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. Sub-categories of vulgar fraction include:
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.
Decimal fraction: A vulgar fraction where the denominator is a powerIn mathematics, exponentiation is a process generalized from repeated multiplication, in much the same way that multiplication is a process generalized from repeated addition. The next operation after exponentiation is sometimes called tetration; repeatin of ten.
Dyadic fraction: A vulgar fraction in which the denominator is a power of twoIn mathematics, a power of two is any of the nonnegative integer powers of the number two; in other words, two times itself a certain number of times. Note that one is a power (the zeroth power) of two. Written in binary, a power of two always has the for.
A Mixed fraction: A mixed fraction is an integer plus a proper fraction.
An irrational fraction is, if all fractions must be capable of being expressed as a vulgar fraction, a contradiction in terms. An irrational numberIn mathematics, an irrational number is any real number that is not a rational number, i. one that cannot be written as a fraction a ''b with a and b integers, and b not zero. It can readily be shown that the irrational numbers are precisely those numbers is, by definition, not rational i.e. it cannot be expressed as a vulgar fraction.
A continued fractionIn mathematics, a continued fraction is an expression such as : where a is some integer and all the other numbers a are positive integers. Longer expressions are defined analogously. If the numerators are allowed to differ from unity, the resulting expres is an expression such as:
where the ai are positive integers.
A compound fraction is a fraction where the numerator or denominator (or both) contain fractions.
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