Page 1 of 5
Ratios
BEFORE
Now
WHY?
You wrote and compared
fractions.
You’ll write and compare
ratios.
So you can write a ratio about
reptiles, as in Ex. 23.
In the Real World
Word Watch
ratio, p. 369
equivalent ratios, p. 369
Baseball How can you compare
a baseball team’s wins to its losses
during spring training?
A ratio uses division to compare
two numbers. There are three ways
to write a ratio of two numbers.
2001 Spring Training
Team
Wins
Losses
San Diego Padres
16
11
L.A. Dodgers
18
13
Chicago Cubs
17
14
Writing a Ratio
Words
Numbers
Algebra
wins to losses
18 to 13
a to b, where b is nonzero.
wins
losses
18
13
a
, where b is nonzero.
b
wins : losses
18 : 13
a : b, where b is nonzero.
All three ways of writing the ratio of two numbers are read “the ratio of
a to b,” so 18 : 13 is read “the ratio of eighteen to thirteen.” Two ratios are
equivalent ratios when they have the same value.
EXAMPLE
1
Writing a Ratio
You can make comparisons about games played by the Cubs.
a. Wins to losses
b. Wins to games played
wins 17, losses 14
17
14
ANSWER 17 : 14, or Your turn now
wins 17, games 17 14 31
17
31
ANSWER 17 : 31, or Use the table above to write the ratio for the Padres.
1. Wins to losses
2. Wins to games played
3. Losses to wins
Lesson 8.1
Ratios
369
Page 2 of 5
EXAMPLE
2
Writing Ratios in Simplest Form
Amusement Parks A ride on a roller coaster lasts 2 minutes. Suppose
1
2
you wait in line for 1 hours to ride the roller coaster. Follow the steps
below to find the ratio of time spent in line to time spent on the ride.
1 Write hours as minutes so that the units are the same.
1
2
1 h h 60 min 30 min
Write hours as minutes.
90 min
Add.
2 Write the ratio of time spent in line to time spent on the ride.
Time in line
90
Ti me on ride
2
45
1
Write ratio.
Simplify fraction.
ANSWER The ratio of time spent in line to time spent on the ride is 45 : 1.
Comparing Ratios To compare ratios, you can write the ratios as
fractions and compare the fractions. However, sometimes it is easier
to write the ratios as decimals and compare the decimals.
EXAMPLE
3
Comparing Ratios
Music Luis and Amber compared
their CD collections. To determine
who has a greater ratio of rock
CDs to pop CDs, write the ratios.
with
Review
Need help with writing
fractions as decimals?
See p. 190.
Rock
Pop
9
24
Luis: 0.375
Rock
Pop
Rock
Pop
Hip-hop
Luis
9
24
16
Amber
42
70
25
42
70
Amber: 0.6
Write ratios as fractions.
Write fractions as decimals.
ANSWER Since 0.6 > 0.375, Amber has a greater ratio of rock to pop CDs.
Your turn now
Refer to Example 3.
4. Does Luis or Amber have a greater ratio of pop CDs to hip-hop CDs?
5. Does Luis or Amber have a greater ratio of hip-hop CDs to rock CDs?
370
Chapter 8
Ratios and Proportions
Page 3 of 5
INTERNET
Exercises
eWorkbook Plus
CLASSZONE.COM
More Practice, p. 712
Getting Ready to Practice
1. Vocabulary Give an example of a ratio in real life.
In Exercises 2–5, write the ratio of the first number to the second
number in three ways.
2. 1, 7
3. 1, 1
4. 3, 10
5. 15, 2
6. Write the following ratios in order from least to greatest: 5 to 8, 3 to 6,
and 15 to 5.
7. Raffle Tickets For a school fundraiser, you sold 33 raffle tickets and
your friend sold 15 raffle tickets. Write the ratio of tickets you sold to
tickets your friend sold as a fraction in simplest form.
Practice and Problem Solving
with
Example
1
2
3
Homework
Exercises
8–11, 13
14–29, 33–34
30–32, 35–36
Online Resources
CLASSZONE.COM
• More Examples
• eTutorial Plus
School The table shows the numbers of boys and girls in the
seventh and eighth grades at a school. Use the table to write the
specified ratio.
