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.

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!

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

Step 2)

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

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

Step 1)

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

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

Step 2)

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

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

Step 1)

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

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

Step 2)

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

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

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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