ratio problem solving activities

• Number Charts
• Multiplication
• Long division
• Basic operations
• Telling time
• Place value
• Roman numerals
• Fractions & related
• Add, subtract, multiply,   and divide fractions
• Mixed numbers vs. fractions
• Equivalent fractions
• Prime factorization & factors
• Fraction Calculator
• Decimals & Percent
• Add, subtract, multiply,   and divide decimals
• Fractions to decimals
• Percents to decimals
• Percentage of a number
• Percent word problems
• Classify triangles
• Classify quadrilaterals
• Circle worksheets
• Area & perimeter of rectangles
• Area of triangles & polygons
• Coordinate grid, including   moves & reflections
• Volume & surface area
• Pre-algebra
• Square Roots
• Order of operations
• Scientific notation
• Proportions
• Ratio word problems
• Write expressions
• Evaluate expressions
• Simplify expressions
• Linear equations
• Linear inequalities
• Graphing & slope
• Equation calculator
• Equation editor
• Elementary Math Games
• Addition and subtraction
• Math facts practice
• The four operations
• Factoring and number theory
• Geometry topics
• Middle/High School
• Statistics & Graphs
• Probability
• Trigonometry
• Logic and proof
• For all levels
• Favorite math puzzles
• Favorite challenging puzzles
• Math in real world
• Problem solving & projects
• For gifted children
• Math history
• Math games and fun websites
• Interactive math tutorials
• Math help & online tutoring
• Assessment, review & test prep
• Online math curricula

Use the generator to make customized ratio worksheets. Experiment with the options to see what their effect is.

Primary Grade Challenge Math by Edward Zaccaro

A good book on problem solving with very varied word problems and strategies on how to solve problems. Includes chapters on: Sequences, Problem-solving, Money, Percents, Algebraic Thinking, Negative Numbers, Logic, Ratios, Probability, Measurements, Fractions, Division. Each chapter’s questions are broken down into four levels: easy, somewhat challenging, challenging, and very challenging.

• Skills by Standard
• Skills by Grade
• Skills by Category

Go to profile

• Assignments
• Assessments
• Report Cards
• Our Teachers

Common Core - State Standards Initiative

Understanding ratios is crucial for solving problems relating to proportions and percents. Math Games makes reviewing this higher-level math skill a breeze, with our suite of enjoyable educational games that students won’t want to stop playing!

Our free resources include mobile-compatible game apps, PDF worksheets, an online textbook and more. Students can use these tools to blend study with play as they practice:

• Describing pictures as ratios
• Calculating percents and prices
• Comparing ratios
• Solving proportions
• Finding the slope of a graph

Help the kids in your life look forward to reviewing math! Our games are tailored to a variety of grade levels and become easier or more challenging depending on how well users are playing. Select one of the skills listed above to check them out!

Reading & Math for K-5

• Kindergarten
• Learning numbers
• Comparing numbers
• Place Value
• Roman numerals
• Subtraction
• Multiplication
• Order of operations
• Drills & practice
• Measurement
• Factoring & prime factors
• Proportions
• Shape & geometry
• Data & graphing
• Word problems
• Children's stories
• Leveled Stories
• Context clues
• Cause & effect
• Compare & contrast
• Fact vs. fiction
• Fact vs. opinion
• Main idea & details
• Story elements
• Conclusions & inferences
• Sounds & phonics
• Words & vocabulary
• Reading comprehension
• Early writing
• Numbers & counting
• Simple math
• Social skills
• Other activities
• Dolch sight words
• Fry sight words
• Multiple meaning words
• Prefixes & suffixes
• Vocabulary cards
• Other parts of speech
• Punctuation
• Capitalization
• Narrative writing
• Opinion writing
• Informative writing
• Cursive alphabet
• Cursive letters
• Cursive letter joins
• Cursive words
• Cursive sentences
• Cursive passages
• Grammar & Writing

Breadcrumbs

Ratio word problems

Download & Print Only $7.90

Use ratios to solve these word problems

Students can use simple ratios to solve these word problems ; the arithmetic is kept simple so as to focus on the understanding of the use of ratios.

These worksheets are available to members only.

Join K5 to save time, skip ads and access more content. Learn More

What is K5?

K5 Learning offers free worksheets , flashcards  and inexpensive  workbooks  for kids in kindergarten to grade 5. Become a member  to access additional content and skip ads.

Our members helped us give away millions of worksheets last year.

We provide free educational materials to parents and teachers in over 100 countries. If you can, please consider purchasing a membership ($24/year) to support our efforts.

Members skip ads and access exclusive features.

Learn about member benefits

This content is available to members only.

• Forgot Password?

