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Lesson 3.6 Terms

- A ratio is a comparison of two numbers by division.
- An equation that has two ratios that are equal is called a proportion.
- To determine whether something is a proportion, you cross multiply to see if the numbers are equal.

Determine whether the ratios and form a proportion. Example 6-1a

Answer:The ratios are equal. Therefore, they form a proportion.

Write the equation.

Find the cross products.

Simplify.

Answer: The cross products are not equal, so . The ratios do not form a proportion.

Example 6-2aUse cross products to determine whether the pair of ratios below forms a proportion.

Do the ratios and form a proportion?Example 6-1b

Use cross products to determine whether the pair of ratios below forms a proportion.

Solve the proportion .

Original equation

Find the cross products.

Simplify.

Divide each side by 8.

Simplify.

Answer:

Example 6-3aBicycling The gear on a bicycle is 8:5. This means that for every eight turns of the pedals, the wheel turns five times. Suppose the bicycle wheel turns about 2435 times during a trip. How many times would you have to turn the pedals during the trip?

turns of the pedals

turns of the pedals

wheel turns

wheel turns

Example 6-4aExploreLet p represent the number of times needed to crank the pedals.

PlanWrite a proportion for the problem.

Original proportion

Solve

Find the cross products.

Simplify.

Divide each side by 5.

Answer: 3896 = p

Simplify.

Example 6-4bExample 6-4c

ExamineIf it takes 8 turns of the pedal to make the wheel turn 5 times, then it would take 1.6 turns of the pedal to make the wheel turn 1 time. So, if the wheel turns 2435 times, then there are 2435 1.6 or 3896 turns of the pedal. The answer is correct.

Example 6-4d

Before 1980, Disney created animated movies using cels. These hand drawn cels (pictures) of the characters and scenery represented the action taking place, one step at a time. For the movie Snow White, it took 24 cels per second to have the characters move smoothly. The movie is around 42 minutes long. About how many cels were drawn to produce Snow White?

Answer:About 60,480 cels were drawn to produce Snow White.

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