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Unit rate math

Here you will learn about unit rate math problems, including the rates that involve whole numbers, decimals, integers, and fractions, and how to use unit rate math to make comparisons between rates.

Students will first learn about unit rate math problems as part of ratios and proportions in 6 th grade and 7 th grade.

What is unit rate math?

Unit rate math problems involve creating equivalent ratios where one part of the ratio is 1. A rate is a ratio comparison of different units that can be used to create different quantities.

For example,

The rate of 500 miles to 2 hours, can be used to create the unit rate of 250 miles per hour or mph. In this case, the original rate is 500\text{:}2 and the equivalent unit rate is 250\text{:}1.

Unit rates are also a key part of converting between different measurement systems.

The conversions 1 foot =12 inches or 100 centimeters =1 meter are examples of unit rates that can be used for problems involving measurement.

Let’s look at a few examples of solving unit rate math problems below.

A bag of 5 apples costs \$ 6.00. What is the price per apple?

The original rate is 5 to \$ 6.00. To find the price per apple ( 1 apple), both sides of the rate are divided by 5, leaving the equivalent ratio 1 to \$ 1.20. Each apple costs \$ 1.20.

Unit rates can also be used to compare different quantities to decide things like, which rate is cheaper.

A grocery store sells 3 pounds of green apples for \$ 2.34 and 2 pounds of red apples for \$ 1.86. Which apples have the better unit price?

Unit price means the price per 1 unit. In this case, the units are pounds of apples.

Divide each side of the green apples rate by 3, to create a rate for 1 pound of green apples.

Each pound of green apples costs \$ 0.78.

Divide each side of the red apples rate by 2, to create a rate for 1 pound of red apples.

Each pound of red apples costs \$ 0.93.

The green apples have a better unit price, because they cost less per pound than the red apples.

Common Core State Standards

How does this relate to 6 th grade math and 7 th grade math?

• Grade 6 – Ratios and Proportional Relationships (6.RP.A.2) Understand the concept of a unit rate \cfrac{a}{b} associated with a ratio a\text{:}b with b ≠ 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is \cfrac{3}{4} cup of flour for each cup of sugar.” “We paid \$ 75 for 15 hamburgers, which is a rate of \$ 5 per hamburger.”
• Grade 6 – Ratios and Proportional Relationships (6.RP.A.3b) Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?
• Grade 7 – Ratios and Proportional Relationships (7.RP.A.1) Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks \cfrac{1}{2} mile in each \cfrac{1}{4} hour, compute the unit rate as the complex fraction \cfrac{\cfrac{1}{2}}{\cfrac{1}{4}} miles per hour, equivalently 2 miles per hour.

How to solve unit rate math problems

In order to solve unit rate math problems:

Write the original rate.

Use multiplication or division to create a unit rate.

Use the unit rate to answer the question.

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Unit rate math examples

Example 1: unit rate calculation – whole number.

6 snack bars cost \$ 18. If all the bars cost the same, what is the price per bar?

6 snack bars cost \ \$ 18 → 6 \text{:}\$ 18

2 Use multiplication or division to create a unit rate.

The price ‘per bar’ refers to 1 bar. Divide each side of the rate by 6, to create a rate for 1 bar.

3 Use the unit rate to answer the question.

One bar costs \$ 3.

Example 2: unit rate calculation – decimal

A car travels 256 miles in 5 hours. If the car travels the same number of miles each hour, what is the miles per hour rate?

256 miles in 5 hours → 256\text{:}5

The miles ‘per hour’ refers to 1 hour. Divide each side of the rate by 5, to create a rate for 1 hour.

The car travels 51.2 miles each hour.

Example 3: unit rate calculation – mixed number

A recipe calls for 3 cups of sugar and 4 cups of flour. What is the rate of cups of flour per cup of sugar?

3 cups of sugar and 4 cups of flour → 3\text{:}4

The cups of flour ‘per cup of sugar’ refers to 1 cup of sugar. Divide each side of the rate by 3, to create a rate for 1 cup of sugar.

There are 1 \cfrac{1}{3} cups of flour for every cup of sugar.

Example 4: unit rate comparison – decimals

A grocery store sells 3 pounds of green grapes for \$ 3.72 and 4 pounds of purple grapes for \$ 4.80. Which has the better unit price?

3 pounds of green grapes for \$ 3.72 → 3\text{:}\$ 3.72

4 pounds of purple grapes for \$ 4.80 → 4\text{:}\$ 4.80

Unit price means the price per 1 unit. In this case, the units are pounds of grapes.

Divide each side of the green grapes rate by 3, to create a rate for 1 pound of green grapes.

Divide each side of the purple grapes rate by 4, to create a rate for 1 pound of purple grapes.

The green grapes cost \$ 1.24 per pound. The purple grapes cost \$ 1.20 per pound, which is less. The purple grapes have a better unit price.

Example 5: unit rate comparison – integers

Temperature gauge A changed by -49 degree in 7 hours. Temperature gauge B changed by -80 degrees in 10 hours. Which gauge showed a slower degree change in temperature per hour?

-49 degree in 7 hours → -49\text{:}7

-80 degrees in 10 hours → -80\text{:}10

The degree change in temperature ‘per hour’ refers to 1 hour. Divide each side of the gauge A rate by 7, to create a rate for 1 hour.

Divide each side of the gauge B rate by 10, to create a rate for 1 hour.

Gauge A dropped 7 degrees each hour. Gauge B dropped 8 degrees each hour.

