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# Fraction (mathematics)

A cake with one quarter removed. The remaining 34 of the cake has been divided into two pieces.

A fraction is a number that shows how many equal parts there are. When we write fractions, we show one number with a line above another number, for example, ${\displaystyle {\tfrac {1}{4}}}$ or 14 or 1/4. The top number tells us how many parts there are, the second number tells us the total number of parts.

## Examples

1. For example, a room where ${\displaystyle {\tfrac {1}{4}}}$ of the people are girls, has 1 girl for every 4 people.
2. Think of a cake made of 4 equal parts. Each is 1 part of 4. In maths, you write this as ${\displaystyle {\tfrac {1}{4}}}$, and it is called a "quarter". 2 parts of the cake (i.e. 2 quarters) is written ${\displaystyle {\tfrac {2}{4}}}$, and this is also known as 1/2, half.

## Mathematical fractions

A fraction is a mathematical expression relating two quantities or numbers, one divided by the other. The numbers may be whole numbers (or integers) – this is a rational number. For example, ${\displaystyle {\tfrac {1}{2}}}$ is a fraction. They can also be polynomials – this is a rational function.

Mathematically, a fraction is a quotient of numbers, representing the number's value when the numerator is divided by the denominator (lower number). Thus ${\displaystyle {\tfrac {1}{2}}}$ means one divided by two, or, in decimals, 0.5.

To find ${\displaystyle {\tfrac {1}{2}}}$ of ${\displaystyle {\tfrac {1}{2}}}$, the denominators are multiplied. That means: denominator 2 multiplied by 2 equals 4 or: ${\displaystyle {\tfrac {1}{2}}}$ x ${\displaystyle {\tfrac {1}{2}}}$ = ${\displaystyle {\tfrac {1}{4}}}$ or: 0.5 x 0.5 = 0.25.

(In this case “${\displaystyle {\tfrac {1}{2}}}$ of” means mathematically "multiplication".)

To find ${\displaystyle {\tfrac {1}{2}}}$ divided by ${\displaystyle {\tfrac {1}{2}}}$, multiply ${\displaystyle {\tfrac {1}{2}}}$ by the reciprocal of ${\displaystyle {\tfrac {1}{2}}}$, which is 2. That answer is 1.