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 one unit. For example, if a car travels 300 miles in 5 hours, the unit rate is 60 miles per hour.

Front

How do you find the unit rate from a ratio?

Back

To find the unit rate from a ratio, divide the first quantity by the second quantity. For example, if the ratio is 4 apples for $2, the unit rate is $2 ÷ 4 apples = $0.50 per apple.

Front

What is the constant of proportionality?

Back

The constant of proportionality is the ratio between two proportional quantities. It is the unit rate that describes how one quantity changes in relation to another.

Front

If a recipe requires 3 cups of flour for 4 servings, how much flour is needed for 1 serving?

Back

0.75 cups of flour (3 cups ÷ 4 servings = 0.75 cups per serving).

Front

What is the formula to calculate unit rate?

Back

Unit Rate = Total Quantity ÷ Number of Units.

Front

If a car travels 150 miles on 5 gallons of gas, what is the unit rate in miles per gallon?

Back

30 miles per gallon (150 miles ÷ 5 gallons = 30 miles/gallon).

Front

When are unit rates useful?

Back

Unit rates are useful when comparing prices, speeds, or any other quantities to determine the best value or efficiency.

Front

If a store sells 10 notebooks for $15, what is the price per notebook?

Back

$1.50 per notebook ($15 ÷ 10 notebooks = $1.50/notebook).

Front

What is a proportion?

Back

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

Front

How can you check if two ratios form a proportion?

Back

Cross-multiply the ratios. If the cross-products are equal, then the ratios form a proportion.