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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 ...
Early exercises deal with addition, subtraction, multiplication, and division of integers. Extensive courses of exercises in school extend such arithmetic to rational numbers . Various approaches to geometry have based exercises on relations of angles , segments , and triangles .
In modular arithmetic, unit fractions can be converted into equivalent whole numbers, allowing modular division to be transformed into multiplication. Every rational number can be represented as a sum of distinct unit fractions; these representations are called Egyptian fractions based on their use in ancient Egyptian mathematics. Many infinite ...
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 .
Beyond primary education, the symbol '÷' for division is seldom used, but is replaced by the use of algebraic fractions, [12] typically written vertically with the numerator stacked above the denominator – which makes grouping explicit and unambiguous – but sometimes written inline using the slash or solidus symbol '/'. [13]
It has two definitions: either the integer part of a division (in the case of Euclidean division) [2] or a fraction or ratio (in the case of a general division). For example, when dividing 20 (the dividend ) by 3 (the divisor ), the quotient is 6 (with a remainder of 2) in the first sense and 6 + 2 3 = 6.66... {\displaystyle 6+{\tfrac {2}{3}}=6 ...
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