Fractions and Percentages (Mathematics Curriculum)

Fractions

What Is a Fraction?

A fraction is a part of a whole number. We use whole numbers to count a whole number of objects (1 apples, 2 balls, 3 cars):

We use fractions when we wish to count parts of whole objects (12 an apple, 13 of marks in a test, 14 of a cake):

Dictionary Definition

The Oxford English Dictionary defines a fraction as "a numerical quantity that is not a whole number (e.g. 1/2, 0.5)."

The Curriculum

The lessons are grouped into mini-curriculum to help you organise your learning. A brief description is given for each mini-curriculum. Click the MORE button to learn more.

Fractions

A fraction is a part of a whole number. It is written as two numbers written on top of each other, separated by a line. In this mini-curriculum, you will learn the basics of fractions.

Fraction
A fraction is a part of a whole number. Here is an example of a fraction:

This is a quarter. It is written as 1 over 4. It represents 1 part in 4.

Numerator
The numerator is the number written above the line of a fraction. The numerator of the fraction below is 1:


Denominator
The denominator is the number written below the line of a fraction. The denominator of the fraction below is 4:


Understanding Fractions
We can visualise a fraction as a cake. Imagine we wanted to find 14 of a cake.
The denominator of our fraction is 4. It tells us to divide the cake into 4 equal parts:

The numerator of our fraction is 1. It tells us how many of these equal parts we have:


Read More

Read more about fractions
Read more about the numerator
Read more about the denominator

Types of Fractions

There are different types of fractions: proper, improper and mixed. In this mini-curriculum, you will learn the types of fractions and how to convert between them.

Proper Fractions
A proper fraction is a fraction where the numerator is less than the denominator.
Here is an example of a proper fraction. The numerator (1) is less than the denominator (4).


Improper Fractions
An improper fraction is a fraction where the numerator is greater than (or equal to) the denominator.
Here is an example of an improper fraction. The numerator (3) is greater than the denominator (2).


Mixed Fractions
A mixed fraction 'mixes' a whole number with a proper fraction.
Here is an example of a mixed fraction. The whole number is 3 and the proper fraction is 13.


Convert Mixed to Improper Fractions
A mixed fraction can be converted to an improper fraction.


Convert Improper to Mixed Fractions
An improper fraction can be converted to a mixed fraction.


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Read more about proper fractions
Read more about improper fractions
Read more about mixed fractions
Read more about how to convert a mixed to an improper fraction
Read more about how to convert an improper to a mixed fraction

Equivalent Fractions and Simplifying Fractions

Different fractions that represent the same value are called equivalent fractions. One of these fractions will be the simplest fraction. In this mini-curriculum, you will learn about equivalent fractions and simplifying fractions.

Equivalent Fractions and the Simplest Form
Equivalent fractions are fractions that show the same part of the whole, even though they look different. The simplest form of a fraction is the equivalent fraction with the smallest possible numbers.


Simplifying a Fraction
Simplifying a fraction makes the fraction as simple as possible. A fraction is as simple as possible when the top and bottom numbers are as small as possible.


Read More
Read more about equivalent fractions and simplest form
Read more about how to simplify fractions

Arithmetic with Fractions

Just like numbers, fractions can be added, subtracted, multiplied and divided. In this mini-curriculum, you will learn arithmetic with fractions.

Adding Fractions
Fractions can be added.


Subtracting Fractions
Fractions can be subtracted.


Multiplying Fractions
Fractions can be multiplied.


Dividing Fractions
Fractions can be divided.


Reciprocal of a Fraction
To find the reciprocal of a fraction, turn the fraction upside down.


Power of a Fraction
To find the power of a fraction, raise the numerator and denominator to the exponent.


Read More

Read more about how to add fractions
Read more about how to subtract fractions
Read more about how to multiply fractions
Read more about how to divide fractions
Read more about how to find the reciprocal of a fraction
Read more about how to find the power of a fraction

Using Fractions

Fractions are useful. We might want to find out what half of an amount is, or express a number of objects as a fraction of the whole. In this mini-curriculum, you will learn about using fractions.

Find a Fraction of a Number
Find a fraction of a number by multiplying the fraction with the number.


Express as a Fraction of a Number
A number can be expressed as a fraction of another number.


Read More

Read more about how to find the fraction of a number
Read more about how to express one number as a fraction of another number

Converting Fractions

Fractions are just one way of expressing a part of a whole. Percentages and decimals are other ways. In this mini-curriculum, you will learn how convert a fraction to a percentage and a decimal.

Convert Fraction to a Percentage
A fraction can be converted to a percentage.


Convert Fraction to a Decimal
A fraction can be converted to a decimal.


Read More
Read more about how to convert a fraction to a percentage
Read more about how to convert a fraction to a decimal

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