Math 7 – Answer Key – Chapters 4 - 6 Chapter 4: Using Integers
4.1 Integers that Represent Different Situations
1. -10 2. +50 3. -$20.00 4. -35 5. -120
6. +15,000 7. -20 + 15 8. 15 – 20 9. 20 + 35 10. -19 – 30 11. 30,000 + 15,000 12. -15,000 – 12,000 13. -60 + 15
14. -15 – 20 15. 1500 + 1000 4.2 Absolute Value of Integers
1. -20 2. 7 3. -22 4. 34 5. 0 6. 9
7. -14 8. -25 9. 13 10. 11 11. 5 12. 17
13. 9
4.3 Comparison of Integers with Absolute Value
1. > 2. > 3. > 4. < 5. > 6. >
7. > 8. = 9. < 10. = 11. = 12. >
13. < 14. < 15. = 4.4 Sums of Integers on a Number line
1. 7 2. 0 3. -6 4. 2 5. -14 6. -8
7. 12 8. 1 9. 7 10. -3 11. -9 12. -5
13. -13 14. 10 15. -4 4.5 Sums of Integers Using Absolute Value
1. 11 2. -15 3. -5 4. -31 5. -7 6. -24
7. -70 8. -14 9. -2 10. -28 11. -2 12. -2
13. -3 14. -27 15. -20
4.6 Simplify Variable Expressions Involving Integer Addition
1. 4z 2. 2z 3. 2x 4. 10y 5. –x 6. 0
7. 11a 8. -11y 9. -11d + 2 10. 4x – 5 11. 4y
12. -6x 13. 11a 14. 3,000 ft. 15. -5 degrees F 4.7 Differences of Integers Using a Number Line
1. 2 2. -8 3. 3 4. 7 5. -9 6. 11
7. 0 8. -9 9. 9 10. -11 11. -61 12. -27
13. -7 14. -75 15. -161
4.8 Differences of Integers Using Absolute Value
1. 8 2. -19 3. -4 4. 22 5. -25 6. 37
7. -3 8. -10 9. 36 10. -5 11. -13 12. 29
13. 14 14. -13 15. 38
4.9 Simplify Variable Expressions Involving Integer Subtraction
1. -11m 2. -6c 3. -15a 4. 16a 5. 2a 6. -5a
7. 17z 8. -34x 9. -37a 10. 34x 11. 28y 12. 88z – (-44x) or 88z + 44x 13. -15a – 8x 14. -15a – 8x – 2 15. -15a – 7y
4.10 Integer Multiplication
1. -27 2. -72 3. 96 4. -28 5. 22 6. -75
7. 30 8. 56 9. 24 10. -9 11. 18 12. 24
13. 54 14. -48 15. 44
4.11 Simplify Variable Expressions Involving Integer Multiplication
1. 42k 2. 24ab 3. -6abc 4. -48ab 5. 36xy 6. -32x
7. 20ab 8. -24abc 9. -144abc 10. 96xz 11. 28ac 12. -132abc 13. 44abc 14. 216ab 15. 63ab
4.12 Integer Division
1. -3 2. 3 3. 6 4. -8 5. 7 6. -5
7. 20 8. -5 9. 9 10. -7 11. -8 12. 4
13. -4 14. 2 15. -6
4.13 Simplify Variable Expressions Involving Integer Division
1. -4t 2. 8n 3. 2 4. -4n 5. 9y 6. -8t
7. -6x 8. 6 9. 4 10. 4a 11. 11y 12. 11ab
13. 12xy 14. 13xy 15. -45xyz 4.14 Properties of Rational Numbers
1. -11/1 2. 19/6 3. 9/1 4. 8/100 5. -34/100
6. 678/1000 7. 4/5 8. -19/1 9. 25/1 10. 17/100
11. 2347/10,000 12. -17/1 13. 347/1 14. 87/1
15. -97/1
4.15 Comparison of Rational Numbers
1. = 2. < 3. > 4. < 5. < 6. >
7. = 8. > 9. > 10. < 11. = 12. >
13. > 14. < 15. .9 , .9, ½, 0 4.16 Exp and the Distributive Property
1. 42 2. 25 3. 96 4. 90 5. 18 6. 9
7. 24 8. 10 9. 28 10. 36 11. 5x + 15
12. 6y – 12 13. 5x + 45 14. 8a + 8b 15. 7x – 7y
4.17 Points in the Coordinate Plane
1. N (-3, 2) M(0, -6) P(3, -2) 2. (-9,7) 3. (-7,-8) 4. (8,7) 5. (7, -9) 6. (-5, 1) 7. (3, 4) 8. (0, -5) 9. (-9, 10) 10. (-7, 1) 11. (-2, -10) 12. (3, 1) 13. (5, 10)
14.
