Unit Rate and Proportions

Front

What is a unit rate?

Back

A unit rate is a ratio that compares a quantity to one unit of another quantity, often expressed as 'per' something, such as miles per hour or price per item.

Front

How do you calculate the unit rate from a total distance and time?

Back

To calculate the unit rate, divide the total distance traveled by the total time taken. For example, if you travel 450 miles in 6 hours, the unit rate is 450 miles ÷ 6 hours = 75 miles per hour.

Front

What is the formula to find the price per item when given the total cost and quantity?

Back

The formula to find the price per item is: Price per item = Total cost ÷ Quantity. For example, if 9 candy bars cost $13.50, then the price per candy bar is $13.50 ÷ 9 = $1.50.

Front

How do you determine miles per gallon (mpg) from total miles and gallons used?

Back

To determine miles per gallon, divide the total miles traveled by the total gallons of gas used. For example, if you drive 231 miles using 7 gallons, then mpg = 231 miles ÷ 7 gallons = 33 miles per gallon.

Front

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

Back

Unit rates help compare different quantities in a standardized way, making it easier to understand costs, speeds, and efficiencies in everyday situations.

Front

If a car travels 150 miles on 5 gallons of gas, what is the unit rate in miles per gallon?

Back

The unit rate is calculated as 150 miles ÷ 5 gallons = 30 miles per gallon.

Front

How can you convert a total cost into a unit price?

Back

To convert a total cost into a unit price, divide the total cost by the number of items purchased. This gives you the cost per individual item.

Front

What is the relationship between proportions and unit rates?

Back

Proportions are equations that express two ratios as equal. Unit rates are a specific type of ratio that can be used to create proportions.

Front

How do you find the total cost if you know the price per item and the quantity?

Back

To find the total cost, multiply the price per item by the quantity purchased. For example, if a candy bar costs $1.50 and you buy 9, the total cost is $1.50 × 9 = $13.50.

Front

What is the unit rate of speed if a person runs 10 miles in 1.5 hours?

Back

To find the unit rate of speed, divide the distance by the time: 10 miles ÷ 1.5 hours = approximately 6.67 miles per hour.