Addition (Basic)

Addition (Multi-Digit)

Algebra & Pre-Algebra

Comparing Numbers

Daily Math Review

Division (Basic)

Division (Long Division)

Hundreds Charts

Measurement

Multiplication (Basic)

Multiplication (Multi-Digit)

Order of Operations

Place Value

Probability

Skip Counting

Subtraction

Telling Time

Word Problems (Daily)

More Math Worksheets

Reading Comprehension

Reading Comprehension Gr. 1

Reading Comprehension Gr. 2

Reading Comprehension Gr. 3

Reading Comprehension Gr. 4

Reading Comprehension Gr. 5

Reading Comprehension Gr. 6

Reading & Writing

Reading Worksheets

Cause & Effect

Fact & Opinion

Fix the Sentences

Graphic Organizers

Synonyms & Antonyms

Writing Prompts

Writing Story Pictures

Writing Worksheets

More ELA Worksheets

Consonant Sounds

Vowel Sounds

Consonant Blends

Consonant Digraphs

Word Families

More Phonics Worksheets

Early Literacy

Build Sentences

Sight Word Units

Sight Words (Individual)

More Early Literacy

Punctuation

Subjects and Predicates

More Grammar Worksheets

Spelling Lists

Spelling Grade 1

Spelling Grade 2

Spelling Grade 3

Spelling Grade 4

Spelling Grade 5

Spelling Grade 6

More Spelling Worksheets

Chapter Books

Charlotte's Web

Magic Tree House #1

Boxcar Children

More Literacy Units

Animal (Vertebrate) Groups

Butterfly Life Cycle

Electricity

Matter (Solid, Liquid, Gas)

Simple Machines

Space - Solar System

More Science Worksheets

Social Studies

Maps (Geography)

Maps (Map Skills)

More Social Studies

Mother's Day

Father's Day

More Holiday Worksheets

Puzzles & Brain Teasers

Brain Teasers

Logic:  Addition Squares

Mystery Graph Pictures

Number Detective

Lost in the USA

More Thinking Puzzles

Teacher Helpers

Teaching Tools

Award Certificates

More Teacher Helpers

Pre-K and Kindergarten

Alphabet (ABCs)

Numbers and Counting

Shapes (Basic)

More Kindergarten

Worksheet Generator

Word Search Generator

Multiple Choice Generator

Fill-in-the-Blanks Generator

More Generator Tools

Full Website Index

Ratio Worksheets

Compare two quantities with ratios. These worksheets feature basic and intermediate-level ratio activities.

Logged in members can use the Super Teacher Worksheets filing cabinet to save their favorite worksheets.

Quickly access your most used files AND your custom generated worksheets!

Please login to your account or become a member and join our community today to utilize this helpful feature.

Learn to calculate the probability of certain events with these printable worksheets.

This page contains the full index of math worksheets on our website.

Images of Worksheets

PDF with answer key:

PDF no answer key:

Ratio Practice Questions

Click here for questions, click here for answers, gcse revision cards.

5-a-day Workbooks

Primary Study Cards

Privacy Policy

Terms and Conditions

Corbettmaths © 2012 – 2024

• Home   |  
• About   |  
• Contact Us   |  
• Privacy   |  
• Newsletter   |  
• Shop   |  
• 🔍 Search Site
• Easter Color By Number Sheets
• Printable Easter Dot to Dot
• Easter Worksheets for kids
• Kindergarten
• All Generated Sheets
• Place Value Generated Sheets
• Addition Generated Sheets
• Subtraction Generated Sheets
• Multiplication Generated Sheets
• Division Generated Sheets
• Money Generated Sheets
• Negative Numbers Generated Sheets
• Fraction Generated Sheets
• Place Value Zones
• Number Bonds
• Addition & Subtraction
• Times Tables
• Fraction & Percent Zones
• All Calculators
• Fraction Calculators
• Percent calculators
• Area & Volume Calculators
• Age Calculator
• Height Calculator
• Roman Numeral Calculator
• Coloring Pages
• Fun Math Sheets
• Math Puzzles
• Mental Math Sheets
• Online Times Tables
• Online Addition & Subtraction
• Math Grab Packs
• All Math Quizzes
• 1st Grade Quizzes
• 2nd Grade Quizzes
• 3rd Grade Quizzes
• 4th Grade Quizzes
• 5th Grade Quizzes
• 6th Grade Math Quizzes
• Place Value
• Rounding Numbers
• Comparing Numbers
• Number Lines
• Prime Numbers
• Negative Numbers
• Roman Numerals
• Subtraction
• Add & Subtract
• Multiplication
• Fraction Worksheets
• Learning Fractions
• Fraction Printables
• Percent Worksheets & Help
• All Geometry
• 2d Shapes Worksheets
• 3d Shapes Worksheets
• Shape Properties
• Geometry Cheat Sheets
• Printable Shapes
• Coordinates
• Measurement
• Math Conversion
• Statistics Worksheets
• Bar Graph Worksheets
• Venn Diagrams
• All Word Problems
• Finding all possibilities
• Logic Problems
• Ratio Word Problems
• All UK Maths Sheets
• Year 1 Maths Worksheets
• Year 2 Maths Worksheets
• Year 3 Maths Worksheets
• Year 4 Maths Worksheets
• Year 5 Maths Worksheets
• Year 6 Maths Worksheets
• All AU Maths Sheets
• Kindergarten Maths Australia
• Year 1 Maths Australia
• Year 2 Maths Australia
• Year 3 Maths Australia
• Year 4 Maths Australia
• Year 5 Maths Australia
• Meet the Sallies
• Certificates

