What are Fractions?
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Fractions, in mathematics mean an expression representing a part, or several equal parts, of a unit.

Components of a Fraction

A fraction is a number that is written in the form:

or a/b

  • The a is the numerator, and the b is the denominator.
  • The line separating the numerator and denominator is a fraction bar.

For example, the following pizza has been cut into three equal parts.


 For the example, the parts are called thirds. A third is written as The fraction 1 over 3.

Fractions are used when representing numbers that describe the parts of a whole. The fraction a/b also can be read as "a out of b," "a over b," or "a divided by b."

There are some restrictions on a and b.

  • Both a and b must be integers, meaning positive and negative whole numbers.
  • The denominator, or b, cannot be zero. This is because one cannot divide by zero.

Click here to learn more on fractions.

t's a good idea to recognise fractions when they are written as words.

fraction word plural
The fraction 1 over 2. One half (A half) halves
The fraction 1 over 3. One third thirds
The fraction 1 over 4. One quarter quarters
The fraction 1 over 5. One fifth fifths
The fraction 1 over 6. One sixth sixths
The fraction 1 over 7. One seventh sevenths
The fraction 1 over 8. One eighth eighths
The fraction 1 over 9. One ninth ninths
The fraction 1 over 10. One tenth tenths


History of Fractions

Fractions as we use them today didn't exist in Europe until the 17th century. In fact, at first, fractions weren't even thought of as numbers in their own right at all, just a way of comparing whole numbers with each other.

The word fracton actually comes from the Latin "fractio" which means to break. To understand how fractions have developed into the form we recognise, we'll have to step back even further in time to discover what the first number systems were like.

Who first used fractions? Were they always written in the same way? How did fractions reach us here? If you would like to read more about Fractions, please click here


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This site was last updated 06/13/06