MSM07G7_RESBK_Ch05_012-019.pe
2/5/06
8:39 PM
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Name
Date
LESSON
Class
Reteach
5-2 Rates
A rate is a ratio that compares two different kinds of quantities or
measurements. Rates can be simplified. Rates sometimes use the
words per and for instead of to, such as 55 miles per hour and
3 tickets for $1.
The scale on a map might be 3 inches equals 60 miles. Simplify by
dividing both numerator and denominator by the same number.
33
1 inch
3 inches
, or 1 inch to 20 miles
60 3
20 miles
60 miles
A unit rate is a rate per 1 unit. So, in a unit rate, the denominator is
always 1.
Miguel can type 180 words in 4 minutes.
180 words
180 4
45 words
, or 45 words per minute
4 minutes
44
1 minute
rate
unit rate
word form
Find each unit rate. Write in both fraction and word form.
1. Film costs $7.50 for 3 rolls.
2. Drive 288 miles on 16 gallons of gas.
$7.50
7.50 3
$ 2.50
3 rolls
33
1 roll
Word form:
18 mi
288 mi
288 16
16 gal
1 gal
16 16
$2.50 er roll
Word form:
3. Earn $52 for 8 hours of work.
4. Use 5 quarts of water for every
2 pounds of chicken.
$52.00
52 8
$ 6.50
8 hr
88
1 hr
Word form:
18 milesallon
5 qt
52
2 lb
22
$6.50 er hour
Word form:
5. Snowfall of 12 inches in 4 hours
2.5 qt
1 lb
2.5ound
6. 90 students and 5 teachers
3 in.
; 3 inches per hour
1 hr
18 students
; 18 students per
1 teacher
teacher
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All rights reserved.
15
Holt Mathematics
MSM07G7_RESBK_Ch05_077-095.pe
2/6/06
9:54 AM
Page 80
Challenge
5-2 The Rate Maze
Reteach
5-2 Rates
LESSON
LESSON
Contestants A–H must make their way through the maze to the
Winners’ Circle. To reach the Winners’ Circle, each contestant
must find a path from his or her current location through sections
containing equivalent unit prices or rates. The contestants can move
only through sections that share a corner.
A rate is a ratio that compares two different kinds of quantities or
measurements. Rates can be simplified. Rates sometimes use the
words per and for instead of to, such as 55 miles per hour and
3 tickets for $1.
The scale on a map might be 3 inches equals 60 miles. Simplify by
dividing both numerator and denominator by the same number.
5
r $6.4
3 lb fo
5
.1
2
$
per lb
180 words
180 4
45 words
, or 45 words per minute
4 minutes
44
1 minute
2. Drive 288 miles on 16 gallons of gas.
$7.50
7.50 3
$ 2.50
3 rolls
33
1 roll
3. Earn $52 for 8 hours of work.
Word form: 18 miles per gallon
$1.15 per
notebook
2.5 qt
1 lb
2
6. 90 students and 5 teachers
3 in.
; 3 inches per hour
1 hr
18 students
; 18 students per
1 teacher
7,
teacher
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
15
Holt Mathematics
850 words
in 17 min
50 word
per mins
40
pe
hr 3
0
rh
min
r
$7
.2
2 h 0 fo
r r
.60
$39 1 yd
1
for
$3.60
per yd
$6.00 for
5 ft
$1.2
per 0
ft
$3.6
0
90 m for
in
$2
pe .4
rh 0
r
s
word
4,50h0r 30 min
in 1
50
s per
word
min
16
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
Holt Mathematics
Reading Strategies
5-2 Build Vocabulary
Problem Solving
5-2 Rates
LESSON
LESSON
A rate is a special ratio that compares two values that are measured in different units.
Write the correct answer.
1. A truck driver drives from Cincinnati
to Boston in 14 hours. The distance
traveled is 840 miles. What is the
truck driver’s average rate of speed?
2. Melanie earns $97.50 in 6 hours.
Earl earns $296.00 in 20 hours. Who
earns a higher rate of pay per hour?
60 miles per hour
Melanie
3. Mr. Tanney buys a 10-trip train ticket
for $82.50. Ms. Elmer buys an
unlimited weekly pass for $100
and uses it for 12 trips during the
week. Write the unit cost per trip
for each person.
4. Metropolitan Middle School has 564
students and 24 teachers. Eastern
Middle School has 623 students and
28 teachers. Which school has the
lower unit rate of students per
teacher?
