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A simple fraction (also known as a common fraction or vulgar fraction, where vulgar is Latin for "common") is a rational number written as a / b or , where a and b are both integers. [9] As with other fractions, the denominator (b) cannot be zero. Examples include 1 2 , − 8 5 , −8 5 , and 8 −5 .
In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/ x or x−1, is a number which when multiplied by x yields the multiplicative identity, 1. The multiplicative inverse of a fraction a / b is b / a. For the multiplicative inverse of a real number, divide 1 by the number. For example, the reciprocal of 5 is one ...
A unit fraction is a positive fraction with one as its numerator, 1/ n. ... (reciprocal) of the denominator of the fraction, which must be a positive natural number ...
So the reciprocal of q is defined to be q − 1 = q ∗ ‖ q ‖ 2 . {\displaystyle q^{-1}={\frac {q^{*}}{\lVert q\rVert ^{2}}}.} Since the multiplication is non-commutative, the quotient quantities p q −1 or q −1 p are different (except if p and q are scalar multiples of each other or if one is a scalar): the notation p / q is ...
The golden ratio's negative −φ and reciprocal φ−1 are the two roots of the quadratic polynomial x2 + x − 1. The golden ratio is also an algebraic number and even an algebraic integer. It has minimal polynomial. This quadratic polynomial has two roots, and. The golden ratio is also closely related to the polynomial.
In mathematics, two sequences of numbers, often experimental data, are proportional or directly proportional if their corresponding elements have a constant ratio. The ratio is called coefficient of proportionality (or proportionality constant) and its reciprocal is known as constant of normalization (or normalizing constant).
In mathematics, a rational number is a number that can be expressed as the quotient or fraction of two integers, a numerator p and a non-zero denominator q. [1] For example, is a rational number, as is every integer (for example, ). The set of all rational numbers, also referred to as " the rationals ", [2] the field of ...
Every real number can be essentially uniquely represented as a continued fraction, namely as the sum of its integer part and the reciprocal of its fractional part which is written as the sum of its integer part and the reciprocal of its fractional part, and so on.
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