Step 1: Multiply means and extremes
How do I
Step 2: Find equivalent fractions
solve
proportions?
Types:
1. The word “to”
a to b
2. Colon a:b
𝐚𝐚
3. Fraction
𝐛𝐛
Unit Rate
Definition: a rate with
a denominator of 1
1
**use proportions to find unit rate
RATIO
Definition: a
comparison of 2
Proportion
Definition: a statement that says
two ratios are EQUAL
𝐚𝐚
𝐛𝐛
different things
=
𝐜𝐜
𝐝𝐝
a:b=c:d
a is to b as c is to d
Rate
Definition: a ratio
that compares 2
quantities measured
in different units
Ratio + units = RATE
Ex. 100 miles per 2 hours
**different units of measurement
Proportions are used to find
values that are MIA
Ex. Doubling a recipe
2 cups of flour is needed to bake
12 cookies, how many cups are
needed to bake 24?
2
12
=
x
24
2(24)=12(x)
x=4
THEREFORE
4 cups of flour is
needed to bake 24
cookies
Express each ratio as a Unit Rate
1. Sandra spent $25 on 3
DVDs. How much is one
DVD?
2. Connor read 10 pages in
3. Brie traveled 250 miles in
2.5 hours. How many pages
5 hours. How many miles
did he read in one hour?
did she travel in one hour?
4. 5 quarts of water for every 5. 48 cupcakes in 3 hours
2 tablespoons of a bleach
6. Typed 120 words in 3
minutes
7. Ran 36 laps in 30 minutes
9. $40.80 for 5 pizzas
8. Shot 18 hoops in 15
seconds
Use Unit Rates to decide whether Store A or Store B has the better deal.
Answer
1.
Store A
1 apple for 0.19
Store B
3 apples for 0.59
2.
20 pounds of pet food for $14.99
50 pounds of pet food for $37.99
3.
A car that travels 308 miles on 11
gallons of gas
A car that travels 406 miles on 14
gallons of gas
Are these true proportions? Show your work.
1)
3
𝑎𝑎𝑎𝑎𝑎𝑎
3)
8
𝑎𝑎𝑎𝑎𝑎𝑎
5)
2
4
6
16
𝑎𝑎𝑎𝑎𝑎𝑎
7
2)
4
4)
12
3
3
24
6)
5
and
4
𝑎𝑎𝑎𝑎𝑎𝑎
25
11
3
4
𝑎𝑎𝑎𝑎𝑎𝑎
4
20
2
7
7
12
Solve the following proportions. Show your work.
1)
𝑥𝑥
3)
24
=
5)
2
𝑎𝑎𝑎𝑎𝑎𝑎
4
=
4
16
30
2)
𝑥𝑥
6
2
3
24
2
=
4)
2
=
6)
3
𝑎𝑎𝑎𝑎𝑎𝑎
𝑥𝑥
5
4
3
18
−8
𝑥𝑥
7
12
Set up each proportion and solve. Show your work.
1. Ed earned $112 for 8 hours of work. At this rate, how much will he earn for 40 hours of
work?
2. Rita traveled 1,250 miles in the first 3 days of her trip. At this rate, how long will it take
her to travel 1,875?
3. Mary is preparing for her college entrance exams. In a practice test, she answered 12
problems in 30 minutes. At this rate, how many questions can she expect to answer in 150
minutes?
4. In order to determine her pulse rate, June’s nurse counted 18 beats in 15 seconds. At this
rate, how many beats would she have in 60 seconds?
Homework
Express each ratio as a Unit Rate
1. Xavier spent $35 on 4
CDs. How much is one CD?
2. Tristen read 84 pages in
3.5 hours. How many pages
did he read in one hour?
3. Bianca traveled 300 miles
in 3.75 hours. How many
miles did she travel in one
hour?
Are these true proportions? Show your work.
4.
5
6
𝑎𝑎𝑎𝑎𝑎𝑎
11
12
5.
36
5
and
45
6
Solve the following proportions. Show your work.
6.
𝑥𝑥
8
=
30
6
7.
5
𝑥𝑥
=
3
18
Set up each proportion and solve. Show your work.
8. Josiah earned $135 for 9 hours of work. At this rate, how much will he earn for 40 hours
of work?