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A simple fraction (also known as a common fraction or vulgar fraction) [n 1] 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 calculus, the quotient rule is a method of finding the derivative of a function that is the ratio of two differentiable functions. Let () = (), where both f and g are differentiable and ()
For example, density (mass divided by volume, in units of kg/m 3) is said to be a "quotient", whereas mass fraction (mass divided by mass, in kg/kg or in percent) is a "ratio". [8] Specific quantities are intensive quantities resulting from the quotient of a physical quantity by mass, volume, or other measures of the system "size". [3]
In abstract algebra, given a magma with binary operation ∗ (which could nominally be termed multiplication), left division of b by a (written a \ b) is typically defined as the solution x to the equation a ∗ x = b, if this exists and is unique. Similarly, right division of b by a (written b / a) is the solution y to the equation y ∗ a = b ...
The story of continued fractions begins with the Euclidean algorithm, [4] a procedure for finding the greatest common divisor of two natural numbers m and n.That algorithm introduced the idea of dividing to extract a new remainder – and then dividing by the new remainder repeatedly.
Long division is the standard algorithm used for pen-and-paper division of multi-digit numbers expressed in decimal notation. It shifts gradually from the left to the right end of the dividend, subtracting the largest possible multiple of the divisor (at the digit level) at each stage; the multiples then become the digits of the quotient, and the final difference is then the remainder.
An Egyptian fraction is a finite sum of distinct unit fractions, ... Egyptian fractions can help in dividing food or other objects into equal shares. [1]
Dividing by exterior division Draw a line segment A S {\displaystyle AS} and construct off the point S {\displaystyle S} a segment S C {\displaystyle SC} perpendicular to A S {\displaystyle AS} and with the same length as A S {\displaystyle AS} .