Ratios and Rates
Ratios and Rates
ratio – a comparison of two
numbers by division written
in several different forms.
This
That

This
That
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 Rates
Ratios can be written in
several different ways.
red to white
3 to 1
3:1
3/1
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 out of 8
1 to 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 : 24
8
24
3 dogs out of 12 animals
3 to 12
3 : 12
3
12
Ratios and Rates
A ratio in fraction form can be
expressed in simplest form by
dividing the numerator and
denominator by a common
factor.
8
÷8
24
÷8
=
1
3
3
÷3
=
1
12 ÷ 3 4
Ratios and Rates
To 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
395 miles
? miles
79 miles
=
5 hours 1 hours per hour
Ratios and Rates
Express each ratio as a rate.
5 inches of rain in 30 days
5 ÷5 1
=
30 ÷ 5 6
inch of rain per day
120 words in 3 minutes
120
? words
40 words
=
3
1 per minute per minute