Unit Rate, Rates & 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 60 miles in 2 hours, the unit rate is 30 miles per hour.

Front

How do you calculate the unit cost of an item?

Back

To calculate the unit cost, divide the total cost by the number of items. For example, if 15 pizzas cost $97.50, the unit cost per pizza is $97.50 ÷ 15 = $6.50.

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

If a car travels 195 miles in 3 hours, what is its speed in miles per hour?

Back

The speed is calculated by dividing the distance by the time. So, 195 miles ÷ 3 hours = 65 miles per hour.

Front

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

Back

Multiply the speed by the time. For example, if a car travels at 65 miles per hour for 5 hours, the total distance is 65 miles/hour × 5 hours = 325 miles.

Front

What is the formula for calculating the rate?

Back

Rate = Quantity / Time. For example, if you earn $96 for mowing 8 lawns, the rate is $96 ÷ 8 lawns = $12 per lawn.

Front

If it snows at a rate of 3 inches per hour, how much snow will accumulate in 2.5 hours?

Back

To find the total accumulation, multiply the rate by the time: 3 inches/hour × 2.5 hours = 7.5 inches.

Front

How do you determine how many customers can be served in a given time?

Back

Use the rate of service to calculate. If 2 customers are served in 8 minutes, the rate is 2 customers/8 minutes = 0.25 customers per minute. In 30 minutes, 0.25 × 30 = 7.5 customers.

Front

What is the relationship between rates and proportions?

Back

Rates can be expressed as proportions. For example, if you have a rate of 30 miles per hour, you can express it as a proportion of distance to time.

Front

How can you convert a rate into a unit rate?

Back

To convert a rate into a unit rate, divide both quantities by the same number to express one quantity as one unit. For example, if a recipe calls for 4 cups of flour for 2 cakes, the unit rate is 2 cups of flour per cake.