Gauge A had a slower degree change per hour.

Example 6: unit rate calculation – fractions

Kai walks 1 \cfrac{1}{2} miles in \cfrac{3}{4} of an hour. If his rate is steady, how many miles does Kai walk in 1 hour?

1 \cfrac{1}{2} miles in \cfrac{3}{4} of an hour → 1 \cfrac{1}{2}\text{:}\cfrac{3}{4}

To create the rate for 1 hour, you need to go from \cfrac{3}{4} to 1. This can be done with division or multiplication:

See also: Multiplying fractions

See also: Dividing fractions

Kai walks 2 miles in 1 hour.

Example 7: unit rate comparison – fractions

A sink leaks \cfrac{1}{3} of a cup of water every 5 minutes. A shower leaks \cfrac{2}{5} of a cup of water every 8 minutes. Which leaks faster per minute?

\cfrac{1}{3} of a cup every 5 minutes → \cfrac{1}{3}\text{:}5

\cfrac{2}{5} of a cup every 8 minutes → \cfrac{2}{5}\text{:}8

The leak rate ‘per minute’ refers to 1 minute. Divide each side of the sink rate by 5, to create a rate for 1 minute.

*Note: You can also multiply each side by \cfrac{1}{5}.

Multiply each side of the shower rate by \cfrac{1}{8}, to create a rate for 1 minute.

*Note: You can also divide each side by 8.

The sink leaks \cfrac{1}{15} of a cup per minute. The shower leaks \cfrac{1}{20} of a cup per minute.

The sink has a faster leak rate per minute.

Teaching tips for unit rate math

• The topic unit rate has endless real-world connections, so it is easy to introduce it through a relevant example and continue to bring in new real world examples as students progress in their understanding.
• Worksheets can be useful, but be sure to include worksheets that include word problems and a variety of solving strategies.
• Students who are struggling may find a step-by-step guide helpful, like the one provided on this page.

Easy mistakes to make

• Calculating the wrong unit rate For example, if 10 tennis balls cost \$ 5, the price per ball would be \$ 5 \div 10=\$ 0.50. An alternative would be to calculate 10 \div 5=2, which is the number of balls per dollar. Each solving method is correct, but they solve for different unit rates. Always pay attention to which unit rate you are being asked to find.
• Adding and subtracting to find a unit rate Ratios and rates represent a multiplicative relationship, so multiplication or division can be used to calculate equivalent rates. Adding or subtracting will lead to the incorrect unit rate.

Related ratio lessons

• Simplifying ratios
• How to write a ratio
• Ratio to percent
• Ratio to fraction
• How to calculate exchange rates
• Ratio problem solving
• Dividing ratios
• How to find the unit rate
• Ratio scale
• Constant of proportionality

Practice unit rate math questions

1. A grocery store is selling 8 watermelons for \$ 16. What is the per price watermelon?

8 watermelons cost \$ 16 → 8\text{:}\$ 16

The price ‘per watermelon’ refers to 1 watermelon. Divide each side of the rate by 8, to create a rate for 1 watermelon.

One watermelon costs \$ 2.

2. A boat travels 58 miles in 3 hours. If the boat drove a consistent speed, how many miles did it travel per hour?

19 \cfrac{1}{3} miles

18 \cfrac{2}{3} miles

58 miles in 3 hours → 58\text{:}3

The miles ‘per hour’ refers to 1 hour. Divide each side of the rate by 3, to create a rate for 1 hour.

The boat travels 19 \cfrac{1}{3} miles per hour.

3. A pizza shop has 3 different offers. Which one is the cheapest per pizza?

Offer \textbf{A} \hspace{1cm} Offer \textbf{B} \hspace{1cm}   Offer \textbf{C}  

3 pizzas \hspace{1cm} 5 pizzas \hspace{1cm} 15 pizzas

\$ 24 \hspace{1.5cm} \$ 35 \hspace{1.6cm} \$ 135

All offers are the same price per pizza

Offer A : 3 pizzas for \$ 24 → 3\text{:}\$ 24

Each pizza in Offer A costs \$ 8.

Offer B : 5 pizzas for \$ 35 → 5\text{:}\$ 35

Each pizza in Offer B costs \$ 7.

Offer C : 15 pizzas for \$ 135 → 15\text{:}\$ 135

Each pizza in Offer C costs \$ 9.

Offer B has the cheapest cost per pizza.

4. A shop is selling the same pens in two different packs.

Which pack is better value for money and how much cheaper is it per pen?

Pack \textbf{A} : 2 pens cost \$ 3.20

Pack \textbf{B} : 3 pens cost \$ 4.65

Pack A ; it is \$ 0.05 cheaper per pen

Pack B ; it is \$ 0.50 cheaper per pen

Pack A ; it is \$ 0.50 cheaper per pen

Pack B ; it is \$ 0.05 cheaper per pen

Pack A : 2 pens for \$ 3.20 → 2\text{:}\$ 3.20

Each pen in Pack A costs \$ 1.60.

Pack B : 3 pens for \$ 4.65 → 3\text{:}\$ 4.65

Each pen in Pack B costs \$ 1.55.

\$1.60-\$1.55 = \$0.05.

Pack B costs \$ 0.05 cheaper than Pack A.

5. \cfrac{2}{3} of an ounce of water evaporates every \cfrac{3}{5} of a second. What is the rate of evaporation per second?

