Learning Fractions
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Welcome to the Math Salamanders Learning Fractions support page.

Here you will find information and support about everything to do with fractions.

We have a huge range of resources, from fraction calculators and fraction conversion sheets to fraction information posters, fraction strips and flashcards.

  • This page contains links to other Math webpages where you will find a range of activities and resources.
  • If you can't find what you are looking for, try searching the site using the Google search box at the top of each page.

Fraction Learning

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.

Learning Fractions Support Page

Common Fraction Questions

Online Fraction Calculators

We have a selection of different fraction calculators which will help you to add, subtract, multiply and divide fractions.

Our fraction calculators will also:

  • convert fractions to simplest form;
  • convert improper fractions to mixed fractions, and mixed fractions to improper fractions;
  • convert fractions to decimals and percentages;
  • convert decimals and percentages to fractions.

Fraction Definitions

What is a fraction?

A fraction is a number which contains parts of a whole.

Fractions can be smaller than or larger than one (one whole).

What do fractions look like?

A fraction is a number with the form: \[ {n \over d} \]

where n and d are two numbers.

  • The number n above the line is called the numerator.
  • The number d below the line is called the denominator.

Alternative notation

Alternative ways of expressing this statement include:

n over d, n/d, n ÷ d

Fraction Notation Example

The fraction \[ {5 \over 6} \] could be expressed as:

  • five-sixths
  • five over six
  • 5/6
  • 5 ÷ 6

Proper and Improper Fractions & Mixed Numbers

A fraction is a number with the form: \[ {n \over d} \]

  • If the numerator is smaller than the denominator (if n < d), then the fraction is called a proper fraction, and its value is less than 1.
  • If the numerator is greater than the denominator (if n > d), then the fraction is called an improper fraction, and its value is greater than 1.
  • If the numerator is equal to the denominator (if n = d), then the fraction's value is equal to 1.
  • A mixed fraction (or mixed number) is a number that has a whole number part to it, and a fraction part to it.

Please note: the comparisons between the numerator and denominator above assume that they are both positive numbers. If either n or d is negative, then we need to compare their absolute values to find outwhether the fraction is a proper fraction or an improper fraction

Types of Fractions Examples

\[{3 \over 7} \; , \; {2 \over 10} \; , \; -{3 \over 5} \; and \; {17 \over 26} \] are all proper fractions.

\[ {31 \over 5} \; , \; {15 \over 10} \; , \; -{17 \over 3} \; and \; {37 \over 23} \] are all improper fractions.

\[ 3{1 \over 5} \; , \; 2 {5 \over 8} \; and \; 4 {1 \over 2} \] are all mixed numbers or mixed fractions.

To get help converting improper fractions to mixed numbers,
use this link.

"Common" or "Vulgar" Fractions

A common or vulgar fraction is simply an ordinary fraction.

The numerator and denominator must be integers, or whole numbers, and the denominator cannot equal zero.

\[ {35 \over 45} \; , \; {5 \over 9} \; and \; {51 \over 16} \] are all common or vulgar fractions.

\[ {3.2 \over 4.5} \; , \; {5 \over 0} \; and \; {0.57 \over 1.6} \] are NOT common or vulgar fractions.

Decimal Fractions

A decimal fraction is a fraction where the denominator is a power of ten.

\[{7 \over 10} \; , \; {5 \over 100} \; , \; {537 \over 1000} \] are all decimal fractions.

They are equal to 0.7, 0.05 and 0.537 respectively.

\[{3 \over 5} \; , \; {2 \over 12} \; and \; {263 \over 500} \] are not decimal fractions.

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Basic Fraction Arithmetic

Here are the formulas for adding, subtracting, multiplying and dividing two fractions:

Formula for adding two fractions

\[{a \over b} + {c \over d} = {ad + bc \over bd} \]

Formula for subtracting two fractions

\[{a \over b} - {c \over d} = {ad - bc \over bd} \]

Formula for multiplying two fractions

\[{a \over b} \times {c \over d} = {ac \over bd} \]

Formula for dividing two fractions

\[{a \over b} \div {c \over d} = {ad \over bc} \]

How to add and subtract fractions support

How to multiply and divide fractions support

Fractions Decimals Percents

Below are some common conversions for fractions into decimals and percents.

