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"Math Salamanders Free Math Sheets"

Welcome to the Math Salamanders Learning Fractions support page.

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

This page contains links to other Math webpages where you will find a range of activities and resources.

Each webpage has a short description of what the page is about and the math learning it covers.

If you cannot find what you are looking for, try searching the site using the Google search box on the right hand side on this page.

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

What is a fraction?

How do you add and subtract fraction?

What is simplest form?

What does is mean if 2 fractions are equivalent?

What are proper and improper fractions?

How can I convert a mixed number into a fraction?

All these answer and more you will find on this page!

Free Online Fraction Calculator

Here you will find the Math Salamanders Free Online Fraction Calculator.

This calculator will enable you to:

- add, subtract, multiply and divide fractions
- convert fractions to simplest form
- convert improper fractions to mixed fractions
- convert fractions to decimals and percentages
- convert decimals and percentages to fractions.

There are also support sheets to help you learn these fraction skills further down the page.

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).

A fraction is a number with the form
**
n
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

A fraction is a number with the form
**
n
d
**

Alternative ways of expressing this statement include:

"n over d", n ÷ d

Example

The fraction
**
5
6
**
could be expressed as:

five-sixths, five over six, 5 ÷ 6

Proper and Improper Fractions & Mixed Numbers

A fraction is a number with the form
**
n
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, then the fraction's value is equal to 1.

A **mixed number (or mixed fraction)** is a number that has
a whole number part to it, and a fraction part to it.

Examples

3 7, 2 10 and 17 26 are all proper fractions.

31 5, 15 10 and 37 23 are all improper fractions.

3 1 5, 1 2 3 and 12 7 10 are all mixed numbers or mixed fractions.

"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 45, 5 9 and 51 16 are all common or vulgar fractions.

3.2
4.5,
5
0 and
0.57
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 10, 5 100 and 537 1000 are all decimal fractions.

They are equal to 0.7, 0.05 and 0.537 respectively.

3
5,
2
12 and
263
500
are **not** decimal fractions.

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 0.33 30.66 71.0 0.25 0.5 0.75 1.0 0.2 0.4 0.6 0.8 1.0 0.16 70.33 30.5 0.666 0.83 31.0 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%.

Equivalent Fractions

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

A quick way to tell whether or not two fractions are equivalent is to change them both into decimals using a calculator.

If the two decimals are identical, then the fractions have the same value.

The printable fraction page below contains more support, examples and practice using equivalent fractions.

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.

If the two fractions have the same denominator, then it is quite easy to add or subtract the fractions by simply adding the numerators together.

If the fractions have different denominators, then they need to be changed into equivalent fractions with the same denominator before they can be added or subtracted.

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

Multiplying and Dividing Fractions

To multiply two fractions together, simply multiply the two numerators together, then multiply the 2 denominators together.

To divide one fraction by a second fraction, you need to invert the numerator and denominator of the second fraction so that the 'old denominator' is on the top, and the 'old numerator' is on the bottom half of the fraction. They can then be multiplied together to give an answer.

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

Converting Fractions to Decimals

To convert a fraction to a decimal is a straightforward task if you have a calculator to hand.

Simply divide the numerator by the denominator to give you the decimal form.

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

Converting Fractions to 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.

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