Minds On
Emily's brother drove 340 miles and used 17
gallons of gas. How many miles per gallon
(mpg) did he get?
Answer:
20 miles per gallon
or 20 mpg
Rates & Unit
Rates
Read this slide, then talk about it with a partner!
What is a rate?
A rate is a ratio that is used to compare measurements with
different units.
What is a unit rate?
A Unit Rate - is a rate with a denominator of 1.
Rate
$32 in 4 hours
36 students at 9 tables
120 miles in 2 hours
$5.94 for 6 sodas
=
=
=
=
Unit Rate
$8 in 1 hour
4 students at 1 table
60 miles in 1 hour
$0.99 for 1 soda
Read this slide, then talk about it with a partner!
There are 672 students in a school and there are 28
teachers. How many students per teacher?
To find the unit rate (or students per 1 teacher) divide
both the numerator and the denominator by the
denominator.
students
teachers
672 ÷ 28 = 24
28 ÷ 28
1
There are 24 students per teacher.
Try these.
Find the unit rates.
20 toys for 5 dogs =
4 toys for 1 dog
click
$735 per week =
(Hint: 5 day work week)
$147 per week
click
For every 12 laps Evan
runs Lucas runs 4
=
Evan runs 3 laps
Lucas runs 1
click
Richard read 27 pages
=
in 3 hours
Richard read 9
click
pages in 1 hour
For each of the
following questions,
answer on a whiteboard
or in your journal
BEFORE you check the
answer 
Emily drove 825 miles in 15 hours.
How many miles per hour (mph) did she drive?
A
815 miles per hour
B
60 miles per hour
C
55 miles per hour
D
15 miles per hour
Answer: C
55 miles per hour
Margot bought 16 oranges for $4. How much does
1 orange cost? (Read carefully!!)
Answer:
We need to find the rate of DOLLARS
per ORANGE (not oranges per dollar )
$4 ÷ 16 = $0.25 per orange
Brian bought 3 pounds of chicken for $10.47. How
much was one pound of chicken?
Answer:
Again, we need to find the rate of
DOLLARS per POUND of chicken
$10.47 ÷ 3 = $3.49 per pound
Unit rate is very useful to compare costs of the same
item in different quantities. Because the cost cannot be
compared by the packaged amount, use the unit rate of
each to do a comparison.
Compare these products:
Everyday
Low Price
1 roll for $.99
9 for $10.44
Everyday
Low Price
9 for $10.44
1 roll for $.99
C
A
B
# of
Rolls
Total
Cost
Divide
by
Cost
per roll
Deal
1
.99
1
.99
A
8
7.76
8
.97
B
9
10.44
9
1.16
C
Everyday
Low Price
9 for $10.44
1 roll for $.99
C
A
B
# of
Rolls
Total
Cost
Divide
by
Cost
per roll
Deal
1
0.99
.99
11
$0.99
.99
A
8
7.76
7.76
88
$0.97
.97
BEST!
B
9
10.44
10.44
9
$1.16
1.16
C
A store was selling 8 mangos for $10 at the farmers market.
Keisha said,
"That means we can write the ratio 10 : 8, or $1.25 per
mango."
Luis said,
"I thought we had to write the ratio the other way, 8 : 10,
or 0.8 mangos per dollar."
Can we write different ratios for this situation?
Explain why or why not.
A store was selling 8 mangos for $10 at the farmers market.
Keisha said,
"That means we can write the ratio 10 : 8, or $1.25 per
mango."
Luis said,
"I thought we had to write the ratio the other way, 8 : 10,
or 0.8 mangos per dollar."
Can we write different ratios for this situation?
Although we COULD use either ratio, it is more reasonable to use
the ratio of dollars per mango since you cannot buy less than one
mango 
150 ÷ 20 = 7.5 min per mile so 7.5 x 6 = 45 minutes to run 6 miles
20 ÷ 150 = 0.13 mile per min so 0.13 x 15 = about 2 miles in one minute
20 ÷ 150 = 0.13 mile per min then 0.13 x 60 = 7.8 miles per hour
150 ÷ 20 = 7.5 min per mile
Which would be the best deal?
A
5 candy bars for $6.25
B
8 candy bars for $7.28
C
10 candy bars for $ 9.70
D
12 candy bars for $11.04
Answer:
A
B
C
D
$6.25 ÷ 5 = $1.25 per candy bar
$7.28 ÷ 8 = $0.91 per candy bar
$9.70 ÷ 10 = $0.97 per candy bar
$11.40 ÷ 12 = $0.95 per candy bar
Tim ran 1 mile in 11 minutes, Bob ran 4 miles in 43
minutes, Rosana ran 15 miles in 158 minutes and
Carrie ran 23 miles in 230 minutes. Who ran the
fastest?
A
Tim
B
Bob
C
Rosana
D
Carrie
Answer:
A
B
C
D
11 min ÷ 1 mi = 11 min per mile
43 min ÷ 4 mi = 10.75 min per mile
158 min ÷ 15 mi = 10.5 min per mile
230 min ÷ 23 mi = 10 min per mile