Answer Key
Chapter 8 – Ratios, Proportions, and Percents 8.1 Equivalent Ratios Answers 1. 1: 5, 1/5, 1 to 5
2. 1: 2, 1 to 2, ½
3. 2 to 5, 2:5, 2/5
4. 1:5, 1/5, 1 to 5
5. 2 to 5, 2:5, 2/5
6. 1 to 2, 1:2, ½
7. 3:3, 3/3, 3 to 3
8. 2 to 2, 2/2, 2:2
9. 2 to 2, 2/2, 2:2
10. 4: 22, 4/22, 4 to 22
11. 2:2, 2 to 2, 2/2
12. 22: 4, 22/4, 22 to 4
13. 22: 6, 22 to 6, 22/6
14. 2: 22, 2/22, 2 to 22
15. 2 to 22, 2: 22, 2/22
8.2 Ratios in Simplest Form Answers 1. ½
2. ½
3. 1/3
4. 1/15
5. 2/3
6. 2/3
7. 1/3
8. ¾
9. ¼
10. ¼
11. 5/6
12. 1/3
13. ½
14. 1/3
15. 9/10
16. 4/5
17. 9/40
8.3 Comparison of Ratios in Decimal Form Answers 1. .75
2. .5
3. .20
4. .25
5. .5
6. .8
7. .3
8. .25
9. .83
10. .5
12. .2
13. .75
14. .33
15. .75
11. .4
8.4 Identification and Writing of Equivalent Rates Answers There are several possible answers – here is one possible choice 1. 28 apples to 4 barrels
2. 16 crayons in 1 box
3. 6 bottles in 1 carrier
4. 40 students on 8 teams
5. 50 students on 10 teams
6. 25 students in 1 class
7. 30 students on 1 bus
8. 1 student ate 2 cupcakes
9. 24 campers in 4 tents
10. 48 hikers on 2 trails
11. 12 campers in 2 tents
12. 3 tents
Middle School Math Concepts - Grade 6
1
Answer Key
Chapter 8 – Ratios, Proportions, and Percents 13. 5 tents
14. 72 campers
15. 12 students on 1 team
Middle School Math Concepts - Grade 6
2
Answer Key
Chapter 8 – Ratios, Proportions, and Percents 8.5 Comparison of Unit Rates Answers 1. 7/1
2. 16/1
3. 6/1
4. 5/1
5. 5/1
6. 25/1
7. 30/1
8. ½
9. 6/1
10. 24/1
11. 4/1
12. 12/1
13. 3/1
14. 4/1
15. $12/1
8.6 Proportions Using Cross Products Answers 1. yes
2. Yes
3. No
4. Yes
5. No
6. Yes
7. no
8. Yes
9. Yes
10. Yes
11. Yes
12. No
13. yes
14. No
15. No
8.7 Mental Math to Solve Proportions Answers 1. 4
2. 10
3. 12
4. 4
5. 8
6. 10
7. 7
8. 9
9. 5
10. 6
13. 4
14. 16
11. 10
12. 20
15. 42
8.8 Proportions to Find Dimensions Answers 1. 25 feet
2. 35 feet
3. 75 feet
4. 40 feet
5. 27 feet
6. 21 feet
7. 9 feet
8. 250 miles
9. 150 miles
11. 6’ x 9’ = 54 sq. ft.
12. 10 x 10 = 100 sq. ft
14. 30 x 30 = 900 sq. ft
15. 24 x 24 = 576 sq. ft
10. 250 kilometers
13. 20 x 20 = 400 sq. ft.
