MATH M010 Unit 2, Answers Section 2.1 Page 72 Practice 1 a) 1/2 b) 3/7 c) 5/8 d) 4/10 e) 5/15 f) 2/4 Page 73 Practice 2 a) two-fifths b) three-eighths c) one-tenth d) two-thirds e) four-ninths f) one quarter or one fourth Page 74 Practice 3 a) 6/7 b) 7/10 c) 5/50 d) ½ e) 8/15 f) 3/4 Page 75 Practice 4 a) 3/20 b) 6/7 c) 2/3 d) 58/60 e) 6/9 Page 75 Practice 5 a) 3/3 b) 5/5 c) 12/12 d) 7/7 e) 22/22 Page 77 Practice 6 a) improper fraction seven-sixths b) mixed number four and one-fifth c) proper fraction two-thirds d) improper fraction nine-quarters or nine fourths e) mixed number eight and three-sixths Page 79 Practice 7 a) 27% b) 27% Page 81 Practice 8 a) 1/2 b) 2/5 c) 4/5 d) 7/10 e) 3/5 f) 8/9 g) ½ h) 11/20 Page 82 Section 2.1 Exercises 1. a) four-fifths b) one-third c) one-tenth d) one-half e) five-twelfths f) three-quarters or three fourths 2. a) 1/3 b) 2/4 c) 5/6 d) ½ e) 3/30 f) 7/8 1 P a g e
3. a) 6/10 b) 2/6 c) 5/8 d) 4/7 e) 42/50 Page 83 Section 2.1 Exercises 4. a) 6/10 b) 9/14 c) 2/5 d) 3/4 5. a) 5/5 b) 17/17 c) 8/8 d) 331/331 6. a) improper fraction nine-eighths b) mixed number three and two-sevenths c) proper fraction two-thirds Page 84 Section 2.1 Exercises 7. a) 79% b) 6% 8. a) 1/2 b) 3/5 c) 1/3 d) 4/5 e) 5/6 f) 1/5 g) 7/8 h) 3/5 Section 2.2 Page 87 Practice 1 a) ones or units b) thousandths c) hundredths d) tenths Page 87 Practice 2 7 4 6. 2 7 8 4 6 2 8 4. 6 2 8 4 6. 2 8 3 4 6. 5 Page 88 Practice 3 a) tenths b) hundredth s c) thousandths d) tenths Page 88 Practice 4 a) zero point eight b) zero point two five c) one point four six one d) fifty-seven point eight two nine Page 89 Practice 5 a) six-tenths b) thirty-seven hundredths c) fifty-five hundredths d) six hundred twenty-four thousandths Page 89 Practice 6 a) three and seven-tenths b) twenty and forty-nine hundredths c) nine and two hundred sixty-one thousandths d) eight and nine thousandths 2 P a g e
Page 90 Practice 7 a) 0.88 b) 9.632 c) 78.2 d) 6200.335 Page 91 Practice 8 a) 0.07 b) 0.026 c) 0.229 d) 7.046 e) 12.23 f) 1.001 Page 92 Practice 9 a) 0.7 0.70 0.700 b) 33.9 33.90 33.900 c) 0.8 0.80 0.800 d) 0.3 0.30 0.300 Page 94 Practice 10 a) > b) > c) < d) > e) < f) > Page 96 Practice 11 a) 0.5 b) 0.9 c) 0.8 d) 0.3 e) 0.5 f) 0.4 Page 96 Practice 12 a) 0.51 b) 0.48 c) 0.19 d) 0.92 e) 0.58 f) 1.00 Page 97 Practice 13 a) 0.512 b) 0.477 c) 0.192 d) 0.925 e) 0.599 f) 2.000 Page 98 Practice 14 a) 0.8 b) 0.7 c) 2.5 d) 7.8 e) 0.57 f) 1.35 g) 0.10 h) 3.00 i) 0.373 j) 5.081 3 P a g e
