Ratios and Rates

Ratios and Rates

ratio – a comparison of two

numbers by division written

in several different forms.

That

This

That

This

Ratios and Rates

rate – a ratio that compares

different kinds of units by

division to obtain a unit rate

or rate per unit.

Ratios and Rates

The order of the numbers in

a ratio should match the

order of the words in a ratio.

apples to oranges

2 to 3

Ratios and RatesRatios can be written in

several different ways.

3 to 1

3 : 1

3/1

red to white

Ratios and Rates

Ratios can show comparisons

between:

part to part

red to green

1 to 2

green to red

2 to 1

Ratios and Rates

Ratios can show comparisons

between:

part to whole

red to whole

1 to 3

green to whole

2 to 3

Ratios and Rates

Ratios can show comparisons

between:

whole to part

whole to red

3 to 1

whole to green

3 to 2

Ratios and Rates

Compare octagon to all shapes

1 to 8

1 out of 8 1 : 8

1/8

Ratios and Rates

Compare all shapes to trapezoid

8 to 1 8 : 1 8/1

Ratios and Rates

Compare pentagons to hexagons

2 to 3 2 : 3 2/3

Ratios and Rates

Give each ratio in three forms.

8 roses out of 24 flowers

8 to 24 8 : 2424

8

3 dogs out of 12 animals

3 to 12 3 : 1212

3

Ratios and RatesA ratio in fraction form can be

expressed in simplest form by

dividing the numerator and

denominator by a common

factor.

24

8 ÷ 8

÷ 8

=

3

1

12

3 ÷ 3

÷ 3

=

4

1

Ratios and RatesTo express a ratio as a rate per

unit, write the ratio as a fraction

and then divide the numerator

by the denominator.

395 miles in 5 hours

5

395=

79 miles

per hour

miles

hours 1

? miles

hours

Ratios and RatesExpress each ratio as a rate.

5 inches of rain in 30 days

30

5=

6

1inch of rain per day

120 words in 3 minutes

3

120=

40 words

per minute1

? wordsper minute

÷ 5

÷ 5