Name
Understanding Ratios
P 6-1
A string quartet consists of 2 violins, 1 viola, and 1 cello. Write a ratio
for each comparison in three ways.
1. violins to cellos
2. cellos to violas
3. violins to all instruments
4. Number Sense How are the ratios in Exercises 1 and 2 different
from the ratio in Exercise 3?
Midland Orchards grows a large variety of apples. The orchard
contains 12 rows of Granny Smith trees, 10 rows of Fuji trees, 15
rows of Gala trees, 2 rows of Golden Delicious trees, and 2 rows of
Jonathan trees. Write each ratio in three ways.
5. rows of Granny Smith trees to rows of
Golden Delicious trees
6. rows of Fuji trees to the total number of
rows of trees
Test Prep
© Pearson Education, Inc. 6
7. A grade school has 45 students who walk to school and
150 students who ride the bus. The other 50 students are driven
to school. Which shows the ratio of students who walk to school
to the total number of students in the school?
A. 45:50
B. 45:195
C. 45:150
D. 45:245
8. Writing in Math Steve said it does not matter which term is first
and which term is second in a ratio, since ratios are different
than fractions. Is he correct? Explain why or why not.
Use with Lesson 6-1.
65
Name
Equal Ratios
P 6-2
Give three ratios that are equal to each ratio.
1. 3 to 9
2. 1:2.5
3.
1
8
9
Tell whether the ratios in each pair are equal.
4.
5
6
and 1120
5. 7:7 and 100:100
6. 1:9 and 0.5:4.5
Write each ratio in simplest form.
7. 51:17
8.
9. 5:25
1.
2
8.4
10. 14 to 35
11. Number Sense What operations can be used to find equal
ratios? What operations cannot be used to find equal ratios?
12. Which ratio is equal to 95:100?
A.
9.5
1.0
B. 100:95
C. 180:200
D.
13. Writing in Math Find a ratio equal to 55:11. Tell what operation
you used to find your answer.
66
Use with Lesson 6-2.
285
300
© Pearson Education, Inc. 6
Test Prep
Name
Rates and Unit Rates
P 6-3
Write each as a unit rate.
1. 120 mi to 10 gal of gas
2. 45 pages in 30 min
3. 500 mi in 25 hr
4. $12.00 for 3 lb
Which is the better buy?
5. 1 lb of apples for $1.98 or
3 lb for $6.95
6. 5 lb of flour for $0.90 or
8 lb for $1.25
Which is the lower rate?
7. 44 people in 4 theaters or 100 people in 10 theaters
8. 8 cashiers for 96 people or 2 cashiers for 20 people
9. Number Sense What makes a unit rate different from other rates?
10. NASA’s space shuttle orbits Earth
1 time in 90 minutes. How many times would
the space shuttle orbit Earth in 6 hours?
© Pearson Education, Inc. 6
Test Prep
11. Which is the unit rate for 39 people in 3 vans?
A. 39 people per van
B. 13 vans per person
C. 13 people per van
D. 3 people per van
12. Writing in Math Explain how you could convert a rate of miles
per hour to a rate of miles per second.
Use with Lesson 6-3.
67
Name
Understanding Proportions
P 6-5
Decide if the ratios form a proportion.
1.
12 m
in 36
ft
30 m
in ; 90 m
in
3. $5.00:1 hr; $200.00:40 hr
5.
32 gal 64 sec
2 s
ec ; 4 g
al
2.
15 mi 25 mi
1 gal ; 1 gal
4.
200
ft 4,00
0 ft
1 sec ; 20 sec
6. $18.75:10 lb; $56.25: 30 lb
12 mi
24 mi
7. Number Sense Explain how you could write 30 m
in and 1 hr
as a proportion.
8. Algebra What value of x would form a proportion?
32 mi
160
mi
x 50 min
9. Which two fruit stands’ apple
to orange ratios are equal?
Fruit Stand Apples Oranges
10. Write a ratio equal to Chloe’s
apple to orange ratio.
Kendra
32
4
Chloe
10
25
Hillary
7
21
16
2
Bethany
Test Prep
45 mi
11. Which of the following ratios forms a proportion with 1 hr ?
© Pearson Education, Inc. 6
A.
21 mi
30 s
ec
B.
4.5
mi
1 min
C.
450
mi
10 hr
D.
45
hr
1 mi
5m
i
12. Writing in Math Write a ratio that is proportional with 20 m
in .
Explain how you found this ratio.
Use with Lesson 6-5.
69
Name
Solving Proportions
P 6-6
Solve each proportion using any method.
1.
12
ft
t hr
20
ft
4 hr
3.
65 mi
1 hr
715
mi
r hr
2.
$45
.00
2 wk
4.
w k
m
3 hr
b
1 wk
900
km
30 hr
35 mi
350 mi
5. Number Sense Explain how you can tell that 30 m
in 300 min
using mental math.
6. How many cups of sand would you use to make
66 c of potting soil?
Potting Soil for Ferns
(Makes 22 c)
7. How many cups of humus would you use to make
11 c of potting soil?
6 c sand
6 c loam
6 c peat moss
8. If you made an amount of potting soil that called
for 78 c of sand, how many cups of humus would
you need?