15.
4.18 Scatter Plots
1. No Correlation 2. 1 3. 2 4. 1 5. 2
6. 3 7. 2 8. True 9. False 10. False
11. Scatter plots – answers vary 12. True 13. False 13. False 14. False 15. 8
Chapter 5: Using Ratios, Rates and Proportions 5.1 Equivalent Ratios
1. yes 2. No 3. No 4. Yes 5. Yes 6. No
7. yes 8. No 9. No 10. Yes 11. Yes 12. No
13. yes 14. Yes 15. No 5.2 Ratios in Simplest Form
1. 1 to 2 2. 1 : 4 3. 9 to 11 4. 9/10 5. 5/11
6. 1 to 7 7. 9 to 5 8. 3 to 1 9. 2 : 1 10. 3 to 2
11. 1 to 2 12. 6 to 1 13. 3 : 1 14. 8 to 1 15. 3/2 5.3 Comparison of Ratios in Decimal Form
1. .25 2. .5 3. .75 4. 1.6 5. .25 6. .8
7. .09 8. .75 9. .36 10. .3 11. .75 12. .43
13. > 14. < 15. =
5.4 Identification and Writing of Equivalent Rates
1. 1 for $5 2. 1 for $5 3. 1 for $2.50 4. 1 for $2.50
5. 1 for $9.00 6. 1 for $4.00 7. 1 mile in 2 minutes 8. 5 miles in 1 hour 9. 5 feet in 1 minute 10. 2 pounds in 1 week
11. 1/5 12. 1/5 13. 1/5 14. ½ 15. 9/1 5.5 Unit Rates
1. 1 for $5 2. 1 for $5 3. 1 for $2.50 4. 1 for $4
5. 9 for $1 6. 1 for $4 7. 1 mile in 2 minutes 8. 5 miles in 1 hour 9. 5 feet in 1 minute 10. 2 pounds in 1 week
11. 2 pounds for $1.00 12. 6 miles in 1 hour 13. 3” for $1.00 14. 15 miles per gallon 15. 50 miles in 1 hour
5.6 Comparison of Unit Rates
1. yes 2. No 3. Yes 4. $3.00 per gallon 5. .69 for 1 6. 160 per hour 7. $1.25 per square foot 8. 62 per minute 9. .30
10. .28 11. 12 ounce/2 cents 12. 47 mph 13. 51 mph
14. Amy 15. 4 mph 5.7 Slope
1. Positive 2. 0 3. Negative 4. 0 5. Positive
6. 0 7. Negative 8. Positive 9. Negative 10. Negative
11. no 12. False 13. True 14. True 15. True
5.8 Slope of a Line Using Two Points
1. 3/2 2. 0 3. -7/3 4. 0 5. 3/2 6. 0
7. -7/3 8. 4/5 9. -2/1 10. -7/5 11. -4/3 12.
13. Positive
14.
15. Negative 5.9 Proportions
1. yes 2. Yes 3. No 4. Yes 5. No 6. No
7. yes 8. No 9. a = 5 10. x = 1 11. n = 14 12. z = 4 13. t = 36 14. k = 30 15. x = 16
5.10 Proportions with Variables in the Numerator
1. 4 2. 10 3. 12 4. 4 5. 8 6. 10
7. 7 8. 9 9. 5 10. 6 11. 9 12. 2
13. 9 14. 18 15. 2.25
5.11 Proportions Using Cross – Products
1. 3 2. 6 3. 20 4. 3.5 5. 2.5 6. 18
7. 5 8. 4.5 9. 12 10. 15 11. 25 12. 18
13. 9 14. 49 15. 4 16. 42.5
5.12 Proportions with Variables in the Denominator
1. 10 2. 30 3. 14 4. 42 5. 99 6. 48
7. 34 8. 30 9. 45 10. 7.5 11. 9.5 12. 12.5
13. 54 14. 24 15. 11.5
5.13 Scale Distances or Dimensions
1. 5” 2. 20” 3. 30” 4. 7 cm 5. 14 cm 6. 21 cm
7. 3” 8. 6” 9. 2 cm 10. 1 cm 11. 4” x 3.5”
12. 12 m 13. 344 miles 14. 18 mm 15. 1670 ft.
