New Mexico Standards: AFG.D.2, GT.B.4

The total number of students who participate in sports programs at Central High School is 520. The total number of students in the school is 1850. Find the athlete-to-student ratio to the nearest tenth.

Answer: The athlete-to-student ratio is 0.3.

To find this ratio, divide the number of athletes by the total number of students.

0.3 can be written as

RatioRatio::

A comparison of two quantities.Ratios can be expressed as

where b ≠ 0, b

a a : b, or a to b

The country with the longest school year is China with 251 days. Find the ratio of school days to total days in a year for China to the nearest tenth. (Use 365 as the number of days in a year.)

Answer: 0.7

Example 1-2aExample 1-2a

Multiple- Choice Test ItemIn a triangle, the ratio of the measures of three sides is 5:12:13, and the perimeter is 90 centimeters. Find the measure of the shortest side of the triangle.

A 15 cm B 18 cm C 36 cm D 39 cm

What are you being asked to do?You are asked determine the true length of the side of the triangle.

Draw a picture5

12

13Do these sides have

a perimeter of 90 cm?

Ratio means all the sides are a multiple of the same number, which is unknown, so . . .

12x

13x5x

Write an equation & solve it:

9013125 xxx

Example 1-2bExample 1-2b

Perimeter

Combine like terms.

Divide each side by 30.

Which side will be the longest side?

3913(3)

13sidelongest

x

Answer: A

A 15 cm B 18 cm C 36 cm D 39 cm

Use this value of x to find the measures of the sides of the triangle.

The shortest side is 15 centimeters. The answer is A.

Check Add the lengths of the sides to make sure that the perimeter is 90.

ProportionProportionAn equation stating that two ratios are equal.

Equivalent fractions set equal to each other form a proportion.

To determine if the two ratios are a proportion, the most useful way is to use cross-products.

Criss-cross and multiply. If the results are equal, the two ratios are a proportion.

What are some other methods?

Original proportion

Cross products

Multiply.

Answer: 27.3

Solve

Divide each side by 6.

How can you quickly check that your answer is correct?

ProportioProportion:n:

An equation stating that two ratios are equal.

Original proportion

Cross products

Simplify.

Answer: –2

Add 30 to each side.

Divide each side by 24.

Solve

How can you quickly check that your answer is correct?

Answer: 4.5

Answer: 9

Solve each proportion.

a.

b.

A boxcar on a train has a length of 40 feet and a width of 9 feet. A scale model is made with a length of 16 inches. Find the width of the model.

Because the scale model of the boxcar and the boxcar are in proportion, you can write a proportion to show the relationship between their measures. Since both ratios compare feet to inches, you need not convert all the lengths to the same unit of measure.

Substitution

Cross products

Multiply.

Divide each side by 40.

Answer: The width of the model is 3.6 inches.

Two large cylindrical containers are in proportion. The height of the larger container is 25 meters with a diameter of 8 meters. The height of the smaller container is 7 meters. Find the diameter of the smaller container.

Answer: 2.24 m

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