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Ratio and Percent Word Problems

Ratio word problems, using table with multiplication.

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Ratio To Percentage

Here we will learn about ratio to percentage, including how to convert from ratios to percentages and how to solve word problems involving converting ratios to percentages.

There are also ratio to percentage 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 to percentage?

Ratio to percentage is when you use a given ratio to calculate a percentage.

A ratio tells us how much there is of one thing in relation to another thing.

For example, if Olivia and Dean share some sweets in the ratio 3:2 then for every 3 sweets Olivia gets, Dean gets 2. You can use this information to write the percentage of sweets Olivia and Dean each get. 

To find the percentage of sweets they each get, first convert the ratio into fractions. 

Step-by-step guide: Ratio to fractions

The ratio 3:2 has 5 parts, so the fractions are \frac{3}{5} : \frac{2}{5}.

Olivia gets three fifths of the sweets and Dean gets two fifths. You can convert these fractions to percentages.

You may be able to recognise what the fractions are as percentages or you may need to use long division to help convert your fractions.

Step-by-step guide: Fractions to percentages

\frac{3}{5}=60\%, so Olivia gets 60\% of the sweets.

\frac{2}{5}=40\%, so Dean gets 40\% of the sweets.

How to convert a ratio to a percentage

In order to convert a ratio to a percentage:

Add the parts of the ratio for the denominator of the fractions.

Convert each part of the ratio to a fraction.

Convert the fractions to percentages.

Explain how to convert a ratio to a percentage

Ratio to percentage worksheet

Get your free ratio to percentage worksheet of 20+ questions and answers. Includes reasoning and applied questions.

Related lessons on ratio

Ratio to percentage 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  
• Simplifying ratios
• Ratio to fraction
• Dividing ratios
• Ratio problem solving
• Ratio scale

Ratio to percentage examples

Example 1: converting a two part ratio to percentages.

The ratio of blue counters to red counters is 3:1. Write the ratio as percentages.

3+1=4. There are 4 parts in total. The denominator is 4.

2 Convert each part of the ratio to a fraction.

3:1 becomes \frac{3}{4}:\frac{1}{4} .

3 Convert the fractions to percentages.

\frac{3}{4} and \frac{1}{4} are common fractions for which you need to know the percentage conversions.

Example 2: converting a two part ratio to percentages

The ratio of green counters to yellow counters is 3:5. What percentage of the counters are green?

3+5=8. There are 8 parts in total. The denominator is 8.

3:5 becomes \frac{3}{8}:\frac{5}{8}.

0.375=37.5\% and 0.625=62.5\% therefore,

\frac{3}{8}:\frac{5}{8}=37.5\%:62.5\% .

Order is important in ratios and in this ratio the number of green counters is first.

Therefore the percentage of counters that are green is 37.5\%.

Example 3: converting a three part ratio to percentages

A garden centre sells three types of bulbs; daffodil, tulip and lily, in the ratio 6:9:5. What percentage of the bulbs sold are tulips?

6 + 9 + 5 = 20. There are 20 parts in total. The denominator is 20.

6:9:5 becomes \frac{6}{20}:\frac{9}{20}:\frac{5}{20}.

Writing each fraction with a denominator of 100,

\frac{6}{20}:\frac{9}{20}:\frac{5}{20}=\frac{30}{100}:\frac{45}{100}:\frac{25}{100} .

\frac{6}{20}:\frac{9}{20}:\frac{5}{20}=30\%:45\%:25\%

In this question we are interested in the number of tulips sold, which is the middle value. The percentage that are tulips is 45\%.

Example 4: solving a problem involving ratio to percentages

In April 2022, Ben and Jacob shared some money in the ratio of their ages. Ben was born in June 2014 and Jacob in January 2019. What percentage of the money does Ben receive?

In April 2022 Ben is 7 and Jacob is 3. The ratio of their ages is 7:3.

7+3=10. There are 10 parts in total. The denominator is 10.

7:3 becomes \frac{7}{10}:\frac{3}{10}.

