Follow Us on Twitter

What Is a Fraction? (Mathematics Lesson)

What Is a Fraction?

A fraction is a part of a whole number.

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)."

A Real Example of a Fraction

A fraction is usually written as one number over another number.

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

A Real Example of What a Fraction Means

Imagine we wanted to find ¼ of a cake.

An Example Question

What does ¼ of a cake look like?
  • The bottom number of our fraction (called the denominator) is 4. It tells us to divide the cake into 4 equal parts.

  • The top number of our fraction (called the numerator) is 1. It tells us how many of these equal parts we have.

How to Visualize Fractions

Thinking of slices of a cake is a useful way of visualizing fractions.

  • The top number (the numerator) tells you have many slices you have.

  • The bottom number (the denominator) tells you how many equal slices the cake is cut into.

Types of Fractions

There are three different types of fractions:

Type of Fraction Example Explanation
Proper fraction The numerator is less than the demoninator
Improper fraction The numerator is greater or equal to the demoninator
Mixed fraction A whole number and a fraction

The slider below shows some more examples of fractions, and how to visualise them.
Quick Test

Here's a second test on fractions.
Here's a third test on fractions.

What's in a Name?

"Fraction" comes from the Latin "fractus", meaning "broken".

A whole is "broken" into parts.

Saying Fractions

Saying fractions is simple.

When the numerator is one, here is a list of the names of fractions:

It continues, one fifth, one sixth, one seventh, one eighth etc. (Note: instead of saying "fourth", you can say "quarter").

When the numerator is more than one, just say the number in the numerator instead of one, and use the plural (halves instead of half etc.):

For mixed fractions, say the name of the whole number, then "and", followed by the name of the fraction:

The Size of Fractions

If you increase the numerator (keeping the denominator the same), you increase the fraction. If we visualise a fraction as a cake, a bigger numerator means more slices.

If you increase the denominator (keeping the numerator the same), you decrease the fraction - the cake is cut into more pieces, so each slice is smaller.

Other Types of Fractional Numbers

Fractional numbers can also be represented by decimals, negative exponents, percentages, and ratios.

For example:

  • A fraction: 1/2
  • A decimal: 0.5
  • A negative exponent: 2-1
  • A percentage: 50%
  • A ratio: 1:2