2 ounces per second

\cfrac{9}{10} ounces per second

1 \cfrac{1}{9} ounces per second

\cfrac{2}{5} ounces per second

\cfrac{2}{3} of an ounce of water every \cfrac{3}{5} of a second → \cfrac{2}{3}\text{:} \cfrac{3}{5}.

The rate ‘per second’ refers to 1 second. Divide each side of the rate by \cfrac{3}{5}, to create a rate for 1 second.

*Note: You can also multiply each side by \cfrac{5}{3}.

1 \cfrac{1}{9} ounces of water evaporates every second.

6. Machine A creates \cfrac{2}{3} of a blanket every 3 minutes. Machine B creates \cfrac{2}{5} of a blanket every 5 minutes. What is the rate of minutes per sweater for the fastest machine?

11 minutes on Machine B

2 minutes on Machine A

4 \cfrac{1}{2} minutes on Machine A

12 \cfrac{1}{2} minutes on Machine B

Machine A : \cfrac{2}{3} of a blanket every 3 minutes → \cfrac{2}{3}\text{:} 3

Machine B : \cfrac{2}{5} of a blanket every 5 minutes → \cfrac{2}{5}\text{:} 5

Divide each side of the Machine A rate by \cfrac{2}{3}, to create a rate for 1 minute.

*Note: You can also multiply each side by \cfrac{3}{2}.

Machine A makes one sweater in 4 \cfrac{1}{2} minutes.

Divide each side of the Machine B rate by \cfrac{2}{5}, to create a rate for 1 minute.

*Note: You can also multiply each side by \cfrac{5}{2}.

Machine B makes one sweater in 12 \cfrac{1}{2} minutes.

Unit rate math FAQs

In middle school, solving unit rate begins with rates involving whole numbers. This sometimes leads to fractional unit rates, but not always (as shown in examples 1\text{-}3 on this page). Then the topic progresses to include rates with rational numbers, including rates with the original number of units as decimals, integers and fractions. Working with these rates requires solving rational operations to calculate the unit rate (as shown in examples 4\text{-}8 on this page).

Yes, the numerator would represent the unit rate and denominator would be 1.

When working with linear graphs in pre-algebra, the unit rate is the slope of a line.

The next lessons are

• Converting fractions, decimals and percentages

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Unit Rate Worksheets with Word Problems

Help students of grade 5 through high school to heighten their logical reasoning with this batch of meticulously drafted unit rate worksheets. Over 60 plus well-researched word problems based on unit rates, unitary method and comparing unit rates are featured here! Answer keys are provided below every worksheet. Browse through some of these worksheets for free.

Unit Rate: Graphs

In this printable practice set, 7th grade and 8th grade students need to carefully observe the graphs where the x coordinate is 1. Find the corresponding y coordinate to determine the unit rate and note down your answers.

• Download the set

Rate and Unit Rate

Read the word problems in these printable high school worksheets. Express the phrases in the form of rates. Then, find the unit rate by simplifying the fractions.

Unit Rate Word Problems: Standard

Assist young learners in grade 6 and grade 7 to improve their analytical skills with this set of diligently prepared unit-rate word problem with factual scenarios. Determine the unit rate in each problem.

Unit Rate Word Problems: Unitary Method

Read the phrases provided in this set of 5th grade pdf worksheets. Determine the unit rate. Then apply the unitary method to solve each problem.

Unit Rate Word Problems: Comparing Unit Rates

Read the word problems. Determine the unit rates to make comparisons. Then, draw conclusions based on the questions provided. Use the download option to access the entire set of worksheets.

Related Worksheets

» Constant of Proportionality

» Solving Proportions

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Unit Rates & Proportions Worksheets

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These free unit rate worksheets will help you find unit rates by setting up and solving proportions.  The first set of rate problems is restricted to whole numbers.   The second set of rate worksheets will help students solve proportions that contain fractions .

These unit rate and proportion worksheets will help students meet Common Core Standards for Ratios & Proportional Relationships  by working with unit rates in multiple representations.  I would recommend these exercise for 5th grade, 6th grade, and 7th grade math students.

Integer Worksheets

Unit Rates and Proportions Worksheet 1 (Integers) –  This 9 problem worksheet features proportions that represent real-life situations where you will have to calculate the unit rate.  The proportions have already been set up for you. Unit Rates & Proportions Worksheet 1 RTF Unit Rates & Proportions Worksheet 1 PDF Preview Unit Rates & Proportions Worksheet 1 in Your Browser View Answers

Unit Rates and Proportions Worksheet 2 (Integers) –  This 9 problem worksheet features proportions that represent real-life situations where you will have to calculate the unit rate.  The proportions have already been set up for you. Unit Rates & Proportions Worksheet 2 RTF Unit Rates & Proportions Worksheet 2 PDF Preview Unit Rates & Proportions Worksheet 2 in Your Browser View Answers

 Unit Rates and Proportions Worksheet 3   (Integers) – This 10 problem worksheet features word problems with proportions that are partially complete.  You will have to complete and solve the proportions to find the unit rate. Unit Rates & Proportions Worksheet 3 RTF Unit Rates & Proportions Worksheet 3 PDF Preview Unit Rates & Proportions Worksheet 3 in Your Browser View Answers

Unit Rates and Proportions Worksheet 4  ( Integers) – This 9 problem worksheet features word problems where you will have to set up and solve proportions to find a unit rate. Unit Rates & Proportions Worksheet 4 RTF Unit Rates & Proportions Worksheet 4 PDF Preview Unit Rates & Proportions Worksheet 4 in Your Browser View Answers