Ben receives 70\% of the money.

Example 5: solving a problem involving ratio to percentages

The ratio of adults to children in a park is 6:4.

One third of the adults are men. What percentage of the people in the park are women?

6 + 4 = 10. There are 10 parts in total. The denominator is 10.

6:4 becomes \frac{6}{10}:\frac{4}{10}.

You have worked out that 60\% of the people are adults. 

One third of the adults are men.

\frac{1}{3} of 60\% = 20\%

20\% of the people in the park are men and therefore 60-20=40\% of the people are women.

Common misconceptions

• Ratios and fractions confusion

For example, the ratio 2:3 is expressed as the fraction \frac{2}{3} and not \frac{2}{5}. This is a misunderstanding of the sum of the parts of the ratio. Be careful with what the question is asking as the denominator may be the part, or the whole amount.

• Ratio written in the wrong order

Order is important in ratio questions and you must maintain the original order throughout your working and answer.

Practice ratio to percentage questions

1. Convert the ratio 1:4 to percentages.

This ratio has 5 parts in total therefore

Converting to percentages,

2. The ratio of people who own a dog to people who don’t own a dog is 9:11. What percentage of people own a dog?

This ratio has 20 parts therefore

45\% of people own a dog.

3. The ratio of teachers to students on a school trip is 1:7. What percentage of those on the trip are students?

The total number of parts in this ratio is 8 therefore

87.5\% of those on the trip are students.

4. Sam, Katrina and Alex share some sweets in the ratio 11:8:6. What percentage of the sweets does Sam get?

The total number of parts in this ratio is 25 therefore

Sam gets 44\% of the sweets.

5. The ratio of the number of boys in a class to the number of girls in a class is 7:3. One fifth of the boys wear glasses. What percentage of the class are boys that wear glasses?

The total number of parts in this ratio is 10 therefore

70\% of the class are boys and one fifth of the boys wear glasses.

\frac{1}{5} of 70\% = 14\% .

14\% of the class are boys who wear glasses.

6. Tony and Anne share some money in the ratio 23:27.

Anne gives a quarter of her share to her friend James.

What percentage of the money does James get?

The total number of parts in this ratio is 50 therefore

Anne gets 46\% of the money and gives one quarter of her share to James.

\frac{1}{4} of 46\% = 11.5\% .

James gets 11.5\% of the money.

Ratio to percentage GCSE questions

1. Write the following ratio as percentages.

Circle your answer.

2. William and Matthew share some money in the ratio 3:7. Matthew gives two fifths of his money to Ellie.

Who receives the most money? Show how you decide.

William 30\%, Matthew 70\%

\frac{2}{5} of 70\%=28\% .

Matthew 42\%, Ellie 28\%

Matthew receives the most money.

3. The ratio of men to women working for an accountancy firm is 5:3.

One fifth of the women are managers and 10\% of the men are managers.

What percentage of all employees are managers?

For converting 5:3 to fractions or percentages, for example 62.5\%:37.5\%.

10\% of 62.5\%=6.25\%

\frac{1}{5} of 37.5\%=7.5\%

Learning checklist

You have now learned how to:

• Convert ratios to percentages and solve problems involving ratios and percentages

The next lessons are

• Compound measures
• Best buy maths

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Maths Genie GCSE Questions & Answers

Proportions

Proportion says that two ratios (or fractions) are equal.

We see that 1-out-of-3 is equal to 2-out-of-6

The ratios are the same, so they are in proportion.

Example: Rope

A rope's length and weight are in proportion.

When 20m of rope weighs 1kg , then:

• 40m of that rope weighs 2kg
• 200m of that rope weighs 10kg

20 1 = 40 2

When shapes are "in proportion" their relative sizes are the same.

Example: International paper sizes (like A3, A4, A5, etc) all have the same proportions:

So any artwork or document can be resized to fit on any sheet. Very neat.

Working With Proportions

NOW, how do we use this?

Example: you want to draw the dog's head ... how long should it be?

