Ratios, Rates, and Proportions

The Language

100

Define ratio. What are the 3 comparison types?

A comparison of two quantities. A ratio can be part-to-part, part-to-whole, or whole-to-part.

200

Define rate.

A rate is a ratio of two quantities using different units.

300

Define unit rate.

A unit rate compares a quantity to one unit of another quantity.

400

Define equivalent rates.

Equivalent rates have the same unit rate.

500

Define unit price.

the price of one item.

Ratios

100

What are the 3 ways we can represent ratios?

a:b, a to b, or a/b

200

Twelve of the 28 students in class have a dog. What is the ratio of students who have a dog to students who do not?

12:16

300

The ratio of vowels to consonants in a word is 5 to 7. Are there more vowels or more consonants? Explain.

More consonants

400

You are comparing apples to oranges in a fruit bowl. Is the ratio 2:3 the same as the ratio 3:2? Explain.

No, because the order of the ratio, follows the order of the description (i.e. 2 apples is not the same as 3 apples)

500

Which ratio does not belong with the other three? Explain your reasoning. 2 parts to 5 parts 2 out of every 5 2 for each 5 2 for every 5

2 out of every 5; it is a part-to-whole comparison whereas the others are part-to-part comparisons

Rates

100

Write a unit rate for the situation: 256 heartbeats in 4 minutes

64 beats per minute

200

Write a unit rate for the situation: $4.80 for 4 apples

$1.20 per apple

300

Decide whether the rates are equivalent using unit rates. Rate 1: 24 laps in 6 minutes Rate 2: 72 laps in 18 minutes

Yes, because each unit rate is 4 laps per minute.

400

Decide whether the rates are equivalent using unit rates. Rate 1: 126 points every 4 games Rate 2: 210 points every 5 games

No, because 31.5 points per game and 42 points per game is not the same unit rate.

500

You can buy 20 ounces of cereal for $4.40 or 16 ounces of the same brand for $3.68. Which is the better buy?

20 oz of cereal because it is cheaper per ounce ($0.22 per ounce)

Miscellaneous

100

Which ratio does not belong with the other three? Explain your reasoning. 3:4 9:12 12:15 12:16

12:15; When reduced, the other three are equivalent to 3:4

200

Describe a unit rate you use in real life.

Example: I drive 70 mph on the highway

300

Create two ratios that are equivalent to the ratio 6:10.

Example: 3:5 and 12:20

400

Describe how to solve a unit price.

The cost of one item.

500

If apples are $1.67 per pound, How much is 4 pounds?

$6.68