Fraction Worksheets

Unit Rates and Proportions Worksheet 1 (Fractions) –  This 9 problem worksheet features proportions that represent real-life situations where you will have to calculate the unit rate.  The proportions have already been set up for you. Unit Rates & Proportions Worksheet 1 RTF Unit Rates & Proportions Worksheet 1 PDF Preview Unit Rates & Proportions Worksheet 1 in Your Browser View Answers

Unit Rates and Proportions Worksheet 2 (Fractions) –  This 9 problem worksheet features proportions that represent real-life situations where you will have to calculate the unit rate.  The proportions have already been set up for you. Unit Rates & Proportions Worksheet 2 RTF Unit Rates & Proportions Worksheet 2 PDF Preview Unit Rates & Proportions Worksheet 2 in Your Browser View Answers

 Unit Rates and Proportions Worksheet 3   (Fractions) – This 10 problem worksheet features word problems with proportions that are partially complete.  You will have to complete and solve the proportions to find the unit rate. Unit Rates & Proportions Worksheet 3 RTF Unit Rates & Proportions Worksheet 3 PDF Preview Unit Rates & Proportions Worksheet 3 in Your Browser View Answers

Unit Rates and Proportions Worksheet 4  ( Fractions) – This 9 problem worksheet features word problems where you will have to set up and solve proportions to find a unit rate. Unit Rates & Proportions Worksheet 4 RTF Unit Rates & Proportions Worksheet 4 PDF Preview Unit Rates & Proportions Worksheet 4 in Your Browser View Answers

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Unit Rate Problems 6th Grade

Welcome to our Unit Rate Problems 6th Grade page. Here you will find our range of 6th Grade Unit Rate worksheets which will help your child apply and practice using unit rates in a range of different contexts.

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Here you will find a range of problem solving worksheets about unit rate.

The sheets involve working out unit rates and finding the best value unit rate.

The sheets have been put in order of difficulty, with the easiest first.

Each problem sheet comes complete with an answer sheet.

Using these sheets will help your child to:

• know how to find the unit rate;
• how to use unit rate to find the best value;
• find the unit rate in graphs and tables.

Some of our sheets, especially those involving money, have a separate UK version.

Quicklinks to ...

• What is the Unit Rate?
• Unit rate problems
• Comparing unit rates
• Unit rate in tables
• Unit rate in graphs
• Unit rates 6th grade online quiz
• More recommended resources

What Is the Unit Rate?

• A rate compares two quantities with different units. It can be written as a fraction or a ratio.
• A Unit rate is the rate of one of a quantity compared to another quantity.
• Usually two different measures are compared, e.g. miles in an hour, number of words in a minute, number of objects in a pack, etc.
• Unit rates can also be thought of as a ratio with a denominator (or consequent) of 1. The unit rate is the value of the numerator.
• Unit rates are useful because they can be used to compare different sets of rates and decide which is the best/most efficient/fastest/slowest etc.

If you would like more help and support with what the unit rate is and how to find it, use the link below.

The Definition of Unit Rate Support Page

Sheet A and Sheet B have similar problems, but Sheet A has easier numbers to work out while Sheet B has harder numbers.

• Unit Rate Problems 6.1A (Easier)
• PDF version
• Unit Rate Problems 6.1B (Harder)
• Unit Rate Problems 6.2A (Easier)
• Unit Rate Problems 6.2B (Harder)

Comparing Unit Rates

These sheets involve finding the unit rate for 3 different items, and then selecting the unit rate which offers the best value.

• Comparing Unit Rates Sheet 6.1
• Comparing Unit Rates Sheet 6.1 UK version

Unit Rates in Tables

These sheets involve using the information in the table to find the unit rate and then fill in the missing information in the table.

• Unit Rates in Tables Sheet 6.1
• Unit Rates in Tables Sheet 6.1 UK version
• Unit Rates in Tables Sheet 6.2

Unit Rates in Graphs

Sheets 6.1 and 6.2 involve using the graphs to find the unit rates.

Sheet 6.3 involves drawing a line on the graph to match the unit rate given.

• Unit Rates in a Graph Sheet 6.1
• Unit Rates in a Graph Sheet 6.1 UK version
• Unit Rates in a Graph Sheet 6.2
• Unit Rates in a Graph Sheet 6.3

Unit Rates in a Graph Walkthrough Video

This short video walkthrough shows several problems from our Unit Rates in a Graph Worksheet 6:1 being solved and has been produced by the West Explains Best math channel.

If you would like some support in solving the problems on these sheets, check out the video!

More Recommended Math Worksheets

Take a look at some more of our worksheets similar to these.

What is Unit Rate Support Page?

• The Definition of Unit Rate

More Ratio Worksheets

These sheets are a great way to introduce ratio of one object to another using visual aids.

The sheets in this section are at a more basic level than those on this page.

We also have some ratio and proportion worksheets to help learn these interrelated concepts.

• Ratio Part to Part Worksheets
• Ratio and Proportion Worksheets

Fraction Problems

Here you will find a range of fraction word problems to help your child apply their fraction learning.

The worksheets cover a range of fraction objectives, from adding and subtracting fractions to working out fractions of numbers. The sheets support fraction learning from 2nd grade to 5th grade.

• Fraction Riddles for kids (easier)
• Free Printable Fraction Riddles (harder)

6th Grade Percentage Worksheets

Take a look at our percentage worksheets for finding the percentage of a number or money amount.

