You have already learned operations with fractions. (Lessons 3–3 and 3–4)

• Write ratios as fractions in simplest form.

• Simplify ratios involving measurements.

Each is read, "the ratio of a to b." Each ratio should be in simplest form.

Find the ratio of boys to girls in this class

Write Ratios in Simplest Form

A team won 12 out of 18 games. Find the ratio of: a) wins to total games

b) wins to losses

a)

÷6

÷6

Divide the numerator and the denominator by the GCF, 6.

1218

23

Write Ratios in Simplest Form

A team won 12 out of 18 games. Find the ratio of:

b) wins to losses

First, find the number of losses:

18 – 12 = 6

Then write the ratio of wins (12) to losses (6) as a fraction.

÷6

÷6

Divide the numerator and the denominator by the GCF, 6.

12 6

21

The ratio of wins to losses is 2 to 1. This means the for every 2 wins the team had 1 loss or the team had twice as many wins as losses.

Express the ratio 8 golden retrievers out of 12 dogs as a fraction in simplest form.

A.

B.

C.

D.

Twelve out of 30 joggers are male. Write this ratio as a fraction in simplest form.

A.

B.

C.

D.

Write Ratios As Fractions

Express the ratio 6 days to 2 weeks as a fraction in simplest form.

The unit needs to be the same, so we have to convert 2 weeks to 14 days.

Then, divide the numerator and denominator by the GCF, 2.

Written in simplest form, the ratio is 3 to 7.

6 days2 weeks

6 days ÷ 214 days ÷ 2

= =37

Write Ratios As Fractions

Express the ratio 21 inches to 2 yards as a fraction in simplest form.

Convert 2 yards to 72 inches. Then, divide the numerator and denominator by the GCF, 3.

Written in simplest form, the ratio is 7 to 24.

21 inches72 inches

1 yard = 36 inches

÷ 3÷ 3

Express the ratio 4 feet to 18 inches as a fraction in simplest form.

A.

B.

C.

D.