fraction of amount problem solving

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Fraction of a Whole Number

Welcome to our Fraction of a Whole Number support page. On this page we can help you learn to find a fraction of a number with clear step-by-step instructions and some worked examples.

We also have lots of practice sheets with different levels of support for you to try.

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• How to find a Fraction of a Whole Number

Fraction of a Whole Number Examples

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• Fraction of a Whole Number Online Quiz

Fraction of a Whole Number Support Page

Here you will find some simple information and advice about Fraction of a Whole Number.

At the bottom of this page you will also find two printable resource sheets which explain about how to calculate fractions in a little more detail.

Before you start learning to calculate fractions of numbers, you should be able to work out fractions of shapes.

How to find a fraction of a whole number

Here are the two easy steps for finding the fraction of a number:

Step 1 - Find the unit fraction by dividing the number by the denominator

Step 2 - Multiply by the numerator .

You should have now found your fraction of a number!

PLEASE NOTE:

Finding a fraction of a whole number is the same as multiplying the fraction by the whole number.

In other words:

\[ {4 \over 5} \; of \; 30 \; is \; the \; same \; as \; {4 \over 5} \times 30 \]

Example 1) \[ Find \; {5 \over 6} \; of \; 24 \]

A unit fraction is a fraction where the numerator is equal to 1.

To find the unit fraction of a number, you need to divide the number by the denominator.

This gives us: \[ {1 \over 6} \; of \; 24 \; = \; 24 ÷ 6 \; = \; 4 \]

To find five-sixths, we need to multiply our answer by the numerator which is 5.

So \[ {5 \over 6} \; of \; 24 = ({1 \over 6} \; of \; 24) \times 5 = 4 \times 5 = 20 \]

Example 2) \[ Find \; {3 \over 7} \; of \; 35\]

To find the unit fraction, we need to divide the number by the denominator.

This gives us: \[ {1 \over 7} \; of \; 35 \; = \; 35 ÷ 7 \; = \; 5 \]

To find three-sevenths, we need to multiply our answer by the numerator which is 3.

So \[ {3 \over 7} \; of \; 35 = ({1 \over 7} \; of \; 35) \times 3 = 5 \times 3 = 15 \]

Example 3) \[ Find \; {3 \over 10} \; of \; $230\]

This gives us: \[ {1 \over 10} \; of \; $230 = $230 ÷ 10 = $23 \]

To find three-tenths, we need to multiply our answer by the numerator which is 3.

So \[ {3 \over 10} \; of \; $230 = ({1 \over 10} \; of \; $230) \times 3 \] and \[ ({1 \over 10} \; of \; $230) \times 3 = $23 \times 3 = $69 \]

Final answer \[ {3 \over 10} \; of \; $230 \; = \; $69 \]

How to calculate fractions - the algebra...

For those of you who like to see things in Algebra...this is what it looks like

If we want to work out: \[ {a \over b} \; of \; a \; number \; n \]

First we work out: \[ {1 \over b} \; of \; n = {n \over b} \; \; or \; n ÷ b \]

Next we need to multiply this by the numerator a.

This gives us: \[ {a \over b} \; of \; n = {n \over b} \times a = {na \over b} \; \; or \; na ÷ b \]

How do you find fractions of a number support sheet

This printable support sheet below gives a little more detail about finding fractions of numbers including a step-by-step visual guide to how and why it works.

• How to find fractions of a number
• PDF version

Fraction of a whole number worksheets

• Fractions of numbers Sheet 1
• Sheet 1 Answers
• Fractions of numbers Sheet 2
• Sheet 2 Answers
• Fractions of numbers Sheet 3
• Sheet 3 Answers
• Fractions of numbers Sheet 4
• Sheet 4 Answers
• Fractions of numbers Sheet 5
• Sheet 5 Answers
• Fractions of numbers Sheet 6
• Sheet 6 Answers

Fraction of a whole number problems

These problems all involve finding the fraction of a whole number.