We have a range of percentage sheets from quite a basic level to much harder.

• Percentage of Numbers Worksheets
• Money Percentage Worksheets
• 6th Grade Percent Word Problems

Unit Rate 6th Grade Online Quiz

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Problem Solving Using Rates, Unit Rates, and Conversions

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Basics on the topic Problem Solving Using Rates, Unit Rates, and Conversions

After this lesson, you will be able to solve real world problems involving rates, unit rates, and conversions.

The lesson begins by teaching you that rates can be combined once they have common units and reduced to unit rates. It leads you to learn how to convert units and reduce rates to unit rates. It concludes by showing you how to solve rate problems involving unit pricing.

Learn about rates, unit rates, and conversions by helping Sally, Bennie, and Evette solve their issues regarding animal rescue.

This video includes key concepts, notation, and vocabulary such as the term rate (a ratio that compares two quantities having different units of measure); unit rate (a ratio of a quantity to one of another); conversion factor (a ratio between two units with equal values and usually used to convert units from one to another); and unit price (a cost per unit of something you want to buy)

Before watching this video, you should already be familiar with ratio, unit rate, and converting measurements, like weeks to days, pounds to kilograms, etc.

After watching this video, you will be prepared to learn solve real world problem involving unit pricing and constant speed. You will also be prepared to learn how to manipulate and transform units appropriately when multiplying or dividing quantities.

Common Core Standard(s) in focus: 6.RP.A.3.B and 6.RP.A.3.D A video intended for math students in the 6th grade Recommended for students who are 11 - 12 years old

Transcript Problem Solving Using Rates, Unit Rates, and Conversions

Sally, Bennie, and Evette are friends who live in the 'burbs. One day on their way home from school, they hear whimpering from a box on the sidewalk. In the box they find 3 abandoned puppies. They bring the puppies home, and try to contact their local animal shelters, but all of them are full. What now? Sally suggests they start their own animal rescue, Ruff Rescue. Starting an animal rescue involves various issues including fundraising rates and pet food comparisons. In order to help the friends solve these issues we can apply problem-solving using rates, unit rates, and conversions. First, Ruff Rescue needs to raise money to pay for all the food and supplies that they want to purchase. The three friends come up with different ideas about how to fundraise. Sally creates an online fitness challenge where she raises money for every mile she runs and posts the video online. Her efforts get some attention, and Sally raises 50 dollars every 48 hours - hashtag puppylove! Bennie likes making treats for our four-legged friends. By selling them he raises 30 dollars in 3 days, what a treat! Evette teaches the puppies some tricks and has the puppies perform the tricks in the park. She earns 350 dollars a week, a spectacular performance! At this rate how much money are the friends earning? We can’t just combined the numbers because each friend is counting the money differently. What rate unit could we use for all of them? Dollars per day is a good option. We already have dollars for each friend. We just need to change the time to days. Looking at Sally's fundraising efforts, 48 hours is 2 days. So, that’s 50 dollars every 2 days. Can we convert that to a unit rate to get the denominator as one day? Yes, reducing the ratio by dividing by 2 gives us the unit rate of 25 dollars per day, strong work! Bennie's rate unit is already dollars per days. To get his unit rate of dollars per day all we need to do is reduce the fraction, giving us 10 dollars per day--every little bit of kibble helps! Evette’s puppy performance earns 350 dollars per week, which is 350 dollars in 7 days. Reducing gives us 50 dollars per day! Looks like those puppy tricks are raking in the most dough! Nevertheless, each of their fundraising efforts matter. So, to find out what they can make together let's combined their unit rates by adding the fractions. The denominators are all the same so adding the numerators results in 85 dollars per day. A good start to their fundraising efforts allows the friends to now research different dog food options. There are two brands they are considering Doggy Delight costs 25.49 for 1.3 kilograms, and it's all natural with extra protein and calcium to strengthen muscles and bones. Bennie Bite is 22.79 for 3 lbs. It's Bennie’s homemade, organic, preparation that the puppies just love. At Ruff Rescue the friends only want to give the best quality to their pups. Nevertheless, they've got to keep an eye on their budget. Therefore, the friends would like to know which option is the least expensive. In order for us to see this clearly, let’s convert the units for each price to the unit rate of dollars per pound. How can we convert Doggie Delight to dollars per pound? By converting the units using a conversion factor. Is there a conversion factor which relates pounds to kilograms? Yes! 1 kilogram is about two point two pounds. We put kilograms on top of the conversion factor to cancel with kilograms on the bottom of our original rate unit, leaving us with dollars per pound. Multiplying through the numerator gives us 25 dollars and 49 cents and also across the denominator gives us 2.86 pounds. Then, using our calculator, we calculate the unit rate by simply dividing. This results in a unit rate of approximately 8.91 dollars per pound. Now we can find the unit rate of Bennie Bite. Bennie already sells his dog food in three pound packages. So to get the unit rate of dollars per pound we just divide by 3. That results in about 7.60 per pound. Bennie's dog food is the best value for Ruff Rescue. Helping puppies is a problem we solved with the use of rates, unit rates, and unit conversions. First we converted the different fundraising rates to a common rate unit, dollars per days. Next, in order to combine the rates we simplified each one to a unit rate using division so the denominator would be one. In the second example, we wanted to compare dog food prices. So, we used a conversion factor to represent each brand with a rate unit of dollars per pounds. Then, we simplified them using division to give us the unit prices. All of these steps can be used in various ways to solve problems involving rates and in this case, to help Ruff Rescue get started. The friends make a poster encouraging people to adopt. But... oh man. Looks like the friends will need to spend some more time training the puppies. They’ve got their work cut out for them. Hashtag Hungry Puppies!

