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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 ...
Quotition is the concept of division most used in measurement. For example, measuring the length of a table using a measuring tape involves comparing the table to the markings on the tape. This is conceptually equivalent to dividing the length of the table by a unit of length, the distance between markings.
In a complex fraction, either the numerator, or the denominator, or both, is a fraction or a mixed number, [22] [23] corresponding to division of fractions. For example, / / and () / are complex fractions. To interpret nested fractions written "stacked" with a horizontal fraction bars, treat shorter bars as nested inside longer bars.
Such an interminable division-by-zero algorithm is physically exhibited by some mechanical calculators. [4] In partitive division, the dividend is imagined to be split into parts, and the quotient is the resulting size of each part. For example, imagine ten cookies are to be divided among two friends.
Dividing by Q(x) this gives () = + (), and then seek partial fractions for the remainder fraction (which by definition satisfies deg R < deg Q). If Q ( x ) contains factors which are irreducible over the given field, then the numerator N ( x ) of each partial fraction with such a factor F ( x ) in the denominator must be sought as a polynomial ...
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.
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