There are 3 versions of each sheet:

• Sheets 1a and 2a are the easiest. They mainly involve finding simple unit fractions of small numbers.
• Sheets 1b and 2b are a little harder. They involve finding (mainly unit) fractions of larger numbers.
• Sheets 1c and 2c are hardest. They involve finding non-unit fractions of larger numbers.

Sheet 1 - Fraction of a number problems

• Fraction of a number problems 1a
• Fraction of a number problems 1b
• Fraction of a number problems 1c

Sheet 2 - Fraction of a number problems

• Fraction of a number problems 2a
• Fraction of a number problems 2b
• Fraction of a number problems 2c

More Recommended Math Worksheets

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Practice your Fraction of a Number skills online

Want to practice your skills online?

We have a fraction of a whole number practice area where you can practice finding different fractions of numbers.

Just follow the link below.

• Online Fraction of Number Practice Zone

More Fractions of a Whole Number Worksheets

We also have a page of 3rd grade worksheets about finding unit fractions of whole numbers.

Unit fractions are fractions with a numerator of 1. The sheets are easier than those on this page.

There is also a randomly worksheet generator for you to make you own fractions of a number worksheets to meet your needs.

Using these sheets will help your child to:

• develop an understanding of fractions as parts of a whole;
• know how to calculate unit fractions of a range of numbers.
• Unit Fraction of Numbers (3rd Grade)
• Fractions of Whole Numbers Worksheets (Randomly Generated)

Learning Fractions Math Help Page

Here you will find the Math Salamanders free online Math help pages about Fractions.

There is a wide range of help pages including help with:

• fraction definitions;
• equivalent fractions;
• converting improper fractions;
• how to add and subtract fractions;
• how to convert fractions to decimals and percentages;
• how to simplify fractions.
• Learning Fractions Support

Fractions of a Whole Number Online Quiz

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One to one maths interventions built for KS4 success

Weekly online one to one GCSE maths revision lessons now available

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Fractions Of Amounts

Here we will learn about fractions of amounts . There are also fractions worksheets, fraction activity sheets and fraction word problems (with answer sheets) based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.

What are fractions of amounts?

Fractions of amounts is the skill of finding a given fraction of a certain amount. 

As we are asked to work out three quarters of 36 , let’s start by working out one quarter:

So to work out three quarters we multiply this by 3 :

You can visualise this using a bar model. 

Finding a fraction of a number is the same as multiplying a fraction by a number. 

\frac{2}{5} of 20 is the same as \frac{2}{5} \times 20

Therefore we could calculate the answer using this method instead. 

\frac{2}{5} of 20 = \frac{2}{5} \times 20 = \frac{2 \times 20}{5} = \frac{40}{5} = 8

We can find fractions of a quantity  including integers (whole numbers), decimals and fractions. When calculating a fraction of a quantity you can use either the method shown in E.g. 1 or E.g. 2 but sometimes one method will be easier to apply than the other. 

Find \frac{5}{6} of 0.4

\frac{5}{6} of 0.4 = \frac{5}{6} \times 0.4 = \frac{5 \times 0.4}{6} = \frac{2}{6} = \frac{1}{3}

One amount as a fraction of another 

Sometimes it is helpful to express an amount of one thing as a fraction of the entire thing. 

For example;

A shop sells rolls of ribbon. A full roll has 7 metres of ribbon on it. Sabastian buys 35 centimetres of ribbon. Express the length of Sabastian’s piece of ribbon as a fraction of a full roll of ribbon. 

7 metres = 700 cm. 

The fraction would therefore be \frac{35}{700}

This can simplify \frac{35 \div 7}{700 \div 7}=\frac{1}{20}

Therefore Sebastian has one twentieth of a full roll of ribbon. 

Sometimes it is helpful to express a value as a fraction of another amount. This can then show the proportion of that value in comparison to the other amount. 

For example,

Ivan has 3 pens in his school bag. 

Jessica has 24 pens in her school bag. 

Express the number of pens Ivan has as a fraction of the amount of pens Jessica has. 

Ivan has 3 pens compared to Jessica’s 24 pens. As a fraction this is \frac{3}{24}

This can simplify

This fraction shows that Ivan has an eighth as many pens as Jessica. 