Problem Solving Using Rates, Unit Rates, and Conversions exercise

Utilize rate to compare and solve a work problem..

A unit rate is expressed as a quantity of $1$.

If Sally makes ＄$84$ in $2$ hours, divide both numbers by $2$ to find that she makes ＄$42$ in $1$ hour or ＄$42$ per hour.

• To convert to the unit rate dollars per hour, multiply $4$ days by $24$ hours to find that $4$ days equals $96$ hours.
• We can now see that Bennie makes ＄$192$ in $96$ hours.
• Dividing both sides by $96$ yields the unit rate ＄$2$ per hour.

1. Since each friend is counting their money differently, we need to choose one time period (hour, day, week, month, year) as the unit.

Sally's units are dollars per hour, Bennie's units are dollars per day, and Evette's units are dollars per week.

The best unit rate to choose for this scenario is dollars per day, since the number can be easily converted into dollars per day.

2. Sally walks dogs and makes＄$75$ in $72$ hours. This is the same as＄$75$ in $3$ days because $72$ hours divided by $24$ hours equals $3$ days. Now we can convert to a unit rate to find how much Sally makes in one day. We can divide both sides by $3$ and find that Sally makes＄$25$ per day.

3. Bennie works at the local pet store and makes＄$200$ in four days. To find the unit rate, divide both sides by $4$ to find that Bennie makes＄$50$ per day.

4. Evette teaches puppy school and makes＄$420$ in one week. This is the same as＄$420$ in $7$ days. The unit rate is found by dividing both sides by $7$. Evette makes＄$60$ per day.

• ＄$25$ per day $+$＄$50$ per day $+$＄$60$ per day $=$＄$135$ per day.

Compare using a unit rate.

To find a unit rate, divide both numbers in the ratio by the second number.

It costs $\$16.50$ for $5$ dog bones. Find the unit rate by dividing both numbers by $5$. It costs $\$3.30$ per dog bone.

To find a unit rate, divide by the dollar amount by the number of items.

• Divide both numbers by $95$
• $\$0.31$ per dog treat.
• Divide both numbers by $9$
• $\$2$ per rubber ball.
• Divide both numbers by $8$
• $\$4.06$ per dog bone.
• Divide both numbers by $4$
• $\$4.99$ per dog brush.
• Divide both numbers by $6$
• $\$8.49$ per teddy bear.
• Divide both numbers by $5$
• $\$10.55$ per bag of dog food.

Identify the work problems that can be solved by finding a rate.

Work problems can be solved by finding a unit rate, and non-work problems don't involve unit rates.

An example of a work problem is:

Tony and Sofie are partners for a class project. In the past, Tony completed $3$ projects in $6$ hours, and Sofie completed $4$ projects in $2$ hours. How long will it take Tony and Sofie to complete one project together?

Work Problems : Problems that are solved by finding a unit rate.

• Since the answer to this problem requires you to solve for a unit rate, it is considered a work problem.
• Set up a fraction to represent the work: $\frac{3\text{ houses}}{24\text{ hours}}$ and $\frac{2\text{ houses}}{20\text{ hours}}$
• Divide the numerator by the denominator to find the unit rate: $\frac{0.125\text{ houses}}{1\text{ hour}}$ and $\frac{0.1\text{ houses}}{1\text{ hour}}$
• Since $0.125$ houses per hour is greater than $0.1$ houses per hour, Sam paints at a faster rate than Marcus.
• Set up a fraction to represent the work: $\frac{4\text{ driveways}}{8\text{ hours}}$ and $\frac{5\text{ driveways}}{7.5\text{ hours}}$
• Divide the numerator by the denominator to find the unit rate: $\frac{0.5\text{ driveways}}{1\text{ hour}}$ and $\frac{1.5\text{ houses}}{1\text{ hour}}$
• No. Since $0.5$ driveways per hour is less that $1.5$ driveways per hour, Malia shovels at a slower rate than Kate.
• Set up a fraction to represent the work: $\frac{25\text{ flowers}}{45\text{ minutes}}$ and $\frac{17\text{ flowers}}{38\text{ minutes}}$
• Divide the numerator by the denominator to find the unit rate: $\frac{0.56\text{ flowers}}{1\text{ minute}}$ and $\frac{0.45\text{ flowers}}{1\text{ minute}}$
• Yes. Since $0.56$ flowers per minutes is greater that $0.45$ flowers per minute, Kroy plants faster than Edmond.
• Since the answer to this problem requires you to solve for a ratio and not a unit rate, it is not considered a work problem.
• To solve this type of word problem we need to set up a proportion: $\frac{5.5\text{ hours}}{275\text{ miles}}=\frac{x\text{ hours}}{350\text{ miles}}$
• Cross multiply: $275x=5.5(350)$
• Simplify: $275x=1,925$
• Solve: $x=7$
• Therefore, it will take $7$ hours to drive $350$ miles.
• There are $22$ red and blue marbles in the bag, and a total of $50$ marbles.
• To find the percentage of red and blue marbles, divide $22$ by $50$, then multiply by $100$: $(22\div 50)\cdot 100=44$
• $44\%$ of the marbles are red and blue.