8. Seventh grade boys to eighth grade boys
9. Eighth grade girls to eighth grade boys
10. Seventh grade girls to all seventh graders
Boys
Girls
Seventh
47
42
Eighth
39
41
11. Eighth grade boys to all eighth graders
12. Find the Error Zach was asked to find
9
T-shirts
14
Jeans
the ratio of his T-shirts to his jeans. Zach
has 14 T-shirts and 9 pairs of jeans.
Describe and correct his error.
13. Muscles Your face uses about 13 muscles
to smile and about 43 muscles to frown.
Write the ratio of muscles used for
frowning to muscles used for smiling
in three different ways.
Write the ratio as a fraction in simplest form.
7
14. 14
12
15. 15
16. 8 : 14
17. 9 to 5
18. 20 to 35
19. 32 : 48
20. 30 : 75
21. 65 to 130
22. 54 to 72
Lesson 8.1
Ratios
371
Page 4 of 5
23. Reptiles There are about 4000 known
kinds of lizards and 1600 known kinds
of snakes. Write the ratio of known
kinds of lizards to known kinds of
snakes.
Write the ratio of the first measurement to the
second measurement. Write both measurements
in the same unit.
24. 3 qts, 2 gal
25. 5 ft, 10 in.
26. 2 lb, 18 oz
27. 2 ft, 4 yd
28. 600 m, 5 km
29. 7 min, 25 sec
Copy and complete the statement using <, >, or .
30. 9 : 15 _?_ 8 : 20
31. 18 : 12 _?_ 54 : 36
32. 72 : 96 _?_ 56 : 80
3
33. Restaurants You spend a total of 1 hours at a restaurant with your
4
family. You spend 20 minutes eating your dinner. What is the ratio of
your time spent at the restaurant to your time spent eating?
34. Papier-Mâché A recipe for papier-mâché paste uses 2 quarts of white
glue and 2 pints of water. What is the ratio of pints of glue to pints of
water?
Education The table shows the number of men and women who
earned master’s degrees in the United States in 1970 and in 1998.
35. Write the ratio of degrees earned by
men to degrees earned by women
for each year. Express the ratios as
decimals rounded to the nearest
hundredth.
Master’s Degrees Earned
Year
1970
1998
Men
126,000
184,000
Women
83,000
246,000
36. Which of the ratios in Exercise 35 is
less than the other?
37. Estimate In 15 seconds, your dog ran a distance of 97 yards, and you
ran a distance of 152 feet. Choose the most reasonable estimate of the
ratio of the distance you ran to the distance your dog ran.
A. 1 : 1.5
B. 1 : 2
C. 1.5 : 1
D. 2 : 1
Algebra Find a value for x that makes the first ratio equivalent to
the second ratio.
38. x to 6, 20 to 24
39. x to 72, 5 to 8
40. x to 12, 6 to 9
41. Challenge The ratio of the length of a rectangle to the width of the
rectangle is 5 : 4. If the perimeter of the rectangle is 108 inches, what
are the length and the width of the rectangle?
372
Chapter 8
Ratios and Proportions
Page 5 of 5
Mixed Review
Solve the equation using mental math. (Lesson 1.5)
42. x 3 10
43. 18 z 9
x
45. 6
8
44. 4y 44
Choose a Strategy Use a strategy from
the list to solve the following problem.
Explain your choice of strategy.
Problem Solving Strategies
Find a Pattern
Make a Table
■ Work Backward
■
■
46. On a trip to the mall, you spent $8 at the
first store, then half of your remaining
money at a second store. You spent the
rest of your money, $16, at a third store.
How much money did you start with?
Basic Skills Find the product or quotient.
47. 62 14
48. 437 1000
49. 405 9
50. 588 12
Test-Taking Practice
51. Multiple Choice Which ratio is not equivalent to 6 to 10?
INTERNET
State Test Practice
CLASSZONE.COM
A. 6 : 10
3
5
5
3
C. B. 3 : 5
D. 52. Multiple Choice You used 3 yards of fleece to make a blanket and
2 feet of fleece to make a vest. What is the ratio of fleece used for the
blanket to fleece used for the vest?
2
9
2
3
F. 3
2
G. 9
2
H. I. Something to Celebrate
Replace each ratio with the letter of an equivalent ratio to find the name
of a famous American born on January 1, 1752. Some letters may be used
more than once.
6
24
1
4
B. 6
18
12
16
1
3
E. 4
6
1
2
O. 12
20
7
7
3
5
R. 2
3
S. 15
30
10
15
3
4
T. 12
18
1
1
Y. Lesson 8.1
Ratios
373