Basic Mathematics for College Students

Caution! When a ratio is written as a fraction, the fraction should be in

simplest form. (Recall from Chapter 3 that a fraction is in simplest form,or

lowest terms,when the numerator and denominator have no common factors

other than 1.)

5.1 Ratios 415

EXAMPLE (^1) Write each ratio as a fraction: a.3 to 7 b. 10  11
StrategyWe will identify the numbers before and after the word toand the
numbers before and after the colon.
WHYThe word toand the colon separate the numbers to be compared in a ratio.
Solution
To write the ratio as a fraction, the first number mentioned is the numerator and
the second number mentioned is the denominator.
a.The ratio 3 to7 can be written as. The fraction is in simplest form.
b.The ratio 10:11 can be written as. The fraction is in simplest form.

10
11

10

11





3

7

3

7



Self Check 1

Write each ratio as a fraction:

a.4 to 9 b. 8  15

Now TryProblem 13

EXAMPLE (^2) Write the ratio 35 to 10 as a fraction in simplest form.
StrategyWe will translate the ratio from its given form in words to fractional
form. Then we will look for any factors common to the numerator and denominator
and remove them.
WHYWe need to make sure that the numerator and denominator have no
common factors other than 1. If that is the case, the ratio will be in simplest form.
Solution
The ratio 35 to10 can be written as. The fraction is not in simplest form.
Now, we simplify the fraction using the method discussed in Section 3.1.
The ratio 35 to 10 can be written as the fraction , which simplifies to (read as
“7 to 2”). Because the fractions and represent equal numbers, they are called
equal ratios.
7
2
35
10
7
2
35
10



7

2

Factor 35 as 57 and 10 as 25. Then remove the

(^) common factor of 5 in the numerator and denominator.

35

10



5

1

 7

2  5

1



(^3510)

35

10



Self Check 2

Write the ratio 12 to 9 as a

fraction in simplest form.

Now TryProblems 17 and 23