Welcome to our Ratio Word Problems page. Here you will find our range of 6th Grade Ratio Problem worksheets which will help your child apply and practice their Math skills to solve a range of ratio problems.

For full functionality of this site it is necessary to enable JavaScript.

Here are the instructions how to enable JavaScript in your web browser .

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

The sheets involve using and applying knowledge to ratios to solve problems.

The sheets have been put in order of difficulty, with the easiest first. They are aimed at students in 6th grade.

Each problem sheet comes complete with an answer sheet.

Using these sheets will help your child to:

• apply their ratio skills;
• apply their knowledge of fractions;
• solve a range of word problems.
• Ratio Problems 1
• PDF version
• Ratio Problems 2
• Ratio Problems 3
• Ratio Problems 4

Ratio and Probability Problems

• Ration and Probability Problems 1
• Sheet 1 Answers
• Ration and Probability Problems 2
• Sheet 2 Answers

More Recommended Math Worksheets

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

More Ratio & Unit Rate 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
• Unit Rate Problems 6th Grade

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

How to Print or Save these sheets 🖶

Need help with printing or saving? Follow these 3 steps to get your worksheets printed perfectly!

• How to Print support

Subscribe to Math Salamanders News

Sign up for our newsletter to get free math support delivered to your inbox each month. Plus, get a seasonal math grab pack included for free!

• Newsletter Signup

Return to 6th Grade Math Worksheets

Return to Math Problem Worksheets

Return from Ratio Word Problems to Math Salamanders Homepage

Math-Salamanders.com

The Math Salamanders hope you enjoy using these free printable Math worksheets and all our other Math games and resources.

We welcome any comments about our site or worksheets on the Facebook comments box at the bottom of every page.

New! Comments

TOP OF PAGE

© 2010-2024 Math Salamanders Limited. All Rights Reserved.

• Privacy Policy
• Copyright Policy

Ratio Worksheets

• Kindergarten

One to one maths interventions built for KS4 success

Weekly online one to one GCSE maths revision lessons now available

In order to access this I need to be confident with:

This topic is relevant for:

Ratio Problem Solving

Here we will learn about ratio problem solving, including how to set up and solve problems. We will also look at real life ratio problems.

There are also ratio problem solving worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.

What is ratio problem solving?

Ratio problem solving is a collection of word problems that link together aspects of ratio and proportion into more real life questions. This requires you to be able to take key information from a question and use your knowledge of ratios (and other areas of the curriculum) to solve the problem.

A ratio is a relationship between two or more quantities . They are usually written in the form a:b where a and b are two quantities. When problem solving with a ratio, the key facts that you need to know are,

• What is the ratio involved?
• What order are the quantities in the ratio?
• What is the total amount / what is the part of the total amount known?
• What are you trying to calculate ?

As with all problem solving, there is not one unique method to solve a problem. However, this does not mean that there aren’t similarities between different problems that we can use to help us find an answer. 

The key to any problem solving is being able to draw from prior knowledge and use the correct piece of information to allow you to get to the next step and then the solution.

Let’s look at a couple of methods we can use when given certain pieces of information.

When solving ratio problems it is very important that you are able to use ratios. This includes being able to use ratio notation. 

For example, Charlie and David share some sweets in the ratio of 3:5. This means that for every 3 sweets Charlie gets, David receives 5 sweets.

Charlie and David share 40 sweets, how many sweets do they each get?

We use the ratio to divide 40 sweets into 8 equal parts. 

Then we multiply each part of the ratio by 5.

3 x 5:5 x 5 = 15:25

This means that Charlie will get 15 sweets and David will get 25 sweets.

• Dividing ratios

Step-by-step guide: Dividing ratios (coming soon)

Ratios and fractions (proportion problems)

We also need to consider problems involving fractions. These are usually proportion questions where we are stating the proportion of the total amount as a fraction.

Simplifying and equivalent ratios

• Simplifying ratios

Equivalent ratios

Units and conversions ratio questions

Units and conversions are usually equivalent ratio problems (see above).