Fraction Equivalent to Decimal Percent
1/2
2/2

1/3
2/3
3/3

1/4
2/4
3/4
4/4

1/5
2/5
3/5
4/5
5/5

1/6
2/6
3/6
4/6
5/6
6/6

1/8
2/8
3/8
4/8
5/8
6/8
7/8
8/8

1/10
2/10
3/10
4/10
5/10
6/10
7/10
8/10
9/10
10/10
1/2
1

1/3
2/3
1

1/4
1/2
3/4
1

1/5
2/5
3/5
4/5
5/5

1/6
1/3
1/2
2/3
5/6
1

1/8
1/4
3/8
1/2
5/8
3/4
7/8
1

1/10
1/5
3/10
2/5
1/2
3/5
7/10
4/5
9/10
1
0.5
1.0

0.333
0.667
1.0

0.25
0.5
0.75
1.0

0.2
0.4
0.6
0.8
1.0

0.167
0.333
0.5
0.666
0.833
1.0

0.125
0.25
0.375
0.5
0.625
0.75
0.875
1.0

0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
50%
100%

33.3%
66.7%
100%

25%
50%
75%
100%

20%
40%
60%
80%
100%

16.7%
33.3%
50%
66.7%
83.3%
100%

12.5%
25%
37.5%
50%
62.5%
75%
87.5%
100%

10%
20%
30%
40%
50%
60%
70%
80%
90%
100%

Where a digit is underlined, it means that the number has been rounded to 3 decimal places, or to the nearest 0.1%.

Fraction Information Cards

Here is our collection of printable fraction information cards.

Each card has a fraction in the middle and a range of different representations of the fractions around the outside.

It is a great resource for developing fraction knowledge and useful for any fraction display.

Each card also contains decimal and percent facts for each fraction.

There are 3 versions of each card, one for display and two worksheets which test the children on their fraction knowledge.

Using these cards will help your child to:

  • understand different representation of a range of fractions;
  • begin to learn how to place fractions correctly on a fraction line;
  • know decimal and percent equivalence for each fraction;
  • being to learn about fraction equivalences.

These cards will help your child get to grips with fractions in a visual and fun way.

Free Printable Fraction Strips

Here you will find a selection of Fraction Strips designed to help your child understand their unit Fractions.

Using Fraction Strips is a great way to learn your Fraction facts and help you to understand exactly how much fractions are worth.

Using these fraction strips will help your child to:

  • understand Fraction as lengths;
  • understand equivalent fractions;
  • understand visually how much each unit fraction is worth.

Free Printable Fraction Flashcards

Here you will find a selection of Fraction Flash Cards designed to help your child learn their Fractions.

Using these flashcards will help your child to:

  • understand fractions as parts of a whole;
  • practice their equivalent fraction facts.

What is a Mixed Number

This support page introduces mixed numbers with some examples and an interactive teaching app.

There are also some practice worksheets to help you identify and write mixed numbers.

Equivalent Fractions

Equivalent fractions are fractions which have the same value as each other.

We have a support page to help you understand all about equivalent fractions, and also some equivalent fractions worksheets.

Simplifying Fractions

This is also sometimes called reducing fractions to their simplest form.

This involves dividing both the numerator and denominator by a common factor to reduce the fraction to the equivalent fraction with the smallest possible numerator and denominator.

The printable fraction page below contains more support, examples and practice about simplifying fractions.

How to Convert Improper Fractions

This support page shows how to convert improper fractions to mixed numbers, and how to convert mixed numbers to improper fractions.

You will also find printable support sheets, and several practice math worksheets for this learning fractions skill.

Adding and Subtracting Fractions

Adding and subtracting fractions works differently from adding and subtracting integers or decimals.

The printable learning fractions pages below contains more support, examples and practice adding and subtracting fractions.

Formula for adding two fractions

\[{a \over b} + {c \over d} = {ad + bc \over bd} \]

Formula for subtracting two fractions

\[{a \over b} - {c \over d} = {ad - bc \over bd} \]

Multiplying and Dividing Fractions

The printable fraction pages below contains more support, examples and practice multiplying and dividing fractions.

Formula for multiplying two fractions

\[{a \over b} \times {c \over d} = {ac \over bd} \]

Formula for dividing two fractions

\[{a \over b} \div {c \over d} = {ad \over bc} \]

Converting Fractions to Decimals & Percentages

To convert a fraction to a percentage follows on simply from converting a fraction to a decimal.

Simply divide the numerator by the denominator to give you the decimal form. Then multiply the result by 100 to change the decimal into a percentage.

The printable learning fraction page below contains more support, examples and practice converting fractions to decimals.

Fractions of Numbers

Often when we are talking about and using fractions, we are looking at fractions of numbers or quantities.

To find a fraction of a number or quantity, we need to first divide the number or quantity by the denominator. Then multiply this by the numerator to give the answer.

The printable learning fractions page below contains more support, examples and practice finding fractions of numbers.

Math Fraction Games

Here is our collection of Math games involving fractions.

These games are suitable for kids aged from 3rd grade and upwards.

Playing games is a great way to learn fraction skills in a fun way.

Fraction equivalence, fraction to decimal conversion and properties of fractions are all explored in our fun games to play.

Interactive Fraction Builder

This interactive fraction builder is a great way of exploring fractions and having a go at some online fraction challenges.

It has been created by PhET Interactive Simulations from the University of Colorado.

You can create fractions and mixed fractions as well as trying some interactive fraction challenges.

 

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