Page 99 Practice 15 a) 7.5 x 10 5 b) 5.74 x 10 8 c) 8.2 x 10 3 d) 4.06 x 10 5 e) 8.2 x 10 2 f) 4.56 x 10 7 Page 100 Practice 16 a) 51 000 b) 770 c) 460 000 d) 4320 e) 123 400 f) 26 000 000 Page 102 Practice 17 a) 2.4 x 10-3 b) 5.6 x 10-5 c) 6 x 10-7 d) 2.04 x 10-3 e) 3.45 x 10-2 f) 4.9 x 10-1 Page 103 Practice 18 a) 0.000 046 b) 0.0021 c) 0.000 003 25 d) 0.0106 e) 0.000 78 f) 0.000 000 820 4 Page 104 Practice 19 a) 5.5 x 10 13 55 000 000 000 000 b) 7.3 x 10-14 0.000 000 000 000 073 c) 1.04 x 10-11 0.000 000 000 010 4 d) 6.35 x 10 10 63 500 000 000 e) 9.3 x 10-12 0.000 000 000 009 3 f) 9.9 x 10 17 990 000 000 000 000 000 Page 105 Section 2.2 Exercises 1. a) units/ones b) tenths c) hundredths d) thousandths 2. a) tenths b) thousandths c) hundredths d) tenths 3. a) zero point eight b) zero point two five c) twelve point one d) six point two five nine e) three hundred fifty point one two f) zero point nine nine zero 4. a) eight-tenths b) twenty-five hundredths c) twelve and one-tenth d) six and two hundred fifty-nine thousandths e) three hundred fifty and twelve hundredths f) nine hundred ninety thousandths Page 106 Section 2.2 Exercises 5. a) 0.17 b) 0.573 c) 70.26 d) 11.015 e) 6.002 f) 221.306 6. a) 0.75 b) 0.032 c) 14.54 d) 2.004 7. a) 0.6 0.60 0.600 b) 0.8 0.80 0.800 c) 9.4 9.40 9.400 d) 0.2 0.20 0.200 4 P a g e
8. a) > b) > c) < d) > e) < f) > 9. a) 0.5 b) 0.8 c) 0.7 d) 0.4 e) 0.2 f) 1.0 Page 107 Section 2.2 Exercises 10. a) 0.47 b) 0.78 c) 0.66 d) 0.49 e) 0.50 f) 1.00 11. a) 0.882 b) 2.292 c) 11.449 d) 0.339 e) 0.573 f) 2.000 12. a) 0.84 b) 0.4 c) 1.120 d) 2,.50 e) 6.145 f) 3.3 g) 1.0 h) 1.00 i) 23.8 j) 6.200 13. a) 7.5 x 10-11 0.000 000 000 075 b) 4.1 x 10-8 0.000 000 041 c) 1.04 x 10-3 0.0014 d) 6.35 x 10 4 63 500 Section 2.3 Page 109 Practice 1 a) 0.7 b) 0.6 c) 0.83 d) 1.6 e) 3.96 f) 5.78 Page 110 Practice 2 a) 3 10 b) 27 100 c) 13 2 100 d) 88 30 100 e) 22 1 100 f) 9 10 g) 35 4 100 h) 167 1000 Page 111 Practice 3 a) 3 10 b) 27 100 c) 13 2 100 d) 22 30 25 e) 11 1 50 f) 9 10 g) 7 4 20 h) 167 1000 Page 112 Practice 4 a) 0.89 b) 0.37 c) 0.47 d) 0.99 e) 0.09 f) 0.025 g) 0.0829 h) 1 i) 3.85 j) 35 Page 113 Practice 5 a) 48% b) 17% c) 20% d) 48.7% e) 82.16% f) 100% g) 238% h) 0.2% i) 0.575% j) 2380% Page 114 Practice 6 a) 3/10 b) 8/100 = 2/25 c) 6/100 = 3/50 5 P a g e
Page 114 Practice 7 a) 50 1 2 2 b) 100 2 5 1 3 3 c) 100 20 25 1 2 2 d) 100 4 97 97 1 1 100 100 e) 52 13 5 2 f) 100 25 1 1 1 1 100 100 Page 115 Practice 8 a) 230% b) 41.7% c) 37.5% d) 55.6% e) 405% f) 68.75% g) 350% h) 0.7% Page 116 Practice 9 a) d) g) 23 0.46 46% 50 b) 45 9 0.45 45% c) 100 20 2 2 0.6 66 % e) 3 3 4 0.8 80% 5 1 1 1.2 120% 5 f) 3 0.003 0.3% 1000 4 2 2.8 280% 5 h) 525 21 0.525 52.5% i) 1000 40 Page 117 Practice 10 a) 2/5 b) 0.42 c) 2/5 d) 235% Page 118 Practice 11 199 0.995 99.5% 200 a) c) 42 50 0.88 90% 0.91 94% 8 9 2.1 1.99 150% 5 10 Page 119 Section 2.3 Exercises b) 5 3 0.66 0.7 72% 8 4 1. a) 0.75 b) 0.875 c) 0.55 d) 0.92 e) 7.8 f) 5.58 2. a) b) c) d) e) f) g) h) 3. a) 0.35 b) 0.89 c) 0.52 d) 0.058 e) 0.06 f) 0.025 g) 0.0041 h) 2 4. a) 31 % b) 49 % c) 90 % d) 45.8 % e) 4.25 % f) 300 % Page 120 Section 2.3 Exercises 5. a) b) c) d) e) f) 6 P a g e
