Unit Rates and Proportions

Front

What is a unit rate?

Back

A unit rate is a comparison of two different quantities where one of the quantities is expressed as a quantity of one. For example, if you travel 150 miles in 5 gallons of gas, the unit rate is 30 miles per gallon.

Front

How do you calculate a unit rate?

Back

To calculate a unit rate, divide the first quantity by the second quantity. For example, if you earn $50 for 4 hours of work, the unit rate is $50 ÷ 4 hours = $12.50 per hour.

Front

What is a proportion?

Back

A proportion is an equation that states that two ratios are equal. For example, if 1/2 = 2/4, then 1/2 and 2/4 are in proportion.

Front

How can you find the constant of proportionality?

Back

The constant of proportionality can be found by dividing one quantity by the other in a proportional relationship. For example, if Craig earns $64.75 for 7 hours, the constant is $64.75 ÷ 7 = $9.25 per hour.

Front

If a recipe calls for 2 cups of flour for every 3 cups of sugar, what is the ratio of flour to sugar?

Back

The ratio of flour to sugar is 2:3.

Front

What does it mean if two quantities are directly proportional?

Back

Two quantities are directly proportional if they increase or decrease at the same rate. For example, if you double the amount of hours worked, your earnings also double.

Front

If you travel 240 miles in 4 hours, what is your speed in miles per hour?

Back

Your speed is 240 miles ÷ 4 hours = 60 miles per hour.

Front

What is the relationship between unit rates and proportions?

Back

Unit rates are specific types of ratios that can be used to express proportions. Both concepts involve comparing quantities, but unit rates focus on a single unit.

Front

How do you set up a proportion to solve for an unknown?

Back

To set up a proportion, write two ratios equal to each other and cross-multiply to solve for the unknown. For example, if x/5 = 10/2, then cross-multiply to get 2x = 50.

Front

What is the unit rate for 15 apples that cost $3?

Back

The unit rate is $3 ÷ 15 apples = $0.20 per apple.