Fractions and Percentages (Mathematics Curriculum)
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 (1⁄2 an apple, 1⁄3 of marks in a test, 1⁄4 of a cake):
Dictionary DefinitionThe Oxford English Dictionary defines a fraction as "a numerical quantity that is not a whole number (e.g. 1/2, 0.5)."
The CurriculumThe 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.
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.
The numerator is the number written above the line of a fraction. The numerator of the fraction below is 1:
The denominator is the number written below the line of a fraction. The denominator of the fraction below is 4:
We can visualise a fraction as a cake. Imagine we wanted to find 1⁄4 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 about fractions
Read more about the numerator
Read more about the denominator
Types of 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).
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).
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 1⁄3.
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.
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
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 about equivalent fractions and simplest form
Read more about how to simplify fractions
Arithmetic with Fractions
Fractions can be added.
Fractions can be subtracted.
Fractions can be multiplied.
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 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
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 about how to find the fraction of a number
Read more about how to express one number as a fraction of another number
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 about how to convert a fraction to a percentage
Read more about how to convert a fraction to a decimal
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