Intro to Unit Rates

Overview

Understanding Unit Rates

A rate is a specific type of ratio that compares quantities with different units.
Examples would be cost per item or distance per time. Consider the problem below.

Sarah can ride her bike 30 miles in 2 hours. If she rides at a consistent rate, how
many miles can she ride her bike in 1 hour?

Step 1: Determine the two different units

The two different units are miles and hours.

Step 2: Determine the ratio

The ratio is   

Step 3: Find the unit rate

A unit rate compares two quantities where one of the terms has a quantity of 1.

To find the unit rate, we need to rewrite the ratio as a division problem. We know
that for every 30 miles she rides, Sarah bikes for 2 hours.

This can be written as: 

Now, we need to simplify the ratio to determine how far she can ride in one hour.

So, she can ride her bike 15 miles in one hour.

But what if we needed to know how far she could ride in 6 hours?

Now that we know how far she can ride in 1 hour, we simply need to multiply that
number to determine how far she can ride her bike in 6 hours.

So, she can ride her bike 90 miles in 6 hours.✓

Practice Question 1

Sofia’s car travels 700 miles per 50 gallons of gas. Write a statement to
describe the miles per gallon unit rate.

Reveal the answer

Practice Question 2

A plane flew 874 miles in 2 hours. Write a statement to describe the miles per hour unit rate.

Reveal the answer

Practice Question 3

Lars can swim 100 meters in 10 minutes.
Write a statement to describe the unit rate.

Reveal the answer

Practice Question 4

Olivia can see 45 patients in 5 days. Write a statement to describe the unit rate.

Reveal the answer

Practice Question 5

The recipe calls for 8 cups of sugar for every 4 cups of butter. Write a statement to describe the unit rate.

Reveal the answer