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In terms of partition, 20 / 5 means the size of each of 5 parts into which a set of size 20 is divided. For example, 20 apples divide into five groups of four apples, meaning that "twenty divided by five is equal to four". This is denoted as 20 / 5 = 4, or 20 / 5 = 4. [2] In the example, 20 is the dividend, 5 is the divisor, and 4 is ...
When a whole is divided into equal pieces, if fewer equal pieces are needed to make up the whole, then each piece must be larger. When two positive fractions have the same numerator, they represent the same number of parts, but in the fraction with the smaller denominator, the parts are larger.
The obelus – or division sign – used as a variant of the minus sign in an excerpt from an official Norwegian trading statement form called «Næringsoppgave 1» for the taxation year 2010. The form of the obelus as a horizontal line with a dot above and a dot below, ÷ , was first used as a symbol for division by the Swiss mathematician ...
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.
The combination of these two symbols is sometimes known as a long division symbol or division bracket. [8] It developed in the 18th century from an earlier single-line notation separating the dividend from the quotient by a left parenthesis. [9] [10] The process is begun by dividing the left-most digit of the dividend by the divisor.
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Multiplication by one half is equivalent to division by two, or "halving"; conversely, division by one half is equivalent to multiplication by two, or "doubling". A square of side length one, here dissected into rectangles whose areas are successive powers of one half. A number raised to the power of one half is equal to its square root.
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