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 RatesThe 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 RatesRatios can show comparisons between:part to part

red to green

1 to 2

green to red

2 to 1

Ratios and RatesRatios can show comparisons between:part to whole

red to whole

1 to 3

green to whole

2 to 3

Ratios and RatesRatios can show comparisons between:whole to part

whole to red

3 to 1

whole to green

3 to 2

Ratios and RatesCompare octagon to all shapes

1 to 8

1 out of 8 1 : 8

1/8

Ratios and RatesCompare all shapes to trapezoid

8 to 1 8 : 1 8/1

Ratios and RatesCompare pentagons to hexagons

2 to 3 2 : 3 2/3

Ratios and RatesGive each ratio in three forms.

8 roses out of 24 flowers

8 to 24 8 : 24 24

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