Calculate 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 a car travels 300 miles on 10 gallons of gas, the unit rate is 30 miles per gallon.

Front

How do you calculate the unit price?

Back

To calculate the unit price, divide the total price by the number of units. For example, if 4 cans of beans cost $9, the unit price is $9 ÷ 4 = $2.25 per can.

Front

If a car travels 304 miles on 16 gallons of gas, how do you find the distance it can travel on 5 gallons?

Back

First, find the unit rate: 304 miles ÷ 16 gallons = 19 miles per gallon. Then multiply the unit rate by the number of gallons: 19 miles/gallon × 5 gallons = 95 miles.

Front

What is the formula to find the price of multiple items based on a unit price?

Back

The formula is: Total Price = Unit Price × Number of Items. For example, if the unit price is $2.25 and you want 7 items, Total Price = $2.25 × 7 = $15.75.

Front

How do you convert a price for a certain quantity to a price per unit?

Back

Divide the total price by the total quantity. For example, if 6 pounds of blueberries cost $18, the price per pound is $18 ÷ 6 = $3 per pound.

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 these two ratios are in proportion.

Front

How can you use proportions to solve for an unknown quantity?

Back

Set up a proportion equation based on the known ratios and cross-multiply to solve for the unknown. For example, if x/5 = 10/2, then cross-multiply to get 2x = 50, so x = 25.

Front

What is the relationship between unit rates and proportions?

Back

Unit rates can be used to create proportions. For example, if the unit rate of a car is 30 miles per gallon, you can set up a proportion to find out how far it can go on a different amount of gas.

Front

How do you find the total cost when given a unit price and quantity?

Back

Multiply the unit price by the quantity. For example, if the unit price is $2.25 and you buy 4 items, Total Cost = $2.25 × 4 = $9.

Front

What is the unit price of 1/3 gallon of apple juice that costs $2.44?

Back

To find the unit price, divide the total price by the quantity: $2.44 ÷ (1/3) = $2.44 × 3 = $7.32 per gallon.