Page 150 - ArithBook5thEd ~ BCC

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Example 183. What is the ratio of 3 to 1 ?
4 2
Solution. Converting the mixed numbers to improper fractions, and rewriting the division as multipli-
cation by the reciprocal, we obtain

✚❃
3 1 15 2 ✚ 15 5 ✚ 2 ✚❃ 1 5
3 ÷ 1 = × = × = .
4 2 4 3 ✚❃ 2 ✚❃ 1 2
✚ 4 ✚ 3
The ratio is 5 : 2.

Example 184. What is the ratio of 22.5 to 15?

Solution. We could perform the decimal division 22.5 ÷ 15, but it is easier to simplify the equivalent
fraction
225 3
= .
150 2
The ratio is 3 : 2.

When finding the ratio of two measurable quantities, we must be sure the quantities are expressed
in the same units. Otherwise the ratio will be a skewed or false comparison.
Example 185. Find the ratio of 15 dollars to 30 cents.

15 1
Solution. If we form the ratio = , we imply that a person walking around with $15 in his pocket
30 2
has half as much money as a person walking around with only 30 cents! The proper comparison is
obtained by converting both numbers to the same units. In this case, we convert dollars to cents. The
correct ratio is
1500 cents 50
= .
30 cents 1

Example 186. Manuel gets a five minute break for every hour he works. What is the ratio of work time
to break time?

Solution. Since 1 hour = 60 minutes, the ratio of work time to break time is

55 minutes 11
= .
5minutes 1

Recall that percent (%) means “per hundred.” So a percent can be viewed as a ratio whose second
term (denominator) is 100.

Example 187. At a certain community college, 55% of the students are female. Find (a) the ratio of
female students to the total number of students, and (b) the ratio of female students to male students.

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