Let us write the proportion with the help of the 10/20 ratio from above:

? 42 = 10 20

Now we solve it using a special method:

Multiply across the known corners, then divide by the third number

And we get this:

? = (42 × 10) / 20 = 420 / 20 = 21

So you should draw the head 21 long.

Using Proportions to Solve Percents

A percent is actually a ratio! Saying "25%" is actually saying "25 per 100":

25% = 25 100

We can use proportions to solve questions involving percents.

The trick is to put what we know into this form:

Part Whole = Percent 100

Example: what is 25% of 160 ?

The percent is 25, the whole is 160, and we want to find the "part":

Part 160 = 25 100

Multiply across the known corners, then divide by the third number:

Part = (160 × 25) / 100 = 4000 / 100 = 40

Answer: 25% of 160 is 40.

Note: we could have also solved this by doing the divide first, like this:

Part = 160 × (25 / 100) = 160 × 0.25 = 40

Either method works fine.

We can also find a Percent:

Example: what is $12 as a percent of $80 ?

Fill in what we know:

$12 $80 = Percent 100

Multiply across the known corners, then divide by the third number. This time the known corners are top left and bottom right:

Percent = ($12 × 100) / $80 = 1200 / 80 = 15%

Answer: $12 is 15% of $80

Or find the Whole:

Example: The sale price of a phone was $150, which was only 80% of normal price. What was the normal price?

$150 Whole = 80 100

Whole = ($150 × 100) / 80 = 15000 / 80 = 187.50

Answer: the phone's normal price was $187.50

Using Proportions to Solve Triangles

We can use proportions to solve similar triangles.

Example: How tall is the Tree?

Sam tried using a ladder, tape measure, ropes and various other things, but still couldn't work out how tall the tree was.

But then Sam has a clever idea ... similar triangles!

Sam measures a stick and its shadow (in meters), and also the shadow of the tree, and this is what he gets:

Now Sam makes a sketch of the triangles, and writes down the "Height to Length" ratio for both triangles:

Height: Shadow Length:     h 2.9 m = 2.4 m 1.3 m

h = (2.9 × 2.4) / 1.3 = 6.96 / 1.3 = 5.4 m (to nearest 0.1)

Answer: the tree is 5.4 m tall.

And he didn't even need a ladder!

The "Height" could have been at the bottom, so long as it was on the bottom for BOTH ratios, like this:

Let us try the ratio of "Shadow Length to Height":

Shadow Length: Height:     2.9 m h = 1.3 m 2.4 m

It is the same calculation as before.

A "Concrete" Example

Ratios can have more than two numbers !

For example concrete is made by mixing cement, sand, stones and water.

A typical mix of cement, sand and stones is written as a ratio, such as 1:2:6 .

We can multiply all values by the same amount and still have the same ratio.

10:20:60 is the same as 1:2:6

So when we use 10 buckets of cement, we should use 20 of sand and 60 of stones.

Example: you have just put 12 buckets of stones into a mixer, how much cement and how much sand should you add to make a 1:2:6 mix?

Let us lay it out in a table to make it clearer:

You have 12 buckets of stones but the ratio says 6.

That is OK, you simply have twice as many stones as the number in the ratio ... so you need twice as much of everything to keep the ratio.

Here is the solution:

And the ratio 2:4:12 is the same as 1:2:6 (because they show the same relative sizes)

So the answer is: add 2 buckets of Cement and 4 buckets of Sand. (You will also need water and a lot of stirring....)

Why are they the same ratio? Well, the 1:2:6 ratio says to have :

• twice as much Sand as Cement ( 1 : 2 :6)
• 6 times as much Stones as Cement ( 1 :2: 6 )

In our mix we have:

• twice as much Sand as Cement ( 2 : 4 :12)
• 6 times as much Stones as Cement ( 2 :4: 12 )

So it should be just right!

That is the good thing about ratios. You can make the amounts bigger or smaller and so long as the relative sizes are the same then the ratio is the same.

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