How to calculate fractions of amounts

In order to work out fractions of an amount:

• Multiply the fraction and the amount.
• Write the final answer.

Explain how to work out fractions of amounts in 2 steps

Fractions of amounts worksheet

Get your free fractions of amounts worksheet of 20+ questions and answers. Includes reasoning and applied questions.

Related lessons on fractions

Fractions of amounts  is part of our series of lessons to support revision on  fractions . You may find it helpful to start with the main fractions 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:

• Improper fractions to mixed numbers
• Mixed number to improper fraction
• Numerator and denominator
• Adding and subtracting fractions
• Multiplying and dividing fractions
• Equivalent fractions

Fractions of amounts examples

Example 1: unit fractions of amounts.

Multiply the fraction and the amount .

The “of” means that we multiply the fraction and the amount.

You divide the amount by the denominator (bottom number) of the fraction.

2 Write the final answer .

The final answer is 8 .

Example 2: unit fractions of amounts

Write the final answer .

The final answer is 4 .

Example 3: non-unit fractions

Alternatively, you could split the calculation into two parts. First divide the amount by the denominator (bottom number) of the fraction to find one quarter of 20 . Then, multiply by the numerator (top number):

The final answer is 15 .

Example 4: non-unit fractions

Alternatively, you could split the calculation into two parts. First divide the amount by the denominator (bottom number) of the fraction. Then multiply by the numerator (top number):

The final answer is 6 .

Example 5: calculator allowed

Alternatively, you could split the sum into two parts. First divide the amount by the denominator (bottom number) of the fraction. Then, multiply by the numerator (top number):

The final answer is 37.2 kg .

Example 6: calculator allowed

Alternatively,  you could split the sum into two parts. First divide the amount by the denominator (bottom number) of the fraction. Then multiply by the numerator (top number):

The final answer is 94.5 km .

Common misconceptions

• Not writing money with two decimal places

If the answer to a question involving money is a decimal and the units are £ you need 2 digits after the decimal point for the pence. E.g.

The final answer £1.40

• Not fully answering the question

A common error is to

Practice fractions of amounts questions

1. Work out: \frac{1}{2} \quad of\quad18

2. Work out: \frac{1}{5} \quad of \quad 30

3. Work out: \frac{2}{3} \quad of \quad 24

4. Work out: \frac{5}{8} \quad of \quad 56

5. Calculator allowed. Work out: \frac{3}{7} \quad of \quad 14.7 kg

6. Calculator allowed. Work out: \frac{4}{9} \quad of \quad 14.4 km

Fractions of amounts GCSE questions

1.   A jigsaw normally costs £9.60.

How much does a jigsaw cost in the sale?

\frac{1}{3}\times9.60=9.60\div3=3.2                                                                                                   (1)

The jigsaw costs £6.40 in the sale.

2. The average age of people in an office is 40  years old.

Sam’s age is \frac{11}{8} of  the average.

How old is Sam?

 Sam is 55.

3. A train has 1 first-class carriage and 4 standard carriages.

The first-class carriage has 40 seats.

\frac{7}{8} of the seats are being used.

Each standard class carriage has 60 seats.

\frac{5}{12} of the seats are being used. Are more than half the seats on the train being used?

You must show your working.

For working out the total number of seats on the train.

For working out the half of seats on the train.

For working out the number of seats used the first-class carriage or second class carriage.

For working out the total number of seats used on the train (1)

NO, only 135 seats are used

Learning checklist

You have now learned how to:

• Find the fraction of an amount
• Find the fractions of quantities

The next lessons are

• Negative numbers
• Percentages
• Converting fractions, decimals and percentages

Still stuck?

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Fraction of Amount

Example 1: Find 1 ⁄ 4 of 12.

To find one quarter we need to split our amount into 4 equal parts.

12 ÷ 4 = 3

Each part is worth 3, so 1 ⁄ 4 of 12 = 3

Example 2: Find 1 ⁄ 5 of 30.

