Rates and Unit Rates

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

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 4 pounds of bananas cost $6, the unit rate is $6 ÷ 4 = $1.50 per pound.

Front

If a car travels 160 miles in 4 hours, what is the unit rate in miles per hour?

Back

The unit rate is 160 miles ÷ 4 hours = 40 miles per hour.

Front

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

Back

Multiply the rate by the time. For example, if a car travels at 40 miles per hour for 7 hours, the total distance is 40 miles/hour × 7 hours = 280 miles.

Front

What is the formula for calculating cost per item?

Back

Cost per item = Total cost ÷ Number of items. For example, if 4 concert tickets cost $252, the cost per ticket is $252 ÷ 4 = $63.

Front

If a machine packs 70 boxes in 5 minutes, how many boxes can it pack in 1 minute?

Back

To find the number of boxes packed in 1 minute, divide the total boxes by the time. 70 boxes ÷ 5 minutes = 14 boxes per minute.

Front

What is the relationship between rates and proportions?

Back

Rates can be expressed as proportions, where one quantity is compared to another. For example, if 3 apples cost $1.50, the proportion is 3 apples/1.50 dollars.

Front

How do you convert a rate to a unit rate?

Back

To convert a rate to a unit rate, divide both quantities by the same number to simplify it to a per one unit basis.

Front

What is the significance of unit rates in real-life situations?

Back

Unit rates help compare prices, speeds, and other quantities, making it easier to make informed decisions, such as finding the best deal.