5.14 Unit Scale to find Actual Distances
1. 200 miles 2. 300 miles 3. 25 miles 4. 1000 miles
5. 1100 miles 6. 1250 miles 7. 50 miles 8. 525 miles
9. 40 miles 10. 80 miles 11. 170 miles 12. 380 miles
13. 260 miles 14. 10 miles 15. 30 miles 5.15 Scale Factor to Find Actual Dimensions
1. 10 cm 2. 20 cm 3. 20 cm 4. 10 cm 5. 1.5”
6. 3” 7. 4000 cm 8. 80 mm 9. 8 cm 10. 4”
11. 1.5 mm 12. 108 ft. 13. 6660 ft. 14. a. 7.5 m b. 5.1 m 15. a. 5 m x 4 m b. 20 sq. m
5.16 Problem Solving Plan, Proportions
1. 4 2. Lionel 3. 44 miles 4. .83 m 5. 125 students
6. Brand x 7. 6 miles 8. 20 miles 9. 2” 10. 6”
11. 8 ft. 12. 6 ft. 13. 9 ft. 14. 4 ft. 15. 3”
5.17 Conversion Using Unit Analysis
1. 5280 ft. 2. 97,680 ft. 3. 3750 mL 4. 18,250 mL
5. 6000 pounds 6. 5000 pounds 7. 9,500 pounds 8. 54 feet 9. 48 inches 10. 105 inches 11. 29,500 mL 12. 4 ounces 13. 108 inches 14. $4.50 15. 8 pints
Chapter 6: Using Percents 6.1 Percents
1. 10/100 2. 6/100 3. 22/100 4. 41/100
5. 33/100 6. 70/100 7. 77/100 8. 19/100
9. 25/100 10. 15/100 11. 7/100 12. 29/100
13. 88/100 14. 92/100 15. 90/100
6.2 Percents as Fractions
1. 1/10 2. 3/50 3. 11/50 4. 41/100 5. 33/100
6. 7/10 7. 77/100 8. 19/100 9. 3/25 10. 1/5
11. 1/20 12. ¼ 13. 2/5 14. 3/5 15. 9/10
6.3 Fractions as Percents
1. 50% 2. 25% 3. 75% 4. 11% 5. 20% 6. 50%
7. 17% 8. 125% 9. 250% 10. 233% 11. 54% 12. 50%
13. 42% 14. 40% 15. 50%
6.4 Percent of a Number
1. 2.5 2. 6 3. 20 4. 27 5. 150 6. .8
7. 10 8. 3.8 9. 4.5 10. 3.6 11. 6.75 12. 21.25
13. 27 14. 100 15. 165 6.5 Proportions to Find Percent, p
1. 50% 2. 20% 3. 25% 4. 20% 5. 33.3% 6. 50%
7. 20% 8. 25% 9. 60% 10. 75% 11. 13.3% 12. 33.3%
13. 20% 14. 80% 15. 12.5%
6.6 Proportions to find Part a
1. 4.5 2. 2 3. 7.2 4. 8.8 5. 30 6. 15
7. 32 8. 24 9. 60 10. .6 11. 1 12. 12.8
13. 5.75 14. 8.5 15. 9.9 6.7 Proportions to Find Base b
1. 50 2. 70 3. 50 4. 40 5. 32 6. 28
7. 500 8. 5 9. 72 10. 300 11. 75
12. 138.46 13. 120 14. 32.72 15. 400 6.8 Percents as Decimals
1. .12 2. .15 3. .03 4. .67 5. .18 6. .78
7. .34 8. .07 9. .06 10. .36 11. .28 12. .335
13. .185 14. .1325 15. .0675 6.9 Decimals as Percents
1. 45% 2. 30% 3. 67.5% 4. 90% 5. 8%
6. 78.5% 7. 22% 8. 9.5% 9. 54% 10. 27.5% 11. 4%
12. 4.5% 13. 11.2% 14. 460% 15. 67.2%
6.10 Small and Large Percents as Decimals
1. .0034 2. .005 3. 3.5 4. 6.5 5. .0030 6. .0010
