
No

6.3.8.13.

Answer.
Yes

6.3.8.15.

Answer.
  1. quotient
  2. multiple

6.3.8.17.

Answer.
  1. The quotient of two proportional variables
  2. Divide one variable by the other

6.3.8.19.

Answer.
  1. \(\displaystyle C = 0,04S\)
  2. $8000

6.3.8.21.

Answer.
Subtract the old value from the new value

6.3.8.23.

Answer.
Change in output value divided by change in input value, \(\dfrac{\Delta y}{\Delta y}\)

6.3.8.25.

Answer.
  1. $300
  2. 10 weeks
  3. $50 per week
  4. The rate at which Lynette’s savings increases

6.3.8.27.

Answer.
  1. 5 lbs, 10 lbs
  2. 2.5 lbs per month

6.3.8.29.

Answer.
  1. Cost per pound
  2. $1.50 per lb
  3. $30

6.3.8.31.

Answer.
  1. \(\displaystyle \frac{3}{2}\)
  2. not as steep

6.3.8.33.

Answer.
  1. 25
  2. 75

6.3.8.35.

Answer.
  1. 3
  2. 4.5

6.3.8.37.

Answer.

6.3.8.39.

Answer.

6.3.8.41.

Answer.
  1. -75 miles per hour
  2. The rate at which the distance to home decreases

6.4 Similarity
6.4.7 Practice 6-4

6.4.7.1.

Answer.
Something to multiply by.

6.4.7.3.

Answer.

6.4.7.5.

Answer.

6.4.7.7.

Answer.
\(\dfrac{5}{8}\)

6.4.7.9.

Answer.

6.4.7.11.

Answer.
\(\dfrac{5}{4}\)

6.4.7.13.

Answer.
\(\dfrac{17}{11} \not= \)

6.4.7.15.

Answer.
... and their corresponding angles are equal.

6.4.7.17.

Answer.

6.4.7.19.

Answer.
\(\angle A = \angle B = 37 \degree\)

6.4.7.21.

Answer.
\(\angle A = \angle B = \angle C = 45 \degree, ~ d=5\)

6.4.7.23.

Answer.
\(\angle A = 60 \degree, ~ w=3.5\)

6.4.7.25.

Answer.
\(h=12\)

6.4.7.27.

Answer.
(b) and (d)

6.4.7.29.

Answer.
Yes, The third angles must also be equal.

6.4.7.31.

Answer.
Yes. The sides are proportional.

6.4.7.33.

Answer.
Yes, Corresponding angles are equal.

6.4.7.35.

Answer.
(b) and (e)

6.4.7.37.

Answer.
(b) and (e)

6.4.7.39.

Answer.
  1. \(\displaystyle \dfrac{3}{4}\)
  2. 21

6.4.7.41.

Answer.
  1. \(\displaystyle \dfrac{5}{4}\)
  2. 2.5 mm

6.4.7.43.

Answer.
  1. \(1\dfrac{3}{4}\) in
  2. \(\displaystyle \dfrac{1}{144}\)

6.4.7.45.

Answer.
  1. 2.5 in
  2. \(\displaystyle \dfrac{1}{120}\)

6.4.7.47.

Answer.
  1. \(6\dfrac{2}{3}\) ft
  2. 8

6.4.7.49.

Answer.
  1. 0.878
  2. 153.64 ft

6.4.7.51.

Answer.
  2. 7.5

6.4.7.53.

Answer.
  2. 15

6.5 More About Similarity
6.5.3 Practice 6-5

6.5.3.1.

Answer.
  1. 2
  2. 4
  3. 3
  4. 9
  5. 6 sq cm, 24 sq cm, 54 sq cm

6.5.3.3.

Answer.
Base Height Perimeter Area
Original Rectangle 4 8 24 32
Enlarged by 50% 6 12 36 72
Enlarged by 100% 8 16 46 128
Enlarged by 25% 5 10 30 50

6.5.3.5.

