# 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 **un****it 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.✓

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Sofia’s car travels 700 miles per 50 gallons of gas. Write a statement to

describe the miles per gallon unit rate.

Answer
Sofia’s car can go 14 miles with 1 gallon.

Find the unit rate by setting the ratio as a fraction and simplifying it.

, which is 14 miles per 1 gallon.

Sofia’s car travels 700 miles per 50 gallons of gas. Write a statement to

describe the miles per gallon unit rate.

Sofia’s car can go 14 miles with 1 gallon.

Find the unit rate by setting the ratio as a fraction and simplifying it.

###

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

Answer
The plane can fly 437 miles in 1 hour

Find the unit rate by setting the ratio as a fraction and simplifying it.

, which is 437 miles per 1 hour.

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

The plane can fly 437 miles in 1 hour

Find the unit rate by setting the ratio as a fraction and simplifying it.

###

Lars can swim 100 meters in 10 minutes.

Write a statement to describe the unit rate.

Answer
Lars can swim 10 meters in 1 minute

Find the unit rate by setting the ratio as a fraction and simplifying it.

, which is 10 meters per 1 minute.

Lars can swim 100 meters in 10 minutes.

Write a statement to describe the unit rate.

Lars can swim 10 meters in 1 minute

Find the unit rate by setting the ratio as a fraction and simplifying it.

###

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

Answer
Olivia can see 9 patients in 1 day.

Find the unit rate by setting the ratio as a fraction and simplifying it.

, which is 9 patients per 1 day.

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

Olivia can see 9 patients in 1 day.

Find the unit rate by setting the ratio as a fraction and simplifying it.

###

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

Answer
The recipe calls for 2 cups of sugar for every 1 cup of butter

Find the unit rate by setting the ratio as a fraction and simplifying it.

, which is 2 cups of sugar per 1 cup of butter.

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

The recipe calls for 2 cups of sugar for every 1 cup of butter

Find the unit rate by setting the ratio as a fraction and simplifying it.

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