# 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 (or a slash next to) another number. For example, ${\tfrac {1}{4}}$ , 14 and 1/4.are different ways of writing the same fraction (in this case a quarter). The top number tells us how many parts there are, and the bottom number tells us the total number of parts.

The top part of the fraction is called a numerator. The bottom part of the fraction is called a denominator. For example, for the fraction ${\tfrac {1}{4}}$ , the 1 is the numerator, and the 4 is the denominator.

## Examples

1. A room where ${\tfrac {1}{4}}$ of the people are girls, has 1 girl for every 4 people.
2. A cake can be thought of as being made up of 4 equal parts, where each is 1 part of 4. This can be written as ${\tfrac {1}{4}}$ , and is called a "quarter". Similarly, 2 parts of the cake (2 quarters) can be written ${\tfrac {2}{4}}$ , which is also equal to 1/2 (one-half).

## Mathematical fractions

A fraction is a mathematical expression relating two quantities or numbers, where one divides the other. When the two quantities are whole numbers (or integers), this is called a rational number (such as the fraction ${\tfrac {1}{2}}$ ). When the two quantities are polynomials, this is called a rational function.

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

To find ${\tfrac {1}{2}}$ of ${\tfrac {1}{2}}$ , the denominators are multiplied, and because denominator 2 multiplied by 2 equals 4, we have that ${\tfrac {1}{2}}$ x ${\tfrac {1}{2}}$ = ${\tfrac {1}{4}}$ , or 0.5 x 0.5 = 0.25.

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

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

## Multiplying

To multiply two fractions, the first numerator is multiplied by the other numerator, and the first denominator is multiplied by the other denominator. For example. 24 x 34 = 616. One can simplify this by dividing both numbers by a common factor. This would be 38 after the simplication.