Comparing Unit Rates with Proportional Reasoning

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 in 5 hours, the unit rate is 60 miles per hour.

Front

How do you find the cost of multiple items when given the cost of a certain number of items?

Back

To find the cost of multiple items, first determine the unit price (cost per item) by dividing the total cost by the number of items. Then, multiply the unit price by the desired number of items.

Front

If 4 apples cost $2.40, how much does 1 apple cost?

Back

1 apple costs $0.60.

Front

What is proportional reasoning?

Back

Proportional reasoning involves understanding the relationship between quantities and using that understanding to solve problems involving ratios and rates.

Front

Back

Cross-multiply to get: 10x = 40. Then, divide both sides by 10 to find x = 4.

Front

What does it mean for two rates to be equivalent?

Back

Two rates are equivalent if they represent the same relationship between quantities, even if the numbers are different. For example, 6 miles per gallon is equivalent to 18 miles for 3 gallons.

Front

How do you calculate miles per gallon (mpg)?

Back

To calculate miles per gallon, divide the total miles driven by the total gallons of gas used. For example, if a car drives 231 miles using 7 gallons, the mpg is 231 ÷ 7 = 33 mpg.

Front

If Christina biked 36 miles in 6 hours, what is her speed in miles per hour?

Back

Her speed is 6 miles per hour, calculated by dividing 36 miles by 6 hours.

Front

What is the formula for finding a unit rate?

Back

The formula for finding a unit rate is: Unit Rate = Total Quantity / Number of Units.

Front

How can you determine if a rate is constant?

Back

A rate is constant if it remains the same over time or distance. For example, if a car travels at a constant speed, the miles per hour will not change.