# 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.

##### Interactive Test

**show**

Here's a second test on fractions.

Here's a third test on fractions.

##### Note

# 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