• If £1:\$1.37 and we wanted to convert £10 into dollars, we would multiply both sides of the ratio by 10 to get £10 is equivalent to \$13.70.
• The scale on a map is 1:25,000. I measure 12cm on the map. How far is this in real life, in kilometres? After multiplying both parts of the ratio by 12 you must then convert 12 \times 25000=300000 \ cm to km by dividing the solution by 100 \ 000 to get 3km.

Notice that for all three of these examples, the units are important. For example if we write the mapping example as the ratio 4cm:1km, this means that 4cm on the map is 1km in real life.

Top tip: if you are converting units, always write the units in your ratio.

Usually with ratio problem solving questions, the problems are quite wordy . They can involve missing values , calculating ratios , graphs , equivalent fractions , negative numbers , decimals and percentages .

Highlight the important pieces of information from the question, know what you are trying to find or calculate , and use the steps above to help you start practising how to solve problems involving ratios.

How to do ratio problem solving

In order to solve problems including ratios:

Identify key information within the question.

Know what you are trying to calculate.

Use prior knowledge to structure a solution.

Explain how to do ratio problem solving

Ratio problem solving worksheet

Get your free ratio problem solving worksheet of 20+ questions and answers. Includes reasoning and applied questions.

Related lessons on ratio

Ratio problem solving is part of our series of lessons to support revision on ratio . You may find it helpful to start with the main ratio lesson for a summary of what to expect, or use the step by step guides below for further detail on individual topics. Other lessons in this series include:

• How to work out ratio  
• Ratio to fraction
• Ratio scale
• Ratio to percentage

Ratio problem solving examples

Example 1: part:part ratio.

Within a school, the number of students who have school dinners to packed lunches is 5:7. If 465 students have a school dinner, how many students have a packed lunch?

Within a school, the number of students who have school dinners to packed lunches is \bf{5:7.} If \bf{465} students have a school dinner , how many students have a packed lunch ?

Here we can see that the ratio is 5:7 where the first part of the ratio represents school dinners (S) and the second part of the ratio represents packed lunches (P).

We could write this as

Where the letter above each part of the ratio links to the question.

We know that 465 students have school dinner.

2 Know what you are trying to calculate.

From the question, we need to calculate the number of students that have a packed lunch, so we can now write a ratio below the ratio 5:7 that shows that we have 465 students who have school dinners, and p students who have a packed lunch.

We need to find the value of p.

3 Use prior knowledge to structure a solution.

We are looking for an equivalent ratio to 5:7. So we need to calculate the multiplier. We do this by dividing the known values on the same side of the ratio by each other.

So the value of p is equal to 7 \times 93=651.

There are 651 students that have a packed lunch.

Example 2: unit conversions

The table below shows the currency conversions on one day.

Use the table above to convert £520 (GBP) to Euros € (EUR).

Use the table above to convert \bf{£520} (GBP) to Euros \bf{€} (EUR).

The two values in the table that are important are GBP and EUR. Writing this as a ratio, we can state

We know that we have £520.

We need to convert GBP to EUR and so we are looking for an equivalent ratio with GBP = £520 and EUR = E.

To get from 1 to 520, we multiply by 520 and so to calculate the number of Euros for £520, we need to multiply 1.17 by 520.

1.17 \times 520=608.4

So £520 = €608.40.

Example 3: writing a ratio 1:n

Liquid plant food is sold in concentrated bottles. The instructions on the bottle state that the 500ml of concentrated plant food must be diluted into 2l of water. Express the ratio of plant food to water respectively in the ratio 1:n.

Liquid plant food is sold in concentrated bottles. The instructions on the bottle state that the \bf{500ml} of concentrated plant food must be diluted into \bf{2l} of water . Express the ratio of plant food to water respectively as a ratio in the form 1:n.

Using the information in the question, we can now state the ratio of plant food to water as 500ml:2l. As we can convert litres into millilitres, we could convert 2l into millilitres by multiplying it by 1000.

2l = 2000ml

So we can also express the ratio as 500:2000 which will help us in later steps.

We want to simplify the ratio 500:2000 into the form 1:n.

We need to find an equivalent ratio where the first part of the ratio is equal to 1. We can only do this by dividing both parts of the ratio by 500 (as 500 \div 500=1 ).

So the ratio of plant food to water in the form 1:n is 1:4.

Example 4: forming and solving an equation

Three siblings, Josh, Kieran and Luke, receive pocket money per week proportional to their age. Kieran is 3 years older than Josh. Luke is twice Josh’s age. If Josh receives £8 pocket money, how much money do the three siblings receive in total?

Three siblings, Josh, Kieran and Luke, receive pocket money per week proportional to their ages. Kieran is \bf{3} years older than Josh . Luke is twice Josh’s age. If Luke receives \bf{£8} pocket money, how much money do the three siblings receive in total ?

We can represent the ages of the three siblings as a ratio. Taking Josh as x years old, Kieran would therefore be x+3 years old, and Luke would be 2x years old. As a ratio, we have

We also know that Luke receives £8.

