Ratios, Rates, and Unit Rates
across the Universe
RATIOS
A ratio makes a comparison of two
quantities using division. There
are 3 green aliens and 4 purple
aliens. The ratio of
green aliens to
purple aliens is
3 to 4.
RATIOS
A ratio makes a comparison. The
ratio of green aliens to total aliens
is 3 to 7. The ratio of
total aliens to purple
aliens is 7 to 4.
RATIOS
A ratio makes a
comparison
using division.
Ratios can be
written in three
different ways.
3 to 4
3:4
3
4
Find Each Ratio
1. Purple to total
2. Green to total
3. Purple to green
4. Green to purple
Using Tape Diagrams to Solve
Using Table to Solve
Think About It
• This recipe has a ratio of 3 cups of flour to
4 cups of sugar, so there is 3/4 cup of flour
for each cup of sugar.“
3cups :4 cups
Think About It
• 52 wings:26 beaks
• “The ratio of wings to beaks in the bird
house at the zoo was 2:1, because for
every 2 wings there was 1 beak.”
Write the ratios in simplest form.
•
•
•
•
1. 5 to 13 5/13 because it cannot be simplified.
2. 7 to 35 1/5 because you can divide both by 7.
3. 6 to 9
2/3 because you can divide both by 3.
The ratio of wins to losses for a team with
14 wins and eight losses.
14 = 14/2 = 7 wins
8
8/2 4 losses
Ratio- Real Life Application
• You are painting a room and want to mix
red and blue to make purple. The ratio
should be 15 oz. red to 20 oz. blue. 15:20
Put this in simplest terms:
•
15 = 15/5 = 3 oz. red
20 20/5 4 oz. blue
Solve
RATES
A rate is a ratio that compares quantities that
are measured in different units.
This spaceship travels at a certain speed.
Speed is an example of a rate.
Speed can be measured in many different ways.
This spaceship can travel
100 miles in 5 seconds. 100 miles in 5 seconds is a rate.
RATES
A rate is a ratio that compares quantities that
are measured in different units.
Rates are often written in fraction form.
100 miles in 5 seconds is a rate.
It can be written as…..
100 Miles
5
Seconds
RATES
A rate is a ratio that compares quantities that
are measured in different units.
One key word that often identifies a rate is PER.
Miles per gallon, Points per free throw,
Dollars per pizza, Sticks of gum per pack
Per means DIVIDE
UNIT RATES
Most of the time when we work with rates we
use a unit rate. A unit rate compares a quantity
to one unit of another quantity.
This alien can walk at a rate of 10 miles in 2 hours.
We need to find out how fast he can walk in 1 hours.
Divide 2/2 to get 1 hour. Then divide 10/2 to get 5.
His speed is a unit rate of 5 miles per 1 hour or simply 5
miles per hour.
10
2
Miles
Hours
5
=
1
Miles
Hour
UNIT RATES
A unit rate compares a quantity to one unit of
another quantity. These are all examples of
unit rates.
2 eyes per alien
1 foot per leg
6 tentacles per head
1 tail per body
3 windows per spaceship
3 riders per spaceship
2 people riders per dog rider
Think About It
• "We paid $75 for 15 hamburgers, which
is a rate of $5 per hamburger." How do
we know if this is right? $75 ÷ 15 = 5
Real Life Application
A car traveled 300 miles on 10 gallons of
gas. What is the unit rate (miles per gallon)?
300 = 300/10 = 30 miles
10 10/10
1 gallon of gas
(30 miles per gallon)
Solve It
• JoJo earned $50 in five hours cutting grass.
What is the unit rate?
50 = 50/5 = 10 dollars
5
1
1 hour
($10 per hour)
Real Life Application
• On vacation, Mike hiked 30 miles in six
hours. What is the unit rate?
30 = 30/6 = 5 miles
6
6/6
1 hour
(five miles per hour)
Find the unit rate.
• 1) 84 students in 4 classrooms
84 students
x
4 classrooms = 1
• 2)
21 students/per classroom
$30 for 8 lunches
$30
8
= x
1
$3.75/per lunch
Find the unit rate
• 3) 15,000 cars sold by 2000 dealers
15,000 = x
2,000
1
7.5 cars/dealer
• 4) Your heart beats 70 beats/min. How
many beats per hour is this?
4200 beats/hour