Answer.
  1. 2.25
  2. 33.75 sq in

6.5.3.7.

Answer.
0.75 sq ft

6.5.3.9.

Answer.
  1. 4 times as large
  2. 8 times as large

6.5.3.11.

Answer.
(a) and (e)

6.5.3.13.

Answer.
337.5 cu m

6.5.3.15.

Answer.
156.25 sq cm

6.5.3.17.

Answer.
180,000 lb

6.5.3.19.

Answer.
  1. 3.44 ft
  2. 1.2648 lb

6.5.3.21.

Answer.
one 16-inch pizza

7 Signed Numbers
7.1 Adding Signed Numbers
7.1.6 Practice 7-1

7.1.6.1.

Answer.

7.1.6.3.

Answer.

7.1.6.5.

Answer.

7.1.6.7.

Answer.

7.1.6.9.

Answer.

7.1.6.11.

Answer.
Negative. No.

7.1.6.13.

Answer.
Part of your asset cancels your debt, or vice versa; what’s left is their sum.

7.1.6.15.

Answer.
  1. positive
  2. negative
  3. negative

7.1.6.17.

Answer.
  1. 8 yellow, 6 red; 6; 2 yellow
  2. 8 red, 6 red; 0; 14 red
  3. 8 red, 6 yellow; 6; 2 red

7.1.6.19.

Answer.
\(-5 + (-6) = -11\)

7.1.6.21.

Answer.
\(-8 + (-8) = -16\)

7.1.6.23.

Answer.
\(12 + (-5) = 7\)

7.1.6.25.

Answer.
\(-6 + 13 = 7\)

7.1.6.27.

Answer.
\(-5 + 5 = 0\)

7.1.6.29.

Answer.
\(-6\)

7.1.6.31.

Answer.
\(-13\)

7.1.6.33.

Answer.
\(-9\)

7.1.6.35.

Answer.
\(6\)

7.1.6.37.

Answer.
\(-34\)

7.1.6.39.

Answer.
\(-22\)

7.1.6.41.

Answer.
\(-114\)

7.1.6.43.

Answer.
\(-0.8\)

7.1.6.45.

Answer.
\(-381\)

7.1.6.47.

Answer.
\(-4.5\)

7.1.6.49.

Answer.
\(4.49\)

7.1.6.51.

Answer.
If your debts and assets are equal, your net worth is $0.

7.1.6.53.

Answer.
  1. \(\displaystyle -27+6\)
  2. The net change is \(-21\) pounds.

7.1.6.55.

Answer.
  1. \(\displaystyle 1200 + (-1400)\)
  2. The net change is \(-200\) feet.

7.1.6.57.

Answer.
  1. \(\displaystyle -5000 + -1800\)
  2. The net change is \(-6800\) feet.

7.1.6.59.

Answer.
  1. $1.3 million, -$0.8 million, -$0.2 million, $2.1 million
  2. $2.4 million

7.1.6.61.

Answer.
  1. \(\hphantom{00}\) Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
    Relative water level \(3\) \(6\) \(8\) \(7\) \(6\) \(4\) \(1\) \(-3\) \(-5\) \(-7\) \(-6\) \(-4\)
    Water depth \(37\) \(40\) \(42\) \(41\) \(40\) \(38\) \(35\) \(31\) \(29\) \(27\) \(28\) \(30\)

7.2 Subtracting Signed Numbers
7.2.6 Practice 7-2

7.2.6.1.

Answer.

7.2.6.3.

Answer.

7.2.6.5.

Answer.

7.2.6.7.

Answer.

7.2.6.9.

Answer.
They move in the same direction on the number line.

7.2.6.11.

Answer.
\(9\)

7.2.6.13.

Answer.
\(-15\)

7.2.6.15.

Answer.
\(-10\)

7.2.6.17.

Answer.
\(17\)

7.2.6.19.

