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Such an interminable division-by-zero algorithm is physically exhibited by some mechanical calculators. 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.
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 ...
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 division sign ( ÷) is a mathematical symbol consisting of a short horizontal line with a dot above and another dot below, used in Anglophone countries to indicate the operation of division. This usage, though widespread in some countries, is not universal and the symbol has a different meaning in other countries.
Therefore, the smallest difference between two x solutions is b/g, whereas the smallest difference between two y solutions is a/g. Thus, the solutions may be expressed as x = x 1 − bu/g y = y 1 + au/g. By allowing u to vary over all possible integers, an infinite family of solutions can be generated from a single solution (x 1, y 1).
Extraneous and missing solutions. In mathematics, an extraneous solution (or spurious solution) is one which emerges from the process of solving a problem but is not a valid solution to it. [1] A missing solution is a valid one which is lost during the solution process. Both situations frequently result from performing operations that are not ...
Envy-free cake-cutting. An envy-free cake-cutting is a kind of fair cake-cutting. It is a division of a heterogeneous resource ("cake") that satisfies the envy-free criterion, namely, that every partner feels that their allocated share is at least as good as any other share, according to their own subjective valuation.
Long division. In arithmetic, long division is a standard division algorithm suitable for dividing multi-digit Hindu-Arabic numerals ( Positional notation) that is simple enough to perform by hand. It breaks down a division problem into a series of easier steps.
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