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Date
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Practice B
5-1 Ratios and Rates
The annual dog show has 22 collies, 28 boxers, and 18 poodles.
Write the given ratio in all three forms.
1. collies to poodles
2. boxers to collies
3. poodles to boxers
4. poodles to collies
The Franklin School District has 15 art teachers, 27 math
teachers, and 18 Spanish teachers. Write the given ratio in
all three forms.
5. art teachers to math teachers
6. math teachers to Spanish teachers
Find the unit rates and write them in both fraction and
word form.
8. A store sells 15 pears for $5.
7. Gabrielle bikes 78 miles in 6 hours.
9. A class trip consists of 36 students
and 6 teachers.
10. A landscaper plants 28 bushes and
4 trees.
11. Carmen spends $64 for 4 hats.
12. A car travels 330 miles in 6 hours.
13. Glen has 18 rock CDs and 15 classical CDs in his collection. He
bought 10 of the rock CDs and 12 of the classical CDs. The rest
were gifts. Compare the ratio of the number of rock CDs that he
bought to the number of rock CDs in his collection with the ratio
of the number of classical CDs that he bought to the number of
classical CDs in his collection.
Copyright © by Holt, Rinehart and Winston.
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Holt Middle School Math Course 2
Exploration Recording Sheet
5-1 Ratios and Rates
Are You Ready? Recording Sheet
CHAPTER
5
LESSON
Proportional Reasoning
Use number 1 as a guide to solve 2–5.
Choose the best term from the list to complete each sentence.
common denominator
quadrilateral
equivalent fraction,
is a number that represents a part of a whole.
triangle
2. A closed figure with three sides is called a(n)
equivalent fractions
3. Two fractions are
30 45
!!, !!
34 51
15
!
9. !
17
14 28
!!, !!
22 44
7
6. !1!
1
Possible answers:
1 5
!!, !!
4 20
25
!
7. !
100
30 45
!!, !!
46 69
15
10. !2!
3
12 4
!!, !!
39 13
24
!
11. !
78
2 8
!!, !!
3 12
4
8. !6!
150
!
12. !
325
30 6
!!, !!
65 13
Compare. Write " or # .
5
13. !6!
8
17. !9!
#
2
!!
3
3
14. !8!
"
12
!!
13
5
18. !1!
1
"
2
!!
5
#
6
!
15. !
11
7
!!
21
number of minutes
40
4
2
2
!! ! !! ! !! → !! of a
60
6
3
3
problem per minute
common denominator
Find two fractions that are equivalent to each fraction.
4 6
!!, !!
10 15
.
Compare 40 problems
and 60 minutes.
number of problems
Divide !!! .
if they represent the same number.
4. One way to compare two fractions is to first find a(n)
between them.
2
5. !5!
1. A one-hour exam has 40
problems. How many
problems per minute must
the students complete to
finish the test in time?
triangle
fraction
1. A(n)
fraction
4
!
19. !
10
#
1
!!
4
5
16. !8!
"
11
!!
12
"
3
!!
7
3
20. !4!
#
2
!!
9
Solve each equation.
21. 3x ! 12
x!4
22. 15t ! 75
t!5
23. 2y ! 14
y!7
24. 7m ! 84
m ! 12
25. 25c ! 125
c!5
26. 16f ! 320
f ! 20
27. 11n ! 121
n ! 11
28. 53y ! 318
y!6
2. A cake that serves 10 people
has 1,200 calories. How
many calories per serving
does the cake have?
1200
!! ! 120 calories per
10
serving
3. A school has 500 students
and 20 teachers. How many
students are there per teacher?
500
!! ! 25 students per teacher
20
4. A restaurant owner ordered
15 tables and 75 chairs for her
new restaurant. How many
chairs are there per table?
75
!! ! 5 chairs per table
15
5. A car completed a 150-mile
trip on 13 gallons of gasoline.
How many miles per gallon of
gasoline did the car travel?
150
!! ! 11.54 mi/gal
13
Think and Discuss
6. Explain why division is used to compare two numbers
in a ratio.
Possible answer: A ratio is a type of sharing or partitioning comparison.
Solve. Write each answer in simplest form.
