Science Fair Project Encyclopedia
For other, non-mathematical meanings of this word, see fraction.
- A vulgar fraction is a rational number written as one integer (the numerator) divided by a non-zero integer (the denominator). The line that separates the numerator and the denominator is called the vinculum. Rational numbers are the quotient field of integers.
Particular vulgar fractions
- irreducible fraction: a vulgar fraction "in lowest terms", where the numerator is an integer, the denominator is a positive integer, and the highest common factor of the numerator and the denominator is 1;
- proper fraction: a vulgar fraction with (absolute) value between 0 and 1;
- improper fraction: a vulgar fraction with a (absolute) value greater than 1;
- unit fraction: a vulgar fraction with a numerator of 1;
- Egyptian fraction: the sum of distinct unit fractions;
- decimal fraction: a vulgar fraction where the denominator is a power of 10;
- dyadic fraction: a vulgar fraction in which the denominator is a power of two.
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:
- Partial fractions, used to decompose rational functions.
- Rational functions are the quotient field of polynomials (over some integral domain).
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 , where the ai are integers.
- 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.
In Primary Schools, fractions have been demonstrated through Cuisenaire rods.
See also the external links below.
- Curricula for Teaching about Fractions
- Teaching Fractions: New Methods, New Resources
- Worksheets: Identifying Fractions
- Worksheets: Improper Fractions to Mixed Numbers
- Curricula for Teaching about Equivalent Fractions
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