To find one fifth we need to split our amount into 5 equal parts.

30 ÷ 5 = 6

Each part is worth 6, so 1 ⁄ 5 of 30 = 6

Example 3: Find 3 ⁄ 4 of 28.

We start by splitting 28 into 4 equal parts.

28 ÷ 4 = 7

Each quarter is worth 7. We want 3 ⁄ 4

We need to calculate 3 × 7. 3 × 7 = 21 3 ⁄ 4 of 28 = 21

Example 4: Find 2 ⁄ 5 of 40.

We start by splitting 40 into 5 equal parts.

40 ÷ 5 = 8

Each fifth is worth 8. We want 2 ⁄ 5

We need to calculate 2 × 8. 2 × 8 = 16 2 ⁄ 5 of 40 = 16

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Unit 4: Understand fractions

About this unit.

From cooking measurements to geometry, fractions are all around us. By understanding how the numerator and denominator work together, you'll be able to break down numbers into smaller parts, compare different fractions, and get a grasp on concepts like equivalent fractions.

Fractions intro

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Fractions of an Amount

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Fractions KS2

This collection is one of our Primary Curriculum collections - tasks that are grouped by topic.

Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?

Fraction Match

A task which depends on members of the group noticing the needs of others and responding.

Bryony's Triangle

Watch the video to see how to fold a square of paper to create a flower. What fraction of the piece of paper is the small triangle?

A4 Fraction Subtraction

This task offers opportunities to subtract fractions using A4 paper.

Matching Fractions

Can you find different ways of showing the same fraction? Try this matching game and see.

Round the Dice Decimals 2

What happens when you round these numbers to the nearest whole number?

Fractional Wall

Using the picture of the fraction wall, can you find equivalent fractions?

Would You Rather?

Would you rather: Have 10% of £5 or 75% of 80p? Be given 60% of 2 pizzas or 26% of 5 pizzas?

Round the Dice Decimals 1

Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?

Tumbling Down

Watch this animation. What do you see? Can you explain why this happens?

Linked Chains

Can you find ways to make twenty-link chains from these smaller chains? This gives opportunities for different approaches.

Fractional Triangles

Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.

Forgot the Numbers

On my calculator I divided one whole number by another whole number and got the answer 3.125. If the numbers are both under 50, what are they?

Andy's Marbles

Andy had a big bag of marbles but unfortunately the bottom of it split and all the marbles spilled out. Use the information to find out how many there were in the bag originally.

More Fraction Bars

What fraction of the black bar are the other bars? Have a go at this challenging task!

Fractions in a Box

The discs for this game are kept in a flat square box with a square hole for each. Use the information to find out how many discs of each colour there are in the box.

Extending Fraction Bars

Can you compare these bars with each other and express their lengths as fractions of the black bar?

Route Product

Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?

Fraction Lengths

Can you find combinations of strips of paper which equal the length of the black strip? If the length of the black is 1, how could you write the sum of the strips?

Light Blue - Dark Blue

Investigate the successive areas of light blue in these diagrams.

A4 Fraction Addition

Try adding fractions using A4 paper.

Matching Fractions, Decimals and Percentages

Can you match pairs of fractions, decimals and percentages, and beat your previous scores?

Doughnut Percents

A task involving the equivalence between fractions, percentages and decimals which depends on members of the group noticing the needs of others and responding.

There are three tables in a room with blocks of chocolate on each. Where would be the best place for each child in the class to sit if they came in one at a time?

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Fractions of Amounts - Problem Solving

Subject: Mathematics

Age range: 11-14

Resource type: Worksheet/Activity

Last updated

5 October 2022

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An activity that gets students to practise finding fractions of amounts, which also introduces an element of problem solving.

Students create their own questions. They pick a numerator, pick a denominator, and work out that fraction of the large number at the top of the screen. They’re aiming to create calculations with the given answers on the screen. Some students might pick their fractions completely at random, whereas others may approach things a bit more logically…

There are 6 different activities, with varying degrees of difficulty. Some answers can be made via more than one calculation, but I’ve made a suggestion on how to complete each problem.

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