g) h) 1 i) j) k) l) 1 6. a) 225 % b) 20 % c) 120 % d) 91.67 % 7. a) b) c) d) e) f) Page 121 Section 2.3 Exercises 8. a) b) c) d) 235 % 9. a) 10. a) Section 2.4 Page 123 Practice 1 a) b) c) 5 d) Page 124 Practice 2 a) b) c) d) e) f) g) h) Page 125 Practice 3 a) b) c) Page 126 Practice 4 a) b) c) d) Page 127 Section 2.4 Exercises 7 P a g e
1. a) b) c) d) e) f) g) h) 2. a) b) 3. a) b) C) d) Section 2.5 Page 129 Practice 1 Note: these answers are for the shapes just above the example on page 128. a) 1 : 4, 1 to 4, b) 4 : 5, 4 to 5, c) 5 : 7, 5 to 7, d) 5 : 1, 5 to 1, e) 5 : 2, 5 to 2, Page 130 Practice 2 Page 131 Practice 3 a) Yes, the ratios are equivalent (in proportion). b) Yes, the ratios are equivalent (in proportion). c) No, the ratios are not equivalent (in prop.). d) Yes, the ratios are equivalent (in proportion). 8 P a g e
e) No, the ratios are not equivalent (in prop.). Page 132 Practice 4 a) b) c) d) e) f) g) h) i) Page 134 Practice 5 a) b) c) d) e) Page 135 Section 2.5 Exercises 1. a) 5 : 2, 5 to 2, b) 7 : 5, 7 to 5, c) 1 : 5, 1 to 5, d) 1 : 5, 1 to 5, e) 2 : 5, 2 to 5, 2. 3. a) Yes, the ratios are equivalent (in proportion). b) Yes, the ratios are equivalent (in proportion). c) No, the ratios are not equivalent (in prop.). d) Yes, the ratios are equivalent (in proportion). e) No, the ratios are not equivalent (in prop.). f) No, the ratios are not equivalent (in prop.). 4. a) b) c) d) e) f) g) h) i) 5. a) b) c) d) 9 P a g e
e) Math N01M Unit 2 Skill Builder Answers Section 2.1 A. Recognizing, Reading and Writing Fractions 1. a) b) c) d) 2. a) five eighths b) one quarter or one fourth c) two ninths d) one half e) eleven twentieths f) three fourths or three quarters B. Writing Words as Fractions 2. a) b) c) d) e) f) 3. a) b) c) d) e) C. Proper Fractions, Improper Fractions and Mixed Numbers 4. 5. a) Mixed Number Three and four sevenths b) Improper Fraction Ten quarters or ten fourths c) Proper Fraction One twelfth D. Percent Fractions 10 P a g e
6. a) 91% b) 45% 7. a) b) c) d) ) e) f) g) h) Section 2.2 A. Reading and Writing Decimals 1. a) Hundredths b) tenths c) thousandths d) units or ones 2. a) tenths b) thousandths c) hundredths d) tenths B. Writing Decimals as Words 3. a) zero point two b) zero point three six c) fifty-six point seven d) eight point eight two nine e) seven hundred seventy-one point eight four f) seven point zero zero nine 