Rates, Unit Rates, and Proportional or Nonproportional

Front

What is a rate?

Back

A rate is a ratio that compares two different quantities, often expressed as a fraction. For example, speed is a rate that compares distance to time.

Front

What is a unit rate?

Back

A unit rate is a rate in which the second quantity is one. It tells you how much of one quantity corresponds to one unit of another quantity, such as miles per hour or price per item.

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 have 15 dollars for 10 gallons, the unit rate is 15 ÷ 10 = $1.50 per gallon.

Front

What is a proportional relationship?

Back

A proportional relationship is a relationship between two quantities where the ratio between them remains constant. For example, if you double one quantity, the other quantity also doubles.

Front

What is a nonproportional relationship?

Back

A nonproportional relationship is a relationship where the ratio between two quantities does not remain constant. For example, if you add a fixed amount to one quantity, the other quantity does not change in a consistent way.

Front

How do you determine if a relationship is proportional?

Back

To determine if a relationship is proportional, check if the ratios of the quantities are equivalent. If they are, the relationship is proportional.

Front

If a car travels 300 miles in 5 hours, what is the unit rate of speed in miles per hour?

Back

The unit rate is 300 miles ÷ 5 hours = 60 miles per hour.

Front

How do you find the total distance traveled if you know the speed and time?

Back

To find the total distance, multiply the speed (unit rate) by the total time traveled. For example, if the speed is 60 miles per hour and the time is 4 hours, the distance is 60 × 4 = 240 miles.

Front

What is the formula for calculating miles per gallon?

Back

The formula for calculating miles per gallon is: Miles driven ÷ Gallons of gas used.

Front

If a 6-pack of water costs $3.79, what is the cost per bottle?

Back

To find the cost per bottle, divide the total cost by the number of bottles: $3.79 ÷ 6 = approximately $0.63 per bottle.