Fraction (mathematics)

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}**, '*** 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.

## Names 
Almost every fraction can be read as an ordinal number, with a few exceptions.

\frac{1}{2} is always read as "one half."

\frac{1}{4} is sometimes read as "one quarter."

\frac{1}{100} is sometimes read as "one percent."

Aside from those, fractions are read as ordinal numbers. \frac{1}{5} is read as "one fifth," \frac{1}{27} is read as "one twenty-seventh," and \frac{1}{512} is read as "one five hundred twelfth."

## Numerators and denominators 
The top part of a fraction (example: **1**/4) is a numerator. Numerators can be any real numbers. The numerator can be on the top or to the left when writing fractions. The bottom part of a fraction (example: 1/**4**) is called a denominator. This number cannot be zero. It is on the bottom or on the right when writing fractions.

A proper fraction is a fraction with the numerator smaller than the denominator. An improper fraction is a fraction where the numerator is bigger than the denominator. For example, **\tfrac{1}{4}** is a proper fraction, and **\tfrac{5}{4}*' is an improper fraction.

## Examples of fractions
#A room where \tfrac{1}{4} of the people are girls, has 1 girl for every 4 people.
#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. '*** x **** = ****. One can simplify this by dividing both numbers by a common factor. This would be ***' after the simplification.

## Related pages 
* Algebraic fraction
* Egyptian fraction
* Mixed number
* Ratio

## References 
## Other websites 
* Curricula for Creating Fractions
* Interactive and dynamic worksheets to visualize fractions
* Worksheets: Identifying Fractions 
* Worksheets: Improper Fractions to Mixed Numbers 
* Curricula for Teaching about Equivalent Fractions 
* Free online quizzes about Fractions
* Printable fraction worksheets  for elementary grades.