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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
Because matrix multiplication is not commutative, one can also define a left division or so-called backslash-division as A \ B = A −1 B. For this to be well defined, B −1 need not exist, however A −1 does need to exist. To avoid confusion, division as defined by A / B = AB −1 is sometimes called right division or slash-division in this ...
[12] [6] The 2020 Mathematics Subject Classification contains no less than sixty-three first-level areas. [13] Some of these areas correspond to the older division, as is true regarding number theory (the modern name for higher arithmetic) and geometry. Several other first-level areas have "geometry" in their names or are otherwise commonly ...
Other symbols for division include the slash or solidus /, the colon:, and the fraction bar (the horizontal bar in a vertical fraction). [3] [4] The ISO 80000-2 standard for mathematical notation recommends only the solidus / or "fraction bar" for division, or the "colon" : for ratios; it says that the ÷ sign "should not be used" for division. [1]
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.