What is a Fraction?
A
fraction is a number, written in two parts, separated by a line. Fractions can be written
or 3/4
The number above the line is called the numerator.
The number below the line is called the denominator.
The denominator shows how many equal parts the object or item has been divided into.
The numerator shows how many of these parts have been selected.
Example
For the circle shown, the shaded part is shown by the fraction ^{1}⁄_{4}


The numerator shows the number of shaded parts: ONE

The denominator shows the number of equal parts the circle has been divided into: FOUR

Think of the fraction saying one part out of four parts.
More Examples
Some word examples of Fractions
If a pizza is cut into ten pieces and I eat three of them. 
The fraction of the pizza that I eat is 3/10 
If a school has 500 students and 263 of them are girls.

The fraction of students who are girls is 263/500. 
If I spend $29 of my wages of $120 on food. 
The fraction of my spending on food is 29/120 
Equivalent Fractions
If both the numerator and denominator of a fraction are multiplied by the SAME number, the fraction stays the same.
e.g.
Fraction

Multiply top and bottom

Equivalent fraction

^{1}⁄_{2}

^{1}⁄_{2} × ^{2}⁄_{2}

^{2}⁄_{4}

^{3}⁄_{4}

^{3}⁄_{4} × ^{3}⁄_{3}

^{9}⁄_{12}

^{5}⁄_{8}

^{5}⁄_{8} × ^{4}⁄_{4}

^{20}⁄_{32}

This property allows us to SIMPLIFY fractions, also known as CANCELLING.
We normally give fractions in their SIMPLEST form.
The table below shows some equivalent fractions:
halves





^{1}⁄_{2}





^{2}⁄_{2} = 1

thirds


^{1}⁄_{3}


^{2}⁄_{3}


^{3}⁄_{3} = 1

quarters

^{1}⁄_{4}


^{2}⁄_{4}


^{3}⁄_{4}

^{4}⁄_{4} = 1

fifths



^{1}⁄_{5}




^{2}⁄_{5}


^{3}⁄_{5}




^{4}⁄_{5}



^{5}⁄_{5} = 1

sixths

^{1}⁄_{6}



^{2}⁄_{6}


^{3}⁄_{6}


^{4}⁄_{6}



^{5}⁄_{6}

^{6}⁄_{6} = 1

eighths

^{1}⁄_{8}


^{2}⁄_{8}


^{3}⁄_{8}

^{4}⁄_{8}

^{5}⁄_{8}


^{6}⁄_{8}


^{7}⁄_{8}

^{8}⁄_{8} = 1

These fractions can also be put on a number line:
Mixed Numbers
A mixed number is a number made up of a whole number and a fraction:
A mixed number can also be shown as an improper fraction.
This is because 3 whole ones are equal to 9 thirds (3 × 3) plus the two thirds equals eleven thirds.
Changing Mixed Numbers to Improper Fractions:
Mixed number

Calculation

Improper fraction







Changing Improper Fractions to Mixed Numbers:
Improper fraction

Calculation

Mixed number







Finding a Fraction of a Number
To find a fraction of a number, divide the number by the denominator (bottom number) of the fraction and then multiply the number by the numerator of the fraction (top number).
e.g. To find ^{3}⁄_{4} of 80.
First find ^{1}⁄_{4} of 80 by dividing by 4 = 80 ÷ 4 = 20
Now find ^{3}⁄_{4} of 80 by multiplying by 3 = 20 × 3 = 60
So ^{3}⁄_{4} of 80 is 60
Applications

a

The coach of my soccer team buys 20 pieces of fish and some chips for the team. My friends and I eat ^{3}⁄_{5} of the number of fish.
How many fish do my friends and I eat?


Find one fifth of the number of fish:
20 × ^{1}⁄_{5} = 4
Now find three fifths of the number of fish:
Number of fish = 4 × 3 = 12
My friends and I eat 12 fish.

b

At a World Cup rugby game, ^{5}⁄_{6} of the crowd support the home team. If there are 45 000 people at the game, how many support the home team? 
Find one sixth of the number of home supporters.
45000 × ^{1}⁄_{6} = 7500
Now find five sixths of the number of home supporters.
Number of home supporters = 7500 x 5 = 37500
There are 37500 home supporters.

Operations on Fractions
Later you will need to be able to add, subtract, multiply and divide fractions. You can discover how to do this and see some examples in the extension Topic 47.