2 5
29. !3! • !7!
1 5
33. !5! • !9!
10
!!
21
1
!!
9
1
!!
4
12 3
! • !!
30. !
16 9
7
1
!! or 1!!
6
7 4
34. !8! • !3! 6
4 18
!
31. !9! • !24
25 30
! • !!
35. !
100 90
3
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1
!!
3
1
!!
224
1
50
! • !!
32. !
56 200
1
!!
12
46 3
! • !!
36. !
91 6
23
!!
91
Holt Middle School Math Course 2
7
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
Practice A
5-1 Ratios and Rates
Holt Middle School Math Course 2
Practice B
5-1 Ratios and Rates
LESSON
LESSON
The annual dog show has 22 collies, 28 boxers, and 18 poodles.
Write the given ratio in all three forms.
Match the ratios.
A farmer has 5 pigs, 13 chickens, and
8 cows.
The school orchestra has 9 cellos,
14 flutes, and 17 violins.
1. cows to pigs
13:5
5. cellos to violins
9 to 14
2. chickens to pigs
5:8
6. flutes to cellos
9 to 17
3. cows to chickens
8:5
7. violins to flutes
17 to 14
4. pigs to cows
8:13
8. cellos to flutes
14 to 9
15. Miles spends $36 for 4 T-shirts.
16. A car travels 300 miles in 6 hours.
17. A recipe calls for 4 eggs for
2 batches of brownies.
18. The track team runs 5 miles in
40 minutes.
2
!! ; 0.4 laps per min
5
13
!! ; 13 mi/h
1
3
!! ; 3 pears for $1
1
9. A class trip consists of 36 students
and 6 teachers.
10. A landscaper plants 28 bushes and
4 trees.
6
!! ; 6 students for each teacher
1
50
!! ; 50 mi/h
1
2
!! ; 2 eggs per batch
1
8. A store sells 15 pears for $5.
7. Gabrielle bikes 78 miles in 6 hours.
3
!! ; 3 books per week
1
9
!! ; $9 per T-shirt
1
3
!! ; 3 to 2, 3:2
2
Find the unit rates and write them in both fraction and
word form.
Find the unit rates. Write them in both fraction and word form.
14. Jesse reads 6 books in 2 weeks.
6. math teachers to Spanish teachers
5
!! ; 5 to 9; 5:9
9
5
!! ; 5 to 13; 5:13
13
13. Frieda swims 4 laps in 10 minutes.
9
!! ; 9 to 11; 9:11
11
5. art teachers to math teachers
12. outfielders to entire team
2
!! ; 2 to 5; 2:5
5
4. poodles to collies
The Franklin School District has 15 art teachers, 27 math
teachers, and 18 Spanish teachers. Write the given ratio in
all three forms.
6
!! ; 6 to 5; 6:5
5
11. pitchers to outfielders
3. poodles to boxers
14
!! ; 14 to 11; 14:11
11
9
!! ; 9 to 14; 9:14
14
10. infielders to outfielders
1
!! ; 1 to 3; 1:3
3
2. boxers to collies
11
!! ; 11 to 9; 11:9
9
A baseball team has 4 pitchers, 10 outfielders, and 12 infielders.
Write the given ratio in all three forms.
9. pitchers to infielders
1. collies to poodles
7
!! ; 7 bushes for each tree
1
11. Carmen spends $64 for 4 hats.
12. A car travels 330 miles in 6 hours.
16
!! ; $16 per hat
1
1
!! ; 1 mile every 8 min
8
55
!! ; 55 mi/h
1
13. Glen has 18 rock CDs and 15 classical CDs in his collection. He
bought 10 of the rock CDs and 12 of the classical CDs. The rest
were gifts. Compare the ratio of the number of rock CDs that he
bought to the number of rock CDs in his collection with the ratio
of the number of classical CDs that he bought to the number of
classical CDs in his collection.
19. What is the ratio of the number of dimes in a dollar to the
number of nickels in a dollar?
1:2
They are not the same ratio; 5:9 and 4:5.
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
8
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
Holt Middle School Math Course 2
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
80
9
Holt Middle School Math Course 2
Holt Middle School Math Course 2