Answer.
\(-22\)

7.2.6.21.

Answer.
\(34\)

7.2.6.23.

Answer.
\(6\)

7.2.6.25.

Answer.
  1. \(\displaystyle -3, -2, 3\)
  2. \(\displaystyle -2\)

7.2.6.27.

Answer.
\(106.7\)

7.2.6.29.

Answer.
\(-97\)

7.2.6.31.

Answer.
\(0.402\)

7.2.6.33.

Answer.
\(-0.90\)

7.2.6.35.

Answer.
  1. \(\displaystyle 12\)
  2. Yes

7.2.6.37.

Answer.
  1. \(\displaystyle -12\)
  2. Yes

7.2.6.39.

Answer.
  1. \(\displaystyle 8+(-15); 8-(+15)\)
  2. Your choice

7.2.6.41.

Answer.
  1. \(\displaystyle -12\)
  2. \(\displaystyle -2\)
  3. \(\displaystyle -11\)
  4. \(\displaystyle -7\)

7.2.6.43.

Answer.
\(8\)

7.2.6.45.

Answer.
\(-40\)

7.2.6.47.

Answer.
\(24\)

7.2.6.49.

Answer.
\(-70\)

7.2.6.51.

Answer.
\(35\)

7.2.6.53.

Answer.
\(2\)

7.2.6.55.

Answer.
\(-2\)

7.2.6.57.

Answer.
  1. Year 1995 1996 1997 1998 1999
    Change in exports (billion $) 0.6 0.1 1.9 0.1 \(-1.1\)

7.2.6.59.

Answer.
  1. Year 1996 1997 1998 1999 2000
    Aircraft 754 568 656 391 585
  2. 1996

7.3 Multiplying and Dividing Signed Numbers
7.3.5 Practice 7-3

7.3.5.1.

Answer.
  1. \(\displaystyle -18\)
  2. \(\displaystyle 32\)

7.3.5.3.

Answer.
  1. \(\displaystyle -28\)
  2. \(\displaystyle -45\)

7.3.5.5.

Answer.
  1. \(\displaystyle 7\)
  2. \(\displaystyle -7\)

7.3.5.7.

Answer.
  1. \(\displaystyle 0\)
  2. \(\displaystyle 0\)

7.3.5.9.

Answer.
  1. \(\displaystyle -1\)
  2. \(\displaystyle -144\)

7.3.5.11.

Answer.
  1. \(\displaystyle -16\)
  2. \(\displaystyle 19\)

7.3.5.13.

Answer.
Adding several negative numbers gives a negative sum.

7.3.5.15.

Answer.
Multiplication and division

7.3.5.17.

Answer.
  1. Always negative
  2. Either
  3. Always positive
  4. Always positive

7.3.5.19.

Answer.
  1. \(\displaystyle 8(-6)\)
  2. \(-48~\) feet

7.3.5.21.

Answer.
  1. \(\displaystyle \dfrac{-115}{4}\)
  2. \(-28.75~\) degrees per hour

7.3.5.23.

Answer.
  1. \(\displaystyle -100,000,000,000 \div 100,000,000\)
  2. \(-1000~\) dollars

7.3.5.25.

Answer.
  1. \(\displaystyle 48\)
  2. \(\displaystyle -14\)

7.3.5.27.

Answer.
  1. \(\displaystyle 16\)
  2. \(\displaystyle -3\)

7.3.5.29.

Answer.
  1. \(\displaystyle -32\)
  2. \(\displaystyle 5\)

7.3.5.31.

Answer.
  1. \(\displaystyle -11\)
  2. \(\displaystyle 24\)

7.3.5.33.

Answer.
  1. \(\displaystyle -63\)
  2. \(\displaystyle -2\)

7.3.5.35.

Answer.
\((-5)(8) = -40\)

7.3.5.37.

Answer.
\(-14(-4) = 56\)

7.3.5.39.