Mr. Tanney, $8.25 per trip;
• $8 for 2 pounds of beef
• 12 miles in 3 hours
$8
2 lb
12 mi
3h
pounds compared to dollars
miles compared to hours
5 hours
a rate? Explain.
1. Is the ratio 12 hours
No; it does not compare values that are in different units.
50 yards
a rate? Explain.
2. Is the ratio 18 seconds
Yes; it compares yards to seconds.
Eastern Middle School
375 miles
compare?
3. What does the rate 15 gallons
Ms. Elmer, $8.33 per trip
It compares miles to gallons.
Choose the letter for the best answer.
In a unit rate, the second quantity in the rate is 1 unit. To write a unit rate, write the
rate as a fraction with a denominator of 1.
6. What is the unit price of a 6-ounce
tube of toothpaste that costs $3.75?
F $0.06
G $0.23
H $0.62
J $0.63
嘷
5. Which shows 20 pounds per 5
gallons as a unit rate?
20 lb
A 1 gal
4 lb
B 嘷
1 gal
5 lb
C 1 gal
1 gal
D 4 lb
7. Max bought 16 gallons of gas for
$40.64. Lydia bought 12 gallons of
gas for $31.08. Kesia bought 18
gallons of gas for $45.72. Who got
the best buy?
A Max got the best buy.
B Lydia got the best buy.
C Lydia and Kesia both paid the
same rate, which is better than
Max’s rate.
D Max and Kesia both paid the
嘷
same rate, which is better than
Lydia’s rate.
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
w r
00 r h
, 4 pe
2.
60
$3. r hr
pe
5. Snowfall of 12 inches in 4 hours
rds
wo
00 rs
7,2 in 3 h ords
hr
Word form: 2.5 quarts per pound
$6.50 per hour
$10
.80
fo
$ r4
5p
$0.9
15
$1. pen
per
or
df 5
3 y $8.2
5
$2.7 yd
per
d
4y
for
.40
$14$3.60 per yd
2
for
50
$7. $3.75 per hr
5 qt
52
2 lb
22
5
$5 boo
.7 k
$1.1 5 s fo
r
5p
er b
ook
15 books for ok
$14.25 er bo
8 pens
0
for $9.2
4. Use 5 quarts of water for every
2 pounds of chicken.
$52.00
52 8
$ 6.50
8 hr
88
1 hr
Word form:
6 note
book
for $6.9 s
0
w 5
2 h ord 00
r3 si
0 n
wo50 min
Word form:
$2.50 per roll
18 mi
288 mi
288 16
16 gal
16 16
1 gal
4
1 ,0 0
hr 0
20 wo
wo
mr
rds inds in
per
min
ute
1. Film costs $7.50 for 3 rolls.
50
Find each unit rate. Write in both fraction and word form.
7 lb for
$18.55
$2.65
per lb
4 lb for $8.60
5 lb
$2.1
$7
4 for
hr
$1.
per 7 5
hr
word form
pe rd
rm s
in
unit rate
for
.20
$17 8 lb b
l
5
.1
$2
rate
d
Miguel can type 180 words in 4 minutes.
5 yd
fo
$2 r $13.7
5
.7
5
pe
ry
A unit rate is a rate per 1 unit. So, in a unit rate, the denominator is
always 1.
8y
for d
$22
$2
pe .7
ry 5
d
Find each unit price or rate. Circle the two contestants who will
not be able to get to the Winners’ Circle.
3 inches
33
1 inch
, or 1 inch to 20 miles
60 miles
60 3
20 miles
$8
($8 2)
$4
2 lb
(2 lb 2)
1 lb
rate
Write yes or no to tell if each rate is a unit rate. If it is not a unit
rate, write the unit rate.
$2.75
4. 1h
8. A pack of 12 8-ounce bottles of water
costs $3.36. What is the unit cost per
ounce of bottled water?
F $0.03 per ounce
G $0.04 per ounce
嘷
H $0.28 per bottle
J $0.42 per bottle
17
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
unit rate
Holt Mathematics
100 mi
5. 4 gal
35 lb
6. 1 box
40 ft
7. 5s
Yes
25 mi
No; 1 gal
Yes
8 ft
No; 1s
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All rights reserved.
80
18
Holt Mathematics
Holt Mathematics