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. =. 14 c. 16 24. 206.4 24 p. p 12.9. =. =. =. =. 88 132. p 12.9. 24 24.
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.
Example 1: Solving Proportions
Solve each proportion.
206.4 = 24p
8.6 = p
c = 21
Because percents can be expressed as ratios, you can use the proportion to solve percent problems.
Percent is a ratio that means per hundred.
30% = 0.30 =
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?
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 stride length
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.
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.
Step 1 Graph ∆XYZ. Then draw XB.
The ratio of the corresponding side lengths of similar figures is often called the scale factor.
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).
∆XAB is similar to∆XYZ with a vertex at B(0, 3).
Graph ∆XYZ and ∆XAB on the same grid.
height of ∆XAB width of ∆XAB
height of ∆XYZ width of ∆XYZ
Step 2To find the width of ∆XAB, use a proportion.
9x = 18, so x = 2
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).
Shadow of tree
Height of tree
Shadow of house
Height of house
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.