Solve unit rate word problems.

A unit rate is expressed as a quantity of 1.

To find the unit rate, set up a fraction to represent the situation, then divide the numerator by the denominator.

• The unit rate for $8$ miles in $32$ minutes is represented by the fraction $\frac{8\text{ miles}}{32\text{ minutes}}$.
• Divide the numerator by the denominator: $\frac{0.25\text{ miles}}{1\text{ minute}}$
• Therefore, the unit rate is $0.25$ miles per minute.

In the following problems, to find the unit rate, set up a fraction to represent the situation, then divide the numerator by the denominator.

• Audrey drives $63$ miles per hour ($\frac{315\text{ miles}}{5\text{ hours}}=\frac{63\text{ miles}}{1\text{ hour}}$), and Kai drives $54$ miles per hour ($\frac{243\text{ miles}}{4.5\text{ hours}}=\frac{54\text{ miles}}{1\text{ hour}}$).
• Who drives faster, Audrey or Kai? Audrey because 63 miles per hour is greater than 54 miles per hour.
• Order the girls from the slowest to the fastest rate for collecting eggs: Sofie, Mady, Ada.
• Ada collected her eggs at a rate of 0.65 eggs per minute: $\frac{15\text{ eggs}}{23\text{ minutes}}=\frac{0.65\text{ eggs}}{1\text{ minute}}$
• Sofie collected her eggs at a rate of 0.9 eggs per minute: $\frac{19\text{ eggs}}{21\text{ minutes}}=\frac{0.9\text{ eggs}}{1\text{ minute}}$
• Mady collected her eggs at a rate of 0.68 per minute: $\frac{17\text{ eggs}}{25\text{ minutes}}=\frac{0.68\text{ eggs}}{1\text{ minute}}$
• What is the unit rate for the box of $9$ tomatoes rounded to the nearest hundredth? $2.25$ tomatoes per dollar because $\frac{9\text{ tomatoes}}{\$3.99}=\frac{2.25\text{ tomatoes}}{\$1}$.
• Is the box of $11$ tomatoes a better deal than buying the box of $9$ tomatoes? No because the unit rate for box of $11$ tomatoes is $2.10$ tomatoes per dollar ($\frac{11\text{ tomatoes}}{\$5.25}=\frac{2.10}{\$1}$)
• Sarah ran at a rate of $5.2$ miles per hour on Saturday. Convert minutes to hours by dividing by $60$: $57.5\div 60=0.96$. Now, find the unit rate: $\frac{5\text{ miles}}{0.96\text{ hours}}=\frac{5.2\text{ miles}}{1\text{ hour}}$
• Which day did Sarah run at a faster rate, Saturday or Sunday? Sunday because $\frac{8\text{ miles}}{1.44\text{ hours}}=\frac{5.56\text{ miles}}{1\text{ hour}}$

Convert simple units.

There are $12$ inches in $1$ foot, and $2.54$ centimeters in $1$ inch.

$7$ feet are $84$ inches.

$7$ feet are $213.36$ centimeters.

There are 12 inches in 1 foot, and 2.54 centimeters in 1inch. To convert feet to inches, multiply by 12. To convert feet to centimeters, first multiply by 12, then by 2.54.

• There are 60 inches in 5 feet: $5(12)=60$
• There are 152.4 centimeters in 5 feet: $5(12)(2.54)=152.4$
• There are 69 inches in 5.75 feet: $5.75(12)=69$
• There are 175.26 centimeters in 5.75 feet: $5.75(12)(2.54)=175.26$
• There are 72 inches in 6 feet: $6(12)=72$
• There are 182.88 centimeters in 6 feet: $6(12)(2.54)=182.88$
• There are 78 inches in 6.5 feet: $6.5(12)=78$
• There are 198.12 centimeters in 6.5 feet: $6.5(12)(2.54)=198.12$

Identify the correct solutions to the word problem.

There are $36$ inches in $1$ yard.

There are $3$ feet in $1$ yard.

To find the unit rate, set up a fraction to represent the situation, then divide both the numerator and denominator by the denominator.

Since all of the answer choices are represented in yards, convert the fabrics that are listed in inches and feet to yards.

There are $3$ feet in $1$ yard and $36$ inches in $1$ yard.

The unit rates are as follows:

• $\frac{\$27.96}{4\text{ yards}}=\frac{\$6.99}{1\text{ yard}}$
• The unit rate is $\$6.99$ per yard.
• $\frac{\$24.97}{90\text{ inches}}\cdot \frac{36\text{ inches}}{1\text{ yard}} =\frac{\$898.2}{90\text{ yards}}=\frac{\$9.99}{1\text{ yard}}$
• The unit rate is $\$9.99$ per yard.
• $\frac{\$30.31}{7\text{ feet}}\cdot \frac{3\text{ feet}}{1\text{ yard}} =\frac{\$90.93}{7\text{ yards}}=\frac{\$12.99}{1\text{ yard}}$
• The unit rate is $\$12.99$ per yard.
• $\frac{\$29.96}{3.75\text{ yards}}=\frac{\$7.99}{1\text{ yard}}$
• The unit rate is $\$7.99$ per yard.
• Fleece Fabric costs $\$1$ more per yard than Flannel Fabric. This is correct because $\$7.99-\$6.99=\$1$.
• The unit rate for Quilt Fabric is $\$9.99$ per yard.
• The total cost for $1$ yard of Satin Fabric and $1$ yard of Fleece Fabric is $\$20.98$. This is correct because $\$12.99+\$7.99=\$20.98$.
• The total cost for 1 yard of all 4 fabrics is $\$37.96$. This is correct because $\$6.99+\$9.99+\$12.99+\$7.99=\$37.96$.
• The unit rate for Flannel Fabric is $\$7.99$ per yard.
• The unit rate for Satin Fabric is $\$6.99$.