We want to calculate the total amount of pocket money for the three siblings.

We need to find the value of x first. As Luke receives £8, we can state the equation 2x=8 and so x=4.

Now we know the value of x, we can substitute this value into the other parts of the ratio to obtain how much money the siblings each receive.

The total amount of pocket money is therefore 4+7+8=£19.

Example 5: simplifying ratios

Below is a bar chart showing the results for the colours of counters in a bag.

Express this data as a ratio in its simplest form.

From the bar chart, we can read the frequencies to create the ratio.

We need to simplify this ratio.

To simplify a ratio, we need to find the highest common factor of all the parts of the ratio. By listing the factors of each number, you can quickly see that the highest common factor is 2.

\begin{aligned} &12 = 1, {\color{red} 2}, 3, 4, 6, 12 \\\\ &16 = 1, {\color{red} 2}, 4, 8, 16 \\\\ &10 = 1, {\color{red} 2}, 5, 10 \end{aligned}

HCF (12,16,10) = 2

Dividing all the parts of the ratio by 2 , we get

Our solution is 6:8:5 .

Example 6: combining two ratios

Glass is made from silica, lime and soda. The ratio of silica to lime is 15:2. The ratio of silica to soda is 5:1. State the ratio of silica:lime:soda.

Glass is made from silica, lime and soda. The ratio of silica to lime is \bf{15:2.} The ratio of silica to soda is \bf{5:1.} State the ratio of silica:lime:soda .

We know the two ratios

We are trying to find the ratio of all 3 components: silica, lime and soda.

Using equivalent ratios we can say that the ratio of silica:soda is equivalent to 15:3 by multiplying the ratio by 3.

We now have the same amount of silica in both ratios and so we can now combine them to get the ratio 15:2:3.

Example 7: using bar modelling

India and Beau share some popcorn in the ratio of 5:2. If India has 75g more popcorn than Beau, what was the original quantity?

India and Beau share some popcorn in the ratio of \bf{5:2.} If India has \bf{75g} more popcorn than Beau , what was the original quantity?

We know that the initial ratio is 5:2 and that India has three more parts than Beau.

We want to find the original quantity.

Drawing a bar model of this problem, we have

Where India has 5 equal shares, and Beau has 2 equal shares.

Each share is the same value and so if we can find out this value, we can then find the total quantity.

From the question, India’s share is 75g more than Beau’s share so we can write this on the bar model.

We can find the value of one share by working out 75 \div 3=25g.

We can fill in each share to be 25g.

Adding up each share, we get

India = 5 \times 25=125g

Beau = 2 \times 25=50g

The total amount of popcorn was 125+50=175g.

Common misconceptions

• Mixing units

Make sure that all the units in the ratio are the same. For example, in example 6 , all the units in the ratio were in millilitres. We did not mix ml and l in the ratio.

• Ratio written in the wrong order

For example the number of dogs to cats is given as the ratio 12:13 but the solution is written as 13:12.

• Ratios and fractions confusion

Take care when writing ratios as fractions and vice-versa. Most ratios we come across are part:part. The ratio here of red:yellow is 1:2. So the fraction which is red is \frac{1}{3} (not \frac{1}{2} ).

• Counting the number of parts in the ratio, not the total number of shares

For example, the ratio 5:4 has 9 shares, and 2 parts. This is because the ratio contains 2 numbers but the sum of these parts (the number of shares) is 5+4=9. You need to find the value per share, so you need to use the 9 shares in your next line of working.

• Ratios of the form \bf{1:n}

The assumption can be incorrectly made that n must be greater than 1 , but n can be any number, including a decimal.

Practice ratio problem solving questions

1. An online shop sells board games and computer games. The ratio of board games to the total number of games sold in one month is 3:8. What is the ratio of board games to computer games?

8-3=5 computer games sold for every 3 board games.

2. The volume of gas is directly proportional to the temperature (in degrees Kelvin). A balloon contains 2.75l of gas and has a temperature of 18^{\circ}K. What is the volume of gas if the temperature increases to 45^{\circ}K?

3. The ratio of prime numbers to non-prime numbers from 1-200 is 45:155. Express this as a ratio in the form 1:n.

4. The angles in a triangle are written as the ratio x:2x:3x. Calculate the size of each angle.

5. A clothing company has a sale on tops, dresses and shoes. \frac{1}{3} of sales were for tops, \frac{1}{5} of sales were for dresses, and the rest were for shoes. Write a ratio of tops to dresses to shoes sold in its simplest form.

6. During one month, the weather was recorded into 3 categories: sunshine, cloud and rain. The ratio of sunshine to cloud was 2:3 and the ratio of cloud to rain was 9:11. State the ratio that compares sunshine:cloud:rain for the month.

