Vocabulary
• A proportion is an equation stating that two
ratios are equal.
– Examples:
a c

b d
or
2 8

3 12
– The cross products of a proportion are equal.
a c
2 8
or
b

d
ad  bc
3

12
2(12)  3(8)
24  24
Example #1
4
10
Determine if the ratios
and
form a proportion.
6
15
If two ratios are
proportional, then
their cross products
will be equal.
?
4(15)  6(10)
60  60
Since 60 = 60, then
this is a proportion.
Example #2
1.2
2
Are the ratios
and
proportional?
4
5
If two ratios are
proportional, then
their cross products
will be equal.
?
1.2(5)  4( 2)
68
Since 6 ≠ 8, then
this is NOT a proportion.
Example #3
¾
16
Do the ratios
and
form a proportion?
⅜
8
If two ratios are
proportional, then
their cross products
will be equal.
3
? 3
(8)  (16)
4
8
66
Since 6 = 6, then
this is a proportion.
Example #4
Solve for x in the proportion below.
x 3

35 7
Since this is a proportion, the
cross products are equal.
Divide both sides by 7
to get x alone.
7 x  3(35)
7 x  105
7 x 105

7
7
x  15
Example #5
Solve for y in the proportion below.
5 10

y 8 .4
Since this is a proportion, the
cross products are equal.
Divide both sides by 10
to get y alone.
5(8.4)  10 y
42  10 y
42 10 y

10 10
4 .2  y
Writing a verbal model will help us set up a proportion when
we are solving story problems.
Example #6
A recipe that serves 10 people calls for 3 cups of flour. If you want
to make the recipe for 25 people, how many cups of flour would you need?
Write a verbal model of what you are
comparing.
cups of flour cups of flour

servings
servings
Substitute in the values you are given.
Use x to represent the quantity that
you are looking for.
3 cups
x cups

10 servings 25 servings
3( 25)  10 x
Solve the proportion using cross
products.
You will need 7.5 cups of
flour to serve 25 people.
75  10 x
75 10 x

10 10
7.5 cups  x
We can use proportions to convert units of measurement.
Example #7
The Circleville Pumpkin Show in Circleville, Ohio, boasts the world’s
largest pumpkin pie. The pie weighs 350 pounds and is 5 feet in diameter.
Find the diameter of the pie in centimeters if 1 foot = 30.48 centimeters.
Write a verbal model of what you are
comparing.
feet
feet

centimeters centimeters
When you substitute, the conversion
information is kept together on one
side of the proportion.
1 foot
5 feet

30.48 cm x cm
Solve the proportion using cross
products.
1x  5(30.48)
1x  152.4 cm
The diameter of the pie is 152.4 centimeters.