Middle School Math Concepts - Grade 6
3
Answer Key
Chapter 8 – Ratios, Proportions, and Percents 8.9 Proportions to Find Scale Ratios Answers 1. 1”/2’
2. 1”/2’
3.1”/3’
4. 1”/3’
5. 1”/4’
6. 1”/6’
7. 1”/10’
8. 1”/20 miles
9. 1”/25 miles
10. 1”/200 km
11. 1”/200 km
12. 1”/3000 m
13. 1”/1000 km
14. 1”/200 km
15. 1”/3000 m
8.10
Conversion of Decimals, Fractions and Percent
Answers 1. 23/100
2. .23
3. 18/100
4. 18%
5. .34
6. 34%
7. 57 out of 100
8. 57/100
9. 98/100
10. 98%
11. 77/100
12. .77
13. 77%
14. 12%
15. 15%
8.11
Percents as Decimals
Answers 1. .54
2. .11
3. .06
4. .12
5. .89
6. .83
7. .19
8. .04
9. .09
10. .32
11. .65
12. .88
13. .78
14. .675
15. .182
8.12
Percents as Fractions
Answers 1. 54/100
2. 11/100
3. 6/100
4. 12/100
5. 89/100
6. 83/100
7. 19/100
8. 4/100
9. 9/100
10. 18/100
11. 89/100
12. 100/100
4
Middle School Math Concepts - Grade 6
Answer Key
Chapter 8 – Ratios, Proportions, and Percents 13. 23/100
14. 77/100
15. 98/100
Middle School Math Concepts - Grade 6
16. 2/100
5
Answer Key
Chapter 8 – Ratios, Proportions, and Percents 8.13
Interpretation of Circle Graphs
Answers 1. German
2. 70%
3. 10%
4. 90%
5. 0%
6. 70%
7. 15%
8. 95%
9. 15%
10. 25%
11. 65%
12. 65%
13. False
14. 35%
15. 25%
8.14
Fractions as Percents
Answers 1. 4%
2. 24%
3. 20%
4. 76%
5. 61%
6. 25%
7. 75%
8. 50%
9. 40%
10. 80%
11. 80%
12. 60%
13. 12%
14. 12%
15. 40%
8.15
Decimals as Percents
Answers 1. 31%
2. 56%
3. 43%
4. 8%
5. 1%
6. 40%
7. 60%
8. 65%
9. 33%
10. 19%
11. 30%
12. 90%
13. 11%
14. 18%
15. 34%
16. 99%
17. 21%
18. 88%
8.16
Comparison of Fractions, Decimals and Percents
Answers 1. 16/100, 1/5, .27, 53%
2. .30, 68%, 9/10, 99/100
3. 18/100, 10/20, 87%, .99
4. .18, 1/5, 23%, 88/100
5. 6%, ½, 93/100, .98
6. .37, 2/5, 77/100, 93%
7. 12/100, 13%, 1/3, .76
8. 9/100, .2, 67%, 4/5
9. 2/10, .29, 35%, 88/100
10. >
11. =
12. <
13. >
14. =
15. >
Middle School Math Concepts - Grade 6
6
Answer Key
Chapter 8 – Ratios, Proportions, and Percents 8.17
Percent of a Number
Answers 1. .2
2. 2.5
3. 3
6. 4.4
7. 6.4
11. 2.4
12. 4.25
8.18
4. 4.5
5. 7.2
8. 6.75
9. 20
10. 62.5
13. .36
14. 13.95
15. 14.35
Prices Involving Discounts
Answers 1. $16.96
2. $10.00
3. $31.95
4. $35.00
5. $80.00
6. $52.50
7. $23.96
8. $16.20
9. $42.75
10. $52.50
11. $100.00
12. $202.95
13. $342.00
14. $371.00
15. $660.00
8.19
Prices Involving Sales Tax
Answers 1. $59.02
2. $44.98
3. $67.60
4. $26.52
5. $19.50
6. $61.36
7. $22.36
8. $46.28
9. $130.52
10. $447.20
11. $926.12
12. 1038.28
13. $2451.02
14. $3125.72
15. $5905.38
8.20
Tip Estimation
Answers 1. $1.50
2. $2.70
3. $3.75
4. $4.50
5. $2.25
6. $7.00
7. $13.50
8. $18.00
9. $20.00
10. $16.50 – 17.00
11. $20.00
12. $21.00
13. $15.00
14. $13.50
15. $15.00
Middle School Math Concepts - Grade 6
7
Answer Key
Chapter 8 – Ratios, Proportions, and Percents 8.21
Simple Interest
Answers 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
8.22
Problem Solving Plan, Proportions
Answers 1. 15 feet
2. 6 miles
3. 20 miles
4. 2”
6. 8 feet
7. 6 feet
8. 9 feet
9. 4 feet
10. 3”
11. 2”
12. 2.5”
13. 4”
14. 2”
15. 12”
16. 3”
17. 24 minutes
18. 48 minutes
Middle School Math Concepts - Grade 6
5. 6”
19. 1 mile in 10 minutes
8