Answer.
\(28(-7) = -196\)

7.3.5.41.

Answer.
\(414\)

7.3.5.43.

Answer.
\(31\)

7.3.5.45.

Answer.
\(-18\)

7.3.5.47.

Answer.
\(-7.83\)

7.3.5.49.

Answer.
  1. \(\displaystyle 9\)
  2. \(\displaystyle -8\)
  3. \(\displaystyle -9\)
  4. \(\displaystyle -8\)

7.3.5.51.

Answer.
  1. \(\displaystyle -1\)
  2. \(\displaystyle 1\)
  3. \(\displaystyle -1\)
  4. \(\displaystyle -1\)

7.3.5.53.

Answer.
  1. \(\displaystyle -2, 4, -8, 16, -32, 64\)
  2. negative, odd

7.4 Equations and Graphs
7.4.7 Practice 7-4

7.4.7.1.

Answer.
Operations performed on \(x\) Steps to isolate \(x~~~~\)
1. Multiply by \(-5\) 1. Subtract 2
2. Add 2 2. Divide by \(-5\)

7.4.7.3.

Answer.
Operations performed on \(x\) Steps to isolate \(x~~~~\)
1. Divide by 3 1. Subtract 4
2. Add 4 2. Multiply by 3

7.4.7.5.

Answer.
2

7.4.7.7.

Answer.
11

7.4.7.9.

Answer.
\dfrac{-8}{7}

7.4.7.11.

Answer.
18

7.4.7.13.

Answer.
10

7.4.7.15.

Answer.
4

7.4.7.17.

Answer.
6

7.4.7.19.

Answer.
  1. Time to reach \(-150\) ft: \(t\)
  2. \(\displaystyle -45-15t=-150\)
  3. It will take 7 min.

7.4.7.21.

Answer.
  1. Time to wait: \(t\)
  2. \(\displaystyle 350-11t=75\)
  3. She must wait 25 min.

7.4.7.23.

Answer.
  1. Value of one hand \(w\)
  2. \(\displaystyle 60-12w=-96\)
  3. One hand is worth 13 points.

7.4.7.25.

Answer.

7.4.7.27.

Answer.

7.4.7.29.

Answer.
  1. They are both negative.
  2. \(x\) is negative; \(y\) is positive

7.4.7.31.

Answer.
\(~x~\) \(-2\) \(0\) \(3\)
\(~y~\) \(-2\) \(0\) \(3\)

7.4.7.33.

Answer.
\(~x~\) \(-5\) \(0\) \(4\)
\(~y~\) \(-6\) \(1\) \(3\)

7.4.7.35.

Answer.
\(~x~\) \(-4\) \(0\) \(4\)
\(~y~\) \(8\) \(0\) \(8\)

7.4.7.37.

Answer.
\(~x~\) \(-5\) \(0\) \(4\)
\(~y~\) \(0\) \(-5\) \(-9\)

7.4.7.39.

Answer.
\(~x~\) \(-5\) \(0\) \(3\)
\(~y~\) \(7\) \(3\) \(9\)

7.4.7.41.

Answer.
\(~x~\) \(-4\) \(0\) \(6\)
\(~y~\) \(-6\) \(-4\) \(-1\)

7.4.7.43.

Answer.
  1. \(\displaystyle y=20x\)
  3. 25 hrs

7.4.7.45.

Answer.
  2. 30° C

7.4.7.47.

Answer.
  1. \(\displaystyle y=-800+5x\)
  3. 160 pages

7.4.7.49.

Answer.
  1. \(\displaystyle y=750-120x\)
  3. 8 hrs

7.4.7.51.

Answer.
A horizontal line

7.4.7.53.

Answer.
8.2

7.4.7.55.

Answer.
2

7.4.7.57.

Answer.
19

7.4.7.59.

Answer.
undefined

7.4.7.61.

Answer.
\(-5\)
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