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Reading Math

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Reading Math

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.

16 24

=

14c

1624

206.4 24p

p 12.9

=

=

=

=

88132

p12.9

2424

88c 1848

Example 1: Solving Proportions

Solve each proportion.

14 c

=

A.

B.

88132

206.4 = 24p

88c =1848

88 88

8.6 = p

c = 21

Because percents can be expressed as ratios, you can use the proportion to solve percent problems.

Remember!

Percent is a ratio that means per hundred.

For example:

30% = 0.30 =

30

100

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:

Method 1 Use a proportion.

Method 2 Use a percent equation.

Percent (as decimal) whole = part

22.5(1800) = 100x

0.2251800 = x

405 = x

x = 405

So 405 voters are planning to vote for that candidate.

1.24 m

1 stride length

39.37 in.

1 m

49 in.

1 stride length

≈

600 m

482 strides

x m

1 stride

=

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.

Ex 3:

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

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

600 = 482x

x ≈ 1.24 m

Convert the stride length to inches.

Ryan’s stride length is approximately 49 inches.

Z

Y

Reading Math

B

Step 1 Graph ∆XYZ. Then draw XB.

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

X

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.

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

Ex 4:

∆XAB is similar to∆XYZ with a vertex at B(0, 3).

Graph ∆XYZ and ∆XAB on the same grid.

=

=

Z

Y

height of ∆XAB width of ∆XAB

height of ∆XYZ width of ∆XYZ

3x

A

B

9 6

X

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

9x = 18, so x = 2

Step 3

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

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

=

h ft

9 ft

6 ft

6

22

Shadow of tree

Height of tree

Shadow of house

Height of house

22 ft

=

9

h

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.

6h = 198

h = 33

The house is 33 feet high.