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Investigation 1 Additional Practice1. a. i. ii. iii. iv. v. vi.
b. i. ii. iii. iv. v. vi.
c. The sum of the fractions is 1.
2. a. b. c. 1 to 2
d. 3 to 1 e. ; twice is .
3. a. or
b. 16 to 8 or 2 to 1
4. a. 6 b. c.
5. a. b.
6. a. Shade 8, 16, and 24 squares,
respectively, on the three grids.
Equivalent fractions: , ,b. Shade 9 and 12 squares, respectively,
on the two grids. Equivalent fractions:,
c. Shade 4 and 3 squares, respectively, onthe two grids. Equivalent fractions:
,
7. 2 tanks of gas will be needed for the trip.Two full tanks will be used for the first 800miles. The last 300 miles will use tank.
8. a. b. 4 to 3
9. a. 3 b. c.
10.
11. ,
Investigation 2 Additional Practice1. a. Diagrams may vary. Students should
divide the sandwich into six equalsections.
b. 1 sections 2. a. Diagrams may vary. Students should
divide the sandwich into eight equalsections.
b. sections
3. a. Diagrams may vary. Students shoulddivide the sandwich into four equalsections.
b. 1 sections 4. a. Diagrams may vary. Students should
divide the sandwich into five equalsections.
b. section
5. a. Possible answer: 300 : 4b. 25 : 1
6. a. 90 minutes; 210 minutesb. Jacob: 70 minutes; Matthew: 50 minutesc. Possible answer: Hannah could be 16
and Michael could be 10.
7. a. 12 hours; 60 hoursb. James: 72 hours; Becky: 36 hoursc. Sample answer: Kelly has 3 years of
experience and Mitchell has 5 years ofexperience.
8. a.
b.
c.
d.
9. a. D : A or A : F b. D : Fc. F : B or C : A d. B : A or F : C
10. a.
b. 12 gallonsc. 288 miles
45
14
34
13
14
312
14
34
15
34
34
318
424
1228
921
2430
1620
810
56
18
14
34
13
824
23
13
23
13
12
16
112
38
23
14
712
56
1112
58
13
34
512
Comparing Bits and Pieces Practice Answers
Hours
Pay ($)
1
4 80 100
10
40
20 25 0.2530
120 1
Hours
Pay ($)
1
5 75 150
5
25
15 30 0.238
190 1
Hours
Pay ($)
1
4 60 144
3
12
15 36 0.2548
192 1
Hours
Pay ($)
1
8 72 88
4
32
9 11 0.12516
128 1
Gallonsof Gas
1
2
3
4
5
6
36
72
108
144
180
216
Miles
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11. a.
b. 4 : 1 ($4 per gallon)c. 0.25 : 1 (0.25 gallon per dollar)
12. , , 60 for every 140
13.
14. a. 60b. $1.80c. 12
Skill: Ratios and Rates1–10. Sample answers.
1. 3 : 9, 2 : 6 2. 4 : 10, 8 : 203. 10 : 16, 20 : 32 4. 8 : 18, 28 : 635. 7 : 10, 70 : 100 6. 1 : 2, 50 : 1007. 15 : 18, 5 : 6 8. 8 : 12, 2 : 39. 1 : 3, 10 : 30 10. 7 : 21, 1 : 3
11. 50 miles per hour or 1 mile in 0.02 hour12. $0.80 per can or 1.25 cans per dollar13. 2 batteries per smoke detector or
smoke detector for every battery14. $13.95 per ticket or about 0.07 ticket
per dollar15. 7.5 minutes or hour per tire or 8 tires
per hour16. 105 calories per banana or about 0.01
banana per calorie
Investigation 3 Additional Practice1. a. 0.3 or b. 0.15 or
c. 0.3 or d. 0.25 or
2. a. 0.305 � 0.35 b. 0.123 � 0.1002c. 0.25 � 0.25000 d. 0.25 > 0.025e. 3.45 � 3.045 f. 12.03 � 12.30
3. a. 2.5 � 2 b. 0.65 � c. 0.8 �
d. � 0.625 e. 0.3 � f. 2.1 � 1
g. � h. � 0.5 i. 9 � 8
4. a.
b.
c.
d.
5. Answers will vary. All fractions equivalentto these sample responses are correct.
a. � � b. 1 � 1 � 1
c. � � d. 2 � 2 � 2
e. � � f. � �
6. a. 0.5 b. 0.2 c. 1.75 d. 0.375e. 5.55 f. 0.75
7. a. 2 � 2.375 miles; 30 min � 0.5 hr and
4.75 � 0.5 � 2.375.
b. 2 � 2.125 miles
c. or 0.375 mile; the difference in theirspeed is 0.5 mph.The differencebetween how far they can travel in 0.75 hr is 0.75 � 0.5 � 0.375.