Ratio problem solving GCSE questions

1. One mole of water weighs 18 grams and contains 6.02 \times 10^{23} water molecules.

Write this in the form 1gram:n where n represents the number of water molecules in standard form.

2. A plank of wood is sawn into three pieces in the ratio 3:2:5. The first piece is 36cm shorter than the third piece.

Calculate the length of the plank of wood.

5-3=2 \ parts = 36cm so 1 \ part = 18cm

3. (a) Jenny is x years old. Sally is 4 years older than Jenny. Kim is twice Jenny’s age. Write their ages in a ratio J:S:K.

(b) Sally is 16 years younger than Kim. Calculate the sum of their ages.

Learning checklist

You have now learned how to:

• Relate the language of ratios and the associated calculations to the arithmetic of fractions and to linear functions
• Develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multi-step problems
• Make and use connections between different parts of mathematics to solve problems

The next lessons are

• Compound measures
• Best buy maths

Still stuck?

Prepare your KS4 students for maths GCSEs success with Third Space Learning. Weekly online one to one GCSE maths revision lessons delivered by expert maths tutors.

Find out more about our GCSE maths tuition programme.

Privacy Overview

Child Login

• Kindergarten
• Number charts
• Skip Counting
• Place Value
• Number Lines
• Subtraction
• Multiplication
• Word Problems
• Comparing Numbers
• Ordering Numbers
• Odd and Even
• Prime and Composite
• Roman Numerals
• Ordinal Numbers
• In and Out Boxes
• Number System Conversions
• More Number Sense Worksheets
• Size Comparison
• Measuring Length
• Metric Unit Conversion
• Customary Unit Conversion
• Temperature
• More Measurement Worksheets
• Writing Checks
• Profit and Loss
• Simple Interest
• Compound Interest
• Tally Marks
• Mean, Median, Mode, Range
• Mean Absolute Deviation
• Stem-and-leaf Plot
• Box-and-whisker Plot
• Permutation and Combination
• Probability
• Venn Diagram
• More Statistics Worksheets
• Shapes - 2D
• Shapes - 3D
• Lines, Rays and Line Segments
• Points, Lines and Planes
• Transformation
• Quadrilateral
• Ordered Pairs
• Midpoint Formula
• Distance Formula
• Parallel, Perpendicular and Intersecting Lines
• Scale Factor
• Surface Area
• Pythagorean Theorem
• More Geometry Worksheets
• Converting between Fractions and Decimals
• Significant Figures
• Convert between Fractions, Decimals, and Percents
• Proportions
• Direct and Inverse Variation
• Order of Operations
• Squaring Numbers
• Square Roots
• Scientific Notations
• Speed, Distance, and Time
• Absolute Value
• More Pre-Algebra Worksheets
• Translating Algebraic Phrases
• Evaluating Algebraic Expressions
• Simplifying Algebraic Expressions
• Algebraic Identities
• Quadratic Equations
• Systems of Equations
• Polynomials
• Inequalities
• Sequence and Series
• Complex Numbers
• More Algebra Worksheets
• Trigonometry
• Math Workbooks
• English Language Arts
• Summer Review Packets
• Social Studies
• Holidays and Events
• Worksheets >
• Pre-Algebra >

Ratio Word Problem Worksheets

We are delighted to share this set of extensively well-researched ratio word problem worksheets which will help students in grade 5 through grade 8 to grasp the basics of ratio calculations. These printable worksheets include simple theme-based ratio word problems, finding the ratio between two quantities, word problems that require children to find a part from the whole, part-to-part, a whole from the part, reading pictographs, bar graphs, and pie graphs. Click on the free icon to sample our worksheets.

Express in ratio: Read the themes

Look at the vivid themes and answer the word problems in these 5th grade worksheets. Express in ratio and reduce it to the lowest term. Use the answer key to verify your responses.

• Download the set

Find the ratio between two quantities

This set of well-researched ratio word problem pdf worksheets includes factual and educative real-life scenarios. Find the ratio between the two quantities. Express your answer in the simplest form.

Ratio word problems: Part-to-part

Based on the data given in these colorful worksheets, read and answer the extremely engaging part-to-part ratio word problems that ensue. You have an option to download this set of worksheets in a single click.

Ratio word problems: A part from the whole

This collection of ratio word problems printable worksheets will require 6th grade and 7th grade students to find the parts from the given ratio and the whole. Set up the simple equation and solve the word problems.

Ratio word problems: The whole from the part

Based on one part of the number and the ratio provided in these word problems, the children need to find the share of the other part and the whole. There are five word problems in each worksheet.

Ratio word problems: Mixed bag

This set of assorted word problems for 7th grade and 8th grade students contains a mix of finding part-to-part, part-to-whole, and finding the ratio. Some word problems may require you to find the ratio based on the increase or decrease in quantity and vice versa.

