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Fraction (mathematics)

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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, [math]\tfrac{1}{4}[/math] 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.


  1. For example, a room where [math]\tfrac{1}{4}[/math] 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 [math]\tfrac{1}{4}[/math], and it is called a "quarter". 2 parts of the cake (i.e. 2 quarters) is written [math]\tfrac{2}{4}[/math], 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, [math]\tfrac{1}{2}[/math] 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 [math]\tfrac{1}{2}[/math] means one divided by two, or, in decimals, 0.5.

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

(In this case “[math]\tfrac{1}{2}[/math] of” means mathematically "multiplication".)

To find [math]\tfrac{1}{2}[/math] divided by [math]\tfrac{1}{2}[/math], multiply [math]\tfrac{1}{2}[/math] by the reciprocal of [math]\tfrac{1}{2}[/math], which is 2. That answer is 1.

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