4. a) five tenths b) eighty-nine hundredths c) seven and six tenths d) two and one hundred five thousandths e) two hundred and two hundredths f) nine hundred twenty-one thousandths C. Writing Words as Decimals 5. a) 0.3 b) 1.226 c) 6.14 d) 9.008 e) 7.70 f) 903.502 D. Decimals and Fractions 6. a) 0.49 b) 0.072 c) 12.26 d) 3.015 7. tenths hundredths thousandths 0.4 0.40 0.400 0.3 0.30 0.300 7.2 7.20 7.200 0.6 0.60 0.600 E. Comparing Decimal Numbers 8. a) 7.32 < 8.06 b) 5.41 > 0.64 c) 7.843 < 11.6 d) 0.04 > 0.018 e) 3.0135 <3.0351 f) 6.207 > 6.017 F. Rounding Decimals 9. a) 0.58 = 0.6 b) 0.72 = 0.7 c) 1.39 = 1.4 d) 2.511 = 2.5 e) 0.27 = 0.3 f) 0.995 = 1.0 10. a) 0.336 = 0.34 b) 0.492 = 0.49 c) 0.293 = 0.29 11 P a g e
d) 1.478 = 1.48 e) 0.994 = 0.99 f) 0.998 = 1.00 11. a) 0.2236 = 0.224 b) 2.2922 = 2.292 c) 11.44851 = 11.449 d) 0.44476 = 0.445 e) 0.3395 = 0.340 f) 1.9897 = 1.990 12. a) 0.85 = 0.9 b) 0.32 = 0.3 c) 1.195 = 1.20 d) 3.808 = 3.81 e) 6.14591 = 6.146 f) 3.29 = 3.3 g) 0.799 = 0.8 h) 0.005 = 0.01 i) 15.15 = 15.2 j) 1.05572 = 1.056 G. Scientific Notation & Decimal Form 1. a) 4.5-9 = 4.5 x 10-9 = 0.0000000045 b) 3.7-4 = 3.7 x 10-4 = 0.00037 c) 5.23-5 = 5.23 x 10-5 = 0.0000523 d) 8.35 4 = 8.35 x 10 4 = 83,540 Section 2.3 A. Converting between Fractions and Decimals 1. a) 0.8 b) 0.125 c) 0.2 d) 3 e) 3.5 f) 4.75 2. a) b) c) d) = 4 e) f) g) 2 h) B. Converting between Percent and Decimals 3. a) 0.25 b) 0.14 c) 0.08 d) 0.075 e) 0.99 f) 0.0575 g) 0.0082 h) 1.5 4. a) 20% b) 75% c) 70% d) 42.5% e) 0.3% f) 1000% C. Converting between Percent and Fractions 5. a) b) c) d) 1 e) f) g) 7 h) 1 i) j) k) l) 50 6. a) 140% b) 25% c) 250% d) 87.5% D. Converting between Fractions Decimals and Percents 7. 12 P a g e
Fraction or Mixed Number Decimal Percent a) 0.5 50% b) 0.15 15% c) 2 2.1 210% d) 1 1.25 125% e) 1 1.4 140% f) 0.0275 2.75% E. Comparing and Ordering Fractions, Decimals and Percent 8. Which number is greater? a) (0.66666.) b) ( 0.6) c) (0.6) d) 235% (2.35) 9. 0.78 0.8) 81% (0.81) (0.85) 95% (0.95) 10. Change all to decimals first: (3.5) 3 (300%) 2.9 2.75 (275%) (2.5) 2.41 Section 2.4 A & B. Adding, Subtracting, Multiplying & Dividing Fractions 1. a) b) = c) = 2 d) e) f) g) h) C. Finding a Fraction of a Number 2. a) of 12 = 3 b) of 9 = 6 D Finding Percent of a Number a) 6 b) Dh 45 c) 33.6 = Dh 33.60 d) 0.44 Section 2.5 A. Defining Ratios 1. a) 5 : 7 or or 5 to 7 b) 1 : 7 or or 1 to 7 c) 4 : 5 or or 4 to 5 d) 1 : 5 or or 1 to 5 e) 7 : 5 or or 7 to 5 13 P a g e
B. Equivalent Ratios and Proportions 2. = 3. a) Yes b) Yes c) No d) No e) No f) Yes C. Simplifying Ratios 4. a) b) c) d) e) f) g) h) i) D. Solving Proportions 5. a) = b) = c) = d) = e) = 14 P a g e