In a ÷ b = c ÷ d, b and c are the means, and a and d are the extremes. In a proportion, the product of the means is equal to the product of the extremes.

Reading Math

Solve each proportion.

Example 1: Solving Proportions

A.

206.4 = 24p

=

=16 24 p 12.9

16 24 p 12.9

206.4 24p 24 24

8.6 = p

14 c 88 132

=

=

=

B.

14 c 88 132

88c = 1848

=88c 184888 88

c = 21

Percent is a ratio that means per hundred.

For example:

30% = 0.30 =

Remember!

30100

Because percents can be expressed as ratios, you can use the proportion

to solve percent problems.

Method 1 Use a proportion.

So 405 voters are planning to vote for that candidate.

Method 2 Use a percent equation.

22.5% 0.225

Percent (as decimal) whole = part

0.225 1800 = x

405 = x

x = 405

22.5(1800) = 100x

A poll taken one day before an election showed that 22.5% of voters planned to vote for a certain candidate. If 1800 voters participated in the poll, how many indicated that they planned to vote for that candidate?

Ex 2:

Ryan ran 600 meters and counted 482 strides. How long is Ryan’s stride in inches? (Hint: 1 m ≈ 39.37 in.)

Ex 3:

Use a proportion to find the length of his stride in meters.

600 m 482 strides

x m 1 stride

=

600 = 482x x ≈ 1.24 m

Convert the stride length to inches.

Ryan’s stride length is approximately 49 inches.

≈ 1.24 m

1 stride length39.37 in.

1 m49 in.

1 stride length

A rate is a ratio that involves two different units. You are familiar with many rates, such as miles per hour (mi/h), words per minute (wpm), or dollars per gallon of gasoline. Rates can be helpful in solving many problems.

Similar figures have the same shape but not necessarily the same size. Two figures are similar if their corresponding angles are congruent and corresponding sides are proportional.

The ratio of the corresponding side lengths of similar figures is often called the scale factor.

Reading Math

Ex 4: ∆XYZ has vertices X(0, 0), Y(–6, 9) and Z(0, 9).

∆XAB is similar to ∆XYZ with a vertex at B(0, 3). Graph ∆XYZ and ∆XAB on the same grid.

Step 1 Graph ∆XYZ. Then draw XB. Y

Z

B

X

= height of ∆XAB width of ∆XAB

height of ∆XYZ width of ∆XYZ

=3 x

9 6

9x = 18, so x = 2

Step 2 To find the width of ∆XAB, use a proportion.

The width is 2 units, and the height is 3 units, so the coordinates of A are (–2, 3).

BA

X

YZStep 3

To graph ∆XAB, first find the coordinate of A.

Example 5: Nature Application

The tree in front of Luka’s house casts a 6-foot shadow at the same time as the house casts a 22-fot shadow. If the tree is 9 feet tall, how tall is the house?Sketch the situation. The triangles formed by using the shadows are similar, so Luka can use a proportion to find h the height of the house.

=6

9 h22

=Shadow of tree Height of tree

Shadow of house Height of house

6h = 198

h = 33

The house is 33 feet high.

9 ft

6 ft

h ft

22 ft