From Ratios to Rates and Rates to Ratios

Finding Rates with Division

Comparison Shopping: Unit Price and Related Measurements

Getting the Job Done—Speed

Getting the Job Done—Work

Getting the Job Done: Converting Units of Measurement

What is a Proportional Relationship? 

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On these printable worksheets, student will learn the concept of a unit rate, and they will practice solving word problems related to linear measurement, constant speed, and pricing. These math activities align closely with the following Common Core Standards: CCSS.6.RP.A.2, CCSS.6.RP.A.3.B, and CCSS.7.RP.A.1.

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Unit 1: Module 1: Ratios and unit rates

About this unit.

"In Module 1, students build on their prior work in measurement and in multiplication and division as they study the concepts and language of ratios and unit rates. They use proportional reasoning to solve problems. In particular, students solve ratio and rate using tape diagrams, tables of equivalent ratios, double number line diagrams, and equations. They plot pairs of values generated from a ratio or rate on the first quadrant of the coordinate plane." Eureka Math/EngageNY (c) 2015 GreatMinds.org

Topic A: Representing and reasoning about ratios

• Intro to ratios (Opens a modal)
• Ratio review (Opens a modal)
• Basic ratios (Opens a modal)
• Part:whole ratios (Opens a modal)
• Equivalent ratios (Opens a modal)
• Equivalent ratios: recipe (Opens a modal)
• Equivalent ratio word problems (Opens a modal)
• Understanding equivalent ratios (Opens a modal)
• Basic ratios Get 5 of 7 questions to level up!
• Equivalent ratios Get 3 of 4 questions to level up!
• Equivalent ratios with equal groups Get 3 of 4 questions to level up!
• Equivalent ratio word problems Get 3 of 4 questions to level up!
• Equivalent ratios in the real world Get 3 of 4 questions to level up!
• Understand equivalent ratios in the real world Get 3 of 4 questions to level up!

Topic B: Collections of equivalent ratios

• Ratios and double number lines (Opens a modal)
• Solving ratio problems with tables (Opens a modal)
• Ratio tables (Opens a modal)
• Ratios with tape diagrams (Opens a modal)
• Ratios and measurement (Opens a modal)
• Ratios on coordinate plane (Opens a modal)
• Part to whole ratio word problem using tables (Opens a modal)
• Ratios with double number lines Get 3 of 4 questions to level up!
• Ratio tables Get 3 of 4 questions to level up!
• Create double number lines Get 3 of 4 questions to level up!
• Ratios with tape diagrams Get 3 of 4 questions to level up!
• Relate double number lines and ratio tables Get 3 of 4 questions to level up!
• Ratios and units of measurement Get 3 of 4 questions to level up!
• Ratios on coordinate plane Get 3 of 4 questions to level up!
• Part-part-whole ratios Get 3 of 4 questions to level up!

Topic C: Unit rates

• Intro to rates (Opens a modal)
• Solving unit rate problem (Opens a modal)
• Solving unit price problem (Opens a modal)
• Rate problems (Opens a modal)
• Rate review (Opens a modal)
• Comparing rates example (Opens a modal)
• Unit rates Get 5 of 7 questions to level up!
• Rate problems Get 3 of 4 questions to level up!
• Comparing rates Get 3 of 4 questions to level up!

Topic D: Percents

• The meaning of percent (Opens a modal)
• Meaning of 109% (Opens a modal)
• Percents from fraction models (Opens a modal)
• Finding percentages with a double number line (Opens a modal)
• Finding the whole with a tape diagram (Opens a modal)
• Fraction, decimal, and percent from visual model (Opens a modal)
• Converting percents to decimals & fractions example (Opens a modal)
• Percent of a whole number (Opens a modal)
• Converting between percents, fractions, & decimals (Opens a modal)
• Finding a percent (Opens a modal)
• Ways to rewrite a percentage (Opens a modal)
• Finding common percentages (Opens a modal)
• Converting percents and fractions review (Opens a modal)
• Converting decimals and percents review (Opens a modal)
• Percent word problem: 78 is 15% of what number? (Opens a modal)
• Percent word problem: guavas (Opens a modal)
• Percent word problem: penguins (Opens a modal)
• Percent word problem: recycling cans (Opens a modal)
• Intro to percents Get 5 of 7 questions to level up!
• Percents from fraction models Get 3 of 4 questions to level up!
• Find percents visually Get 5 of 7 questions to level up!
• Equivalent representations of percent problems Get 3 of 4 questions to level up!
• Benchmark percents Get 5 of 7 questions to level up!
• Finding percents Get 5 of 7 questions to level up!
• Percent word problems Get 5 of 7 questions to level up!

Comparing Unit Rates: Word Problems

Find and compare unit rates in the context of real-world scenarios with this sixth-grade math worksheet! Featuring ten relatable word problems, this worksheet asks students to read each scenario's verbal description of two rates. In each problem, learners will need to dissect the word problem, determine each of the unit rates, and then compare the two unit rates to answer the question. For more practice with unit rates, check out this  Unit Rate Word Problems worksheet!

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