Fractions of numbers

Welcome to the Math Salamanders support page about How to
Calculate Fractions of Numbers.

Here you will find information and support about how to
find fractions of different numbers.

Fractions is an area that a lot of kids find hard to understand. One of the problems with fractions is that they have different meanings depending on the context.

For example, you can eat half an apple or cut an orange into fourths. But you can also put the number one-half on a number line, measure a line 3 1/2 cm long, or find a fourth of 24.

Once the concept of fractions as numbers and fractions as parts of a whole has been understood, your child will be well on their way to developing a sound understanding of fractions.

Here you will find some simple information and advice about how to calculate fractions of numbers.

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.

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

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

Step 2 - Multiply by the numerator.

You should have now found your fraction of a number!

*
Example 1) Find
5
6
of 24
*

Step 1)

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 6 of 24 = 24 ÷ 6 = 4

Step 2)

We need to multiply our answer by the numerator which is 5.

*
So
5
6
of 24 = (
1
6
of 24 ) x 5 =
4 x 5 = 20
*

*
Example 2) Find
3
7
of 35
*

Step 1)

The denominator of the first fraction is 7.

This gives us 1 7 of 35 = 35 ÷ 7 = 5

Step 2)

We need to multiply our answer by the numerator which is 3.

*
So
3
7
of 35 = (
1
7
of 35 ) x 3 =
5 x 3 = 15
*

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

*
If we want to work out
a
b
of a number n
*

First we divide n by the denominator b (n ÷ b).

This tells us the value of 1 b of n

Next we need to multiply this by the numerator a.

This gives us:

*
a
b
of n = (n ÷ b) x a
OR
(n x a) ÷ b
OR
n x a
b
*

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.

Here you will find a selection of Fraction worksheets designed to help your child understand how to work out unit fractions of different numbers where the numerator is 1.

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.

All the free Fraction Shape worksheets in this section support the Elementary Math Benchmarks for 3rd Grade.

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.

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- List of Geometric Shapes
- Equivalent Fractions
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- 3d Geometric Shapes
- Perimeter Worksheets
- Reverse Percentage Calculator

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