7. .0009 8. .0022 9. 2.3 10. 5 11. 7 12. .00012
13. .0004 14. .006 15. .0016 6.11 Percent Equation to find Part a
1. 3.6 2. 3 3. 4.5 4. 3.24 5. 5.4 6. 44
7. 9 8. 67.5 9. 8.8 10. 15 11. 1.2 12. 198
13. 10.8 14. 42.55 15. 32.8
6.12 Percent Equation to Find Percent
1. 50% 2. 50% 3. 25% 4. 25% 5. 40% 6. 50%
7. 50% 8. 25% 9. 50% 10. 92% 11. 14% 12. 45%
13. 66% 14. 70.4% 15. 10%
6.13 Percent Equation to Find the Base b
1. 50 2. 50 3. 90 4. 24 5. 37.5 6. 70
7. 320 8. 200 9. 112.5 10. 64 11. 333.3 12. 83.3
13. 140 14. 550 15. 335 6.14 Percent of Increase
1. 60% 2. 100% 3. 178% 4. 264% 5. 12.5% 6. 233%
7. 17.6% 8. 20% 9. 38.5% 10. 25% 11. 50% 12. 40%
13. 14.3% 14. 12.5% 15. 22.2%
6.15 Percent of Decrease
1. 60% 2. 63% 3. 55.5% 4. 6.6% 5. 33.3%
6. 16.6% 7. 25% 8. 7% 9. 19.6% 10. 87%
11. 50% 12. 12% 13. 33% 14. 15% 15. 95%
6.16 Percent of Change
1. 22.5 2. 25.5 3. 16.2 4. 27.3 5. 10.56 6. 77.4
7. 40 8. 86.33 9. 42 10. 12 11. 209 12. 67.5
13. 147.6 14. 1320 15. 13,680 6.17 Prices Involving Discounts
1. $22.80 2. $14.40 3. $21.60 4. $30.00
5. $16.20 6. $11.94 7. $54.00 8. $108.00
9. $102.00 10. $20.40 11. $46.75 12. $30.18 or $30.17
13. $15.30 14. $7.44 15. $21.25
6.18 Prices Involving Sales Tax
1. $3.00 2. $5.60 3. $5.00 4. $7.00 5.$9.00 6. $10.00 7. $18.00 8.$24.00 9. $25.00 10. $22.00 11. $26.00 12. $27.00 13. $19 – 20.00 14. $18.00 15. $20.00
6.19 Total Bill Involving Tip and Tax
1. $70.37 2. $53.63 3. $80.60 4. $31.62 5.$23.25
6. $73.16 7. $26.66 8. $55.18 9. $15.50 10. $53.32
11. $110.98 12. $123.19 13. $292.33 14. $372.62
15. $841.03
6.20 Simple Interest Equation to Find Interest Rate
1. $40 2. $30 3. $200 4. $60 5. $96 6. $45
7. $92 8. $40 9. $625 10. $330 11. $525 12. $2100
13. $3510 14. $8050 15. $25,000 6.21 Simple Interest
1. $45 2. $92 3. $40 4. $625 5. $330 6. $525
7. $2100 8. $138 9. $1787.50 10. $2400 11. 4 years 12. 2.5 years 13. $6.25 14. Avi, $2.60 more 15. $12,916.67
6.22 Interpretation of Circle Graphs
1. Baseball 2. Ice Hockey 3. 15% 4. 60 people 5. 27 people
6 – 8 Answers Vary
9. 0 10. Pizza 11. Chicken Sandwich or Tacos 12. 10% 13. 90%
14. 70% 15. 70% 16. 30%
17 – 18. Answers Vary
6.23 Circle Graphs to Display Data 1 – 3 Answers Vary
4. 43.2°
5. 90°
6. 100.8° or 101°
7. 151.2° or 151°
8. 68.4° or 68°
9. 288°
10. 324°
11. 122.4° or 122°
12. 54°
13. 18°
14. 36°
15. 280.8° or 281°