8. a. 4 b. 2.69. a. 10 b. 4.75
10. a. Agree; possible explanation: 0.3 � is
close to � .3913
310
38
18
38
1524
1016
58
30200
320
15100
1240
620
310
10200
120
5100
2130
1420
710
915
35
610
810
36
1111
1112
910
37
58
47
23
25
14
310
320
310
18
12
2456
614
Comparing Bits and Pieces Practice Answers
0.3 0.60.4 0.5
0.11 0.170.13 0.15
0.03 0.120.06 0.09
0 0.750.25 0.5
Gallonsof Gas
6
5
4
3
2
1
24
20
16
12
8
4
Cost ($)
Hours
1
5
15
25
8
40
120
200
1
Pay ($)
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b. Greater than; possible explanation:Paul’s estimate is greater than 0.3
because is about 0.33, and 0.33 � 0.3.
11.
12. Answers will vary. Possible answers:a. The diver is 120 meters below sea level.b. The business had a loss of $1,200 in
one day.c. The temperature is 7° below zero.d. A song moved down 6 positions on the
music chart.13. Answers will vary. All numbers between
the two given numbers are correct.
a. b. c. -0.5 d. 0.55
14. a. 0.2 b. 2.84 c. d.
15. a. 3.4 b. c. d. -0.6
16. a. -2.56,-0.3, 0.261, 2.1
b. -3, , ,
17. a. �b. �c. �d. �e. �
18. 0.15, ; 0.60,
19.
Skill: Fractions and Decimals1. 0.72; 2. 0.9; 3. 0.04; 4.
5. 6. 7. 8.
9. 10. 11. 12. 0.09
13. 0.28 14. 0.06 15. 0.008
16. twelve and eight hundred seventy-threethousandths
17. eight and five hundred fifty-two ten-thousandths
18. sixty-five hundred-thousandths
Skill: Comparing and OrderingDecimals
1. � 2. � 3. � 4. � 5. �6. � 7. � 8. � 9. �
10.
11.
12. 0.3 � 0.5 and 0.7 � 0.5
13. a. 0.73; 0.84; 0.12 b. 0.12; 0.73; 0.84
Investigation 4 Additional Practice1. Ratios in a–f are possible answers.
a. 4 : 10, , 40% b. 11 : 20, , 55%
c. 9 : 25, , 36% d. 3 : 8, , 37.5%
e. 8 : 16, , 50% f. 9 : 12, , 75%
2. a. 30%, because 100% � 70% � 30%.
b. Half of 70% � 35% � � of the
class does homework 5 nights each week.
c. 35%, because 70% � 35% � 35%.d. No, because percents are comparisons
“out of 100.”You do not know theactual number represented in the whole.
3. a. 6, because of 24 � 6.
b. 3, because of 24 � 3.
c. 8 d. 7 : 24e. 100%, because each student takes one
of the four means of getting to school.
4. a. � 0.625 � 62.5%
b. � 0.75 � 75%
c. � 0.5 � 50% d. � 0.4 � 40%
5. a. ; 0.84; 84% b. ; 0.74; 74%
c. ; 0.36; 36%1850
3750
4250
25
12
34
58
18
14
720
35100
34
12
38
925
1120
25
0 1.00.26
0.3
0.5
0.59
0.7
0 1.00.2 0.5
0.6
129200
1920
45
127200
29100
37501
14
35
125
910
1825
35
320
43
13
223
259
37
56
13
212
1130
13
Comparing Bits and Pieces Practice Answers
�4 �3 �2 �1 0 1 2 3 4
�2 34 114
12
� 52
�1�2�3�4 0 1 2 3 4�1.75 0.253
2� 1
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6.
7. a. 40% b.8. Six students participate in a volunteer
activity after school; More studentsparticipate in an arts-based activity than avolunteer activity after school; Thefraction of the students that do notparticipate in an after school activity is .
Skill: Percents1. 2. 3.
4. 36% 5. 40% 6. 75% 7. 75%8. 80% 9. 85% 10. 78% 11. 84%
12. 76% 13. 87% 14. 90% 15. 80%16. 60% 17. 90% 18. 30% 19. 24%20. 7% 21. 18% 22. 36% 23. 40%24. 70% 25. 16% 26. 64%
Skill: Percents, Fractions, andDecimals
1. 0.46; 2. 0.17; 3. 0.9;
4. 0.05; 5. 2%; 6. 45%;
7. 40%; 8. 92%; 9. 0.6; 60%
10. 0.7; 70% 11. 0.52; 52% 12. 0.85; 85%
13.
2325
25
920
150
120
910
17100
2350
115
15
Comparing Bits and Pieces Practice Answers
1. 2.
3.
4.
5. 6.
7. 8.
9. 10.
6
5
2 3
4
4 0
1 7 1
6
0 02
5
3 5
10
5
0
3
Fraction Decimal
0.88
0.375
0.35
1.25
2.75
37.5%
88%
62.5%
125%
0.625
Percent
35%
38
58
114
234 275%
2225
720
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