PROPORTIONS

Vocabulary

• A proportion is an equation stating that two ratios are equal.– Examples: or

– The cross products of a proportion are equal.or

d

c

b

a

12

8

3

2

d

c

b

a

bcad

12

8

3

2

2424

)8(3)12(2

Example #1

Determine if the ratios and form a proportion.

6060

)10(6)15(4

If two ratios are

proportional, then their cross products will be equal.

Since 60 = 60, then this is a proportion.

?

Example #2

Are the ratios and proportional?

86

)2(4)5(2.1

If two ratios are

proportional, then their cross products will be equal.

Since 6 ≠ 8, then this is NOT a proportion.

?

Example #3

Do the ratios and form a proportion?

66

)16(8

3)8(

4

3

If two ratios are proportional, then their cross products will be equal.

Since 6 = 6, then this is a proportion.

?

Example #4Solve for x in the proportion below.

7

3

35

x

157

105

7

7

1057

)35(37

x

x

x

xSince this is a proportion, the cross products are equal.

Divide both sides by 7 to get x alone.

Example #5Solve for y in the proportion below.

4.8

105

y

y

y

y

y

2.410

10

10

42

1042

10)4.8(5Since this is a proportion, the cross products are equal.

Divide both sides by 10 to get y alone.

Example #6A 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?

Writing a verbal model will help us set up a proportion when we are solving story problems.

servings

flour of cups

servings

flour of cups

servings 25

cupsx

servings 10

cups 3

x

x

x

x

cups 7.510

10

10

75

1075

10)25(3

Write a verbal model of what you are comparing.

Substitute in the values you are given. Use x to represent the quantity that you are looking for.

Solve the proportion using cross products.

You will need 7.5 cups of flour to serve 25 people.

Example #7The 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.

We can use proportions to convert units of measurement.

scentimeter

feet

scentimeter

feet

cmx

feet 5

cm 30.48

foot 1

cm 152.41

)48.30(51

x

x

Write a verbal model of what you are comparing.

When you substitute, the conversion information is kept together on one side of the proportion.

Solve the proportion using cross products.

The diameter of the pie is 152.4 centimeters.