Basic Mathematics for College Students

416 Chapter 5 Ratio, Proportion, and Measurement

Self Check 3

CARRY-ON LUGGAGE

a.Write the ratio of the height to

the length of the carry-on

space shown in the illustration

in Example 3 as a fraction in

simplest form.

b.Write the ratio of the length

of the carry-on space to its

height in simplest form.

Now TryProblem 27

Caution! Since ratios are comparisons of two numbers, it would be incorrect

in Example 2 to write the ratio as the mixed number. Ratios written as

improper fractions are perfectly acceptable—just make sure the numerator

and denominator have no common factors other than 1.

To write a ratio in simplest form, we remove any common factors of the

numerator and denominator as well as any common units.

(^723 12)
EXAMPLE (^3) Carry-on Luggage An airline allows its passengers to
carry a piece of luggage onto an airplane only if it will fit in the space shown below.
a.Write the ratio of the width of the space to its
length as a fraction in simplest form.
b.Write the ratio of the length of the space to
its width as a fraction in simplest form.
StrategyTo write each ratio as a fraction, we
will identify the quantity before the word toand
the quantity after it.
WHYThe first quantity mentioned is the
numerator of the fraction and the second
quantity mentioned is the denominator.
Solution
a.The ratio of the to is.
To write a ratio in simplest form, we remove the common factors andthe common
units of the numerator and denominator.
The width-to-length ratio of the carry-on space is (read as “5 to 12”).
b.The ratio of the to is.
The length-to-width ratio of the carry-on space is (read as “12 to 5”).

12

5



12

5

Factor 24 and 10. Then remove the common

factor of 2 and the common units of inches

from the numerator and denominator.

24 inches

10 inches



2

1

12 inches

2

1

5 inches



24 inches

10 inches

length of the space its width



5

12



5

12

Factor 10 as 25 and 24 as 212. Then remove

the common factor of 2 and the common units

of inches from the numerator and denominator.

10 inches

24 inches



2

1

5 inches

2

1

12 inches



10 inches

24 inches

width of the space its length



Your carry-on item

must fit in this box!

Please check before boarding!

24 inches length^10

inches

width

16 inches height