3 c humus
1 c dried cow manure
Test Prep
9. Which is the correct value for y?
135
mi
12 min
A. 4 mi
B. 36 mi
C. 4 min
10. Writing in Math Find a set of values for x and y to make
4m
i
xy 32 m
in a proportion. Explain how you found the values.
70
Use with Lesson 6-6.
D. 36 min
© Pearson Education, Inc. 6
45 mi
y min
Name
Solving Proportions Using
Cross Products
P 6-7
Solve each proportion using cross products. Round to the nearest
hundredth as needed.
1.
r
45
90
27
0
2.
3
2
h
5.
9
12
3.
45
60
8g1
4.
78
y
98
10
0
5. Number Sense Are the two ratios that make up
a proportion always, sometimes, or never equivalent?
The weight of objects on Earth would vary on other planets. This is
due to the different gravitational force on each planet. The weight of
objects on other planets can be determined by solving proportions.
6. An object that weighs 10 lb on Earth weighs 9 lb on
Venus. What would an object that weighs 90 lb on Earth
weigh on Venus?
7. An object that weighs 100 lb on Earth weighs 112.5 lb
on Neptune. What would an object that weighs 50 lb on
Earth weigh on Neptune?
8. An object that weighs 234 lb on Jupiter weighs 100 lb
on Earth. What would an object that weighs 400 lb on
Jupiter weigh on Earth? (Round your answer to the
nearest hundredth.)
Test Prep
© Pearson Education, Inc. 6
9. Cecelia has read 12 books this summer and has collected
72 tokens from the library’s summer reading program. Which of
the following shows how to solve for the number of tokens
rewarded for each book?
A.
12
72
1t
B.
1
2
1
7t2
C.
12
72
1t
D.
1
1
2
7t2
10. Writing in Math Explain how you would use mental math to
solve the proportion 7w5 12.
Use with Lesson 6-7.
71
Name
Using Formulas
P 6-9
Area Conversion
Use the formulas to solve the problems.
s
a
43.56
1. If the area is 5 acres, what is the
area in square feet?
s 43.56 a
a acres
s square feet
2. If the area is 500.94 ft2, what is the
area in acres?
3. If the area is 1,359.072 ft2, what is the
area in acres?
4. Estimation José says that a quick way to estimate the area
in square feet is to multiply the number of acres by 40. Does his
method make sense? Is it a good way to estimate?
5. Elise’s science teacher had the students count their
pulse for 10 seconds. They then used the formula beats in
10 sec 6 beats per minute. If Elise counted 12 beats
in 10 sec, how many beats would she have in 1 minute?
Test Prep
6. If there are about 28.35 g in 1 oz, about how many grams are
equal to 16 ounces?
© Pearson Education, Inc. 6
A. 0.56 g
B. 1.77 g
C. 453.6 g
D. 4,356 g
7. Writing in Math Explain how you would use the data in Exercise 6
to find the number of ounces in a certain number of grams.
Use with Lesson 6-9.
73
Name
Scale Drawings and Maps
P 6-10
Scale: 1 in. 20 ft
0.5
in.
4.7 in.
0.5
in.
2.5 in.
2.5 in.
Center line
4.7 in.
0.5
in.
Open space
1. What is the actual length and width of a college
basketball court?
2. How far should open space extend from each
side of the court?
3. What is the actual measurement from the end of
the court to the center line?
4. Reasoning What is the scale on a map that shows
two cities that are 400 mi apart as 2.5 in. apart?
5. If the scale of a drawing is 1 in. 2.5 ft, which is the actual size
of an object that is 2 in. long in the drawing?
A. 1 in.
B. 5 in.
C. 2.5 ft
D. 5 ft
6. Writing in Math Explain how you would choose a scale to use
for a map. What things would you need to consider?
74
Use with Lesson 6-10.
© Pearson Education, Inc. 6
Test Prep
Name
PROBLEM-SOLVING APPLICATIONS
P 6-11
Sandwich Shop Hours
Schedule
FRANK’S SANDWICH SHOP
——————
Name
Mon.
Tues.
Wed.
Sasha
9–5
9–5
12–6
Miguel
5–8
5–8
Eric
Thurs.
10–6
Frank
9–6
9–12
9–6
Fri.
Sat.
9–5
9–5
5–8
5–8
Sun.
5–8
5–8
Jen
Week of Aug. 12
9–5
9–6
12–6
12–6
12–5
9–6
12–4
1. What ratio describes the number of hours that
Eric worked to the number of hours that
Frank worked?
2. What ratio describes the number of hours that
Miguel worked to the number of hours that
Frank worked?
3. What ratio describes the number of hours
that Jen worked to the number of hours
all of the employees worked?
© Pearson Education, Inc. 6
4. Since everyone at the sandwich shop gets paid
by the hour, the amount of pay is proportionate
to the amount of work. If Sasha got paid
$304.00 for the week of August 12, what
would she have gotten paid for a week
she worked 30 hr?
5. Using the information in Exercise 4, express
Sasha’s pay as a unit rate.
6. Frank gets paid twice as much as the other
workers. Express Frank’s pay as a unit rate.
7. If Miguel gets paid $9.00 per hour, how much
did he earn the week of August 12?
8. Jen made $212.50 the week of August 12.
Express her pay as a unit rate.
Use with Lesson 6-11.
75