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## Science Fair Project Encyclopedia for Schools!

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# Science Fair Project Encyclopedia

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# Fraction (mathematics)

In mathematics, a fraction is a quotient of numbers, like 34, or more generally, an element of a quotient field.

The word is also used in related expressions, like continued fraction, see Special cases below.

For other, non-mathematical meanings of this word, see fraction.

 Contents

## Special cases

### Other fractions

Fractions which are rational numbers and could be written as vulgar fractions include:

• A mixed fraction: A mixed fraction is an integer plus a proper fraction.
• A compound fraction is a fraction where the numerator or denominator (or both) contain fractions.

Fractions which are not necessarily rational numbers include:

Let us end with the only example on this page where the "fraction" is not an element of a quotient field:

• A continued fraction is an expression such as $a_0 + \frac{1}{a_1 + \frac{1}{a_2 + ...}}$, where the ai are integers.

### Counter examples

• An irrational fraction is, if all fractions must be capable of being expressed as a vulgar fraction, a contradiction in terms. An irrational number is, by definition, not rational i.e. it cannot be expressed as a vulgar fraction.

## Pedagogical tools

In Primary Schools, fractions have been demonstrated through Cuisenaire rods.