Finding the Ratio from Pictographs

Use the key to find the total of each item. Read the pictograph and answer the word problems. The word problems are based on finding ratio between the quantities. Do not forget to reduce the ratio to the lowest term.

Finding the Ratio from Bar Graphs

The data provided in these bar graphs are borrowed from real-life scenarios. Read the bar graphs and write the ratio in the simplest form.

Finding the Ratio from Pie Graphs

The printable worksheet pdfs in this section contain ratio word problems based on pie graphs. Read the pie graph, find the ratio and solve the word problems.

Related Worksheets

» Proportions

» Fractions

» Fraction Word Problems

» Decimal Word Problems

» Division Word Problems

Become a Member

Membership Information

Privacy Policy

What's New?

Printing Help

Testimonial

Copyright © 2024 - Math Worksheets 4 Kids

This is a members-only feature!

Algebra: Ratio Word Problems

Related Pages Two-Term Ratio Word Problems More Ratio Word Problems Algebra Lessons

In these lessons, we will learn how to solve ratio word problems that have two-term ratios or three-term ratios.

Ratio problems are word problems that use ratios to relate the different items in the question.

The main things to be aware about for ratio problems are:

• Change the quantities to the same unit if necessary.
• Write the items in the ratio as a fraction .
• Make sure that you have the same items in the numerator and denominator.

Ratio Problems: Two-Term Ratios

Example 1: In a bag of red and green sweets, the ratio of red sweets to green sweets is 3:4. If the bag contains 120 green sweets, how many red sweets are there?

Solution: Step 1: Assign variables: Let x = number of red sweets.

Step 2: Solve the equation. Cross Multiply 3 × 120 = 4 × x 360 = 4 x

Answer: There are 90 red sweets.

Example 2: John has 30 marbles, 18 of which are red and 12 of which are blue. Jane has 20 marbles, all of them either red or blue. If the ratio of the red marbles to the blue marbles is the same for both John and Jane, then John has how many more blue marbles than Jane?

Solution: Step 1: Sentence: Jane has 20 marbles, all of them either red or blue. Assign variables: Let x = number of blue marbles for Jane 20 – x = number red marbles for Jane

Step 2: Solve the equation

Cross Multiply 3 × x = 2 × (20 – x ) 3 x = 40 – 2 x

John has 12 blue marbles. So, he has 12 – 8 = 4 more blue marbles than Jane.

Answer: John has 4 more blue marbles than Jane.

How To Solve Word Problems Using Proportions?

This is another word problem that involves ratio or proportion.

Example: A recipe uses 5 cups of flour for every 2 cups of sugar. If I want to make a recipe using 8 cups of flour. How much sugar should I use?

How To Solve Proportion Word Problems?

When solving proportion word problems remember to have like units in the numerator and denominator of each ratio in the proportion.

• Biologist tagged 900 rabbits in Bryer Lake National Park. At a later date, they found 6 tagged rabbits in a sample of 2000. Estimate the total number of rabbits in Bryer Lake National Park.
• Mel fills his gas tank up with 6 gallons of premium unleaded gas for a cost of $26.58. How much would it costs to fill an 18 gallon tank? 3 If 4 US dollars can be exchanged for 1.75 Euros, how many Euros can be obtained for 144 US dollars?

Ratio problems: Three-term Ratios

Example 1: A special cereal mixture contains rice, wheat and corn in the ratio of 2:3:5. If a bag of the mixture contains 3 pounds of rice, how much corn does it contain?

Solution: Step 1: Assign variables: Let x = amount of corn

Step 2: Solve the equation Cross Multiply 2 × x = 3 × 5 2 x = 15

Answer: The mixture contains 7.5 pounds of corn.

Example 2: Clothing store A sells T-shirts in only three colors: red, blue and green. The colors are in the ratio of 3 to 4 to 5. If the store has 20 blue T-shirts, how many T-shirts does it have altogether?

Solution: Step 1: Assign variables: Let x = number of red shirts and y = number of green shirts

Step 2: Solve the equation Cross Multiply 3 × 20 = x × 4 60 = 4 x x = 15

5 × 20 = y × 4 100 = 4 y y = 25

The total number of shirts would be 15 + 25 + 20 = 60

Answer: There are 60 shirts.

Algebra And Ratios With Three Terms

Let’s study how algebra can help us think about ratios with more than two terms.

Example: There are a total of 42 computers. Each computer runs one of three operating systems: OSX, Windows, Linux. The ratio of the computers running OSX, Windows, Linux is 2:5:7. Find the number of computers that are running each of the operating systems.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.

