Ratios and Rates
ratio – a comparison of two
numbers by division written
in several different forms.
This This

That That
Rates and Unit Rates
(if you have a particular question move
yourself to the breakout room)
Rate
• A ratio that
compares two
quantities with
different kinds of
units
• Examples:
– 195 miles in 3 hours
– 132 texts in 4 days
– $95 in 5 hours
Unit Rate
• A rate that is
simplified so that it
has a denominator
of 1 unit
• Examples:
– 65 miles per (one)
hour
– 33 texts per (one) day
– $19 per (one) hour
Ratios and Rates
If you have a particular question move
yourself to the breakout room
rate – a ratio that compares
different kinds of units by
division to obtain a unit rate
or rate per unit.
Find the Unit Rate
Mary drove 180 km in 3 hours.
How far did she drive in 1 hour?
A. 9 km
B. 6 km
C. 150 km
D. Answer not given
Find the Unit Rate (if you have a
particular question move yourself to
the breakout room
I purchased hot dogs for my son’s
baseball team. I paid $54 for hot
dogs for 18 players. How much
did each hot dog cost me?
A. $4 each
B. $5 each
C. $3 each
D. $36 each
If you have a particular question move
yourself to the breakout room
Find the unit rate:
160 words typed in 4 minutes
A. 40 wpm
B. 120 wpm
C. 30 wpm
D. Answer not given
If you have a particular question move
yourself to the breakout room
Find the unit rate:
$27.40 for 4 hours
of work
A. $5.75 per hour
B. $6.85 per hour
C. 13.70 for 2
hours
D. Answer not
given
Find the unit rate:
$12.66 for 8 pkgs
of juice boxes
A. $1.58 per pkg
B. $1.59 per pkg
C. $4.66 per pkg
D. $1.25 per pkg
If you have a particular question move
yourself to the breakout room
The price for 12 shirts is $90.
Which of the following represents
the same price per shirt?
• A. 15 shirts for $120
• B. 9 shirts for $69.75
• C. 19 shirts for $142.50
• D. 10 shirts for $72.50
If you have a particular question move
yourself to the breakout room
Adrienne biked 22 miles in 4
hours. If she bikes at the same
rate, how far can she bike in 7
hours?
A. 36.5 miles
B. 38.5 miles
C. 41.5 miles
D. 43.5 miles
If you have a particular question move
yourself to the breakout room
The table shows the cost of calculators.
How much does it cost to purchase 11 calculators
A.
B.
C.
D.
98.50
93.50
107.25
102.15
?
Number of Calculators Total Price
Purchased
2
$19.50
4
$39.00
6
$58.50
8
$78.00
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 1
=
÷
8
3
24
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
=
inch of rain per day
30 ÷ 5 6
120 words in 3 minutes
120 ? words
40 words
=
3 1 per minute per minute