Ratio Worksheets

• Finding Ratios
• Finding Rate
• Kindergarten

Simplifying Ratios Pixel Picture ( Editable Word | PDF | Answers ​ )

Simplifying Ratios Odd One Out ( Editable Word | PDF | Answers )

Equivalent Ratios Match-Up ( Editable Word | PDF | Answers )

Working with Ratio Practice Strips ( Editable Word | PDF | Answers )

Dividing in a Ratio Practice Strips ( Editable Word | PDF | Answers )

Dividing in a Ratio Fill in the Blanks ( Editable Word | PDF | Answers )

Dividing in a Ratio Crack the Code ( Editable Word | PDF | Answers )

Combining Ratios Practice Strips ( Editable Word | PDF | Answers )

Sharing and Combining Ratios Practice Strips ( Editable Word | PDF | Answers )

Solving Ratio Problems Practice Strips ( Editable Word | PDF | Answers )

Solving Ratio Problems Practice Grid ( Editable Word | PDF | Answers )

Harder Ratio Problems Practice Strips ( Editable Word | PDF | Answers )

Fractions and Ratio Worded Problems Practice Strips ( Editable Word | PDF | Answers )

Unitary Method Practice Strips ( Editable Word | PDF | Answers )

Unitary Method Match-Up ( Editable Word | PDF | Answers )

Best Buys Practice Strips ( Editable Word | PDF | Answers )

Currency Conversions Practice Strips ( Editable Word | PDF | Answers )

Proportion Worded Problems Practice Strips ( Editable Word | PDF | Answers )

Proportion Worded Problems Practice Grid ( Editable Word | PDF | Answers )

Mixed Ratio and Proportion Revision Practice Grid ( Editable Word | PDF | Answers ​ )

If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

To log in and use all the features of Khan Academy, please enable JavaScript in your browser.

Praxis Core Math

Course: praxis core math   >   unit 1.

• Rational number operations | Lesson
• Rational number operations | Worked example

Ratios and proportions | Lesson

• Ratios and proportions | Worked example
• Percentages | Lesson
• Percentages | Worked example
• Rates | Lesson
• Rates | Worked example
• Naming and ordering numbers | Lesson
• Naming and ordering numbers | Worked example
• Number concepts | Lesson
• Number concepts | Worked example
• Counterexamples | Lesson
• Counterexamples | Worked example
• Pre-algebra word problems | Lesson
• Pre-algebra word problems | Worked example
• Unit reasoning | Lesson
• Unit reasoning | Worked example

What are ratios and proportions?

What skills are tested.

• Identifying and writing equivalent ratios
• Solving word problems involving ratios
• Solving word problems using proportions

How do we write ratios?

• The ratio of lemon juice to sugar is a part-to-part ratio. It compares the amount of two ingredients.
• The ratio of lemon juice to lemonade is a part-to-whole ratio. It compares the amount of one ingredient to the sum of all ingredients.
• Determine whether the ratio is part to part or part to whole.
• Calculate the parts and the whole if needed.
• Plug values into the ratio.
• Simplify the ratio if needed. Integer-to-integer ratios are preferred.
• 1 5 ‍   of the students on the varsity soccer team are lower-level students.
• 1 ‍   in 5 ‍   students on the varsity soccer team are lower-level students.

How do we use proportions?

• Write an equation using equivalent ratios.
• Plug in known values and use a variable to represent the unknown quantity.
• If the numeric part of one ratio is a multiple of the corresponding part of the other ratio, we can calculate the unknown quantity by multiplying the other part of the given ratio by the same number.
• If the relationship between the two ratios is not obvious, solve for the unknown quantity by isolating the variable representing it.
• (Choice A)   1 : 4 ‍   A 1 : 4 ‍  
• (Choice B)   1 : 2 ‍   B 1 : 2 ‍  
• (Choice C)   1 : 1 ‍   C 1 : 1 ‍  
• (Choice D)   2 : 1 ‍   D 2 : 1 ‍  
• (Choice E)   4 : 1 ‍   E 4 : 1 ‍  
• (Choice A)   1 6 ‍   A 1 6 ‍  
• (Choice B)   1 3 ‍   B 1 3 ‍  
• (Choice C)   2 5 ‍   C 2 5 ‍  
• (Choice D)   1 2 ‍   D 1 2 ‍  
• (Choice E)   2 3 ‍   E 2 3 ‍  
• Your answer should be
• an integer, like 6 ‍  
• a simplified proper fraction, like 3 / 5 ‍  
• a simplified improper fraction, like 7 / 4 ‍  
• a mixed number, like 1   3 / 4 ‍  
• an exact decimal, like 0.75 ‍  
• a multiple of pi, like 12   pi ‍   or 2 / 3   pi ‍  

Things to remember

Want to join the conversation.

• Upvote Button navigates to signup page
• Downvote Button navigates to signup page
• Flag Button navigates to signup page

Virtual Lab School

Installation staff login.

• Reset your password

Ratio Problem Solving Activity