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  2. Karatsuba algorithm - Wikipedia

    en.wikipedia.org/wiki/Karatsuba_algorithm

    Karatsuba multiplication of az+b and cz+d (boxed), and 1234 and 567 with z=100. Magenta arrows denote multiplication, amber denotes addition, silver denotes subtraction and cyan denotes left shift. (A), (B) and (C) show recursion with z=10 to obtain intermediate values. The Karatsuba algorithm is a fast multiplication algorithm.

  3. Extraneous and missing solutions - Wikipedia

    en.wikipedia.org/wiki/Extraneous_and_missing...

    The problem is that multiplication by zero is not invertible: if we multiply by any nonzero value, we can reverse the step by dividing by the same value, but division by zero is not defined, so multiplication by zero cannot be reversed. More subtly, suppose we take the same equation and multiply both sides by . We get

  4. Fraction - Wikipedia

    en.wikipedia.org/wiki/Fraction

    A mixed number (also called a mixed fraction or mixed numeral) is the sum of a non-zero integer and a proper fraction, conventionally written by juxtaposition (or concatenation) of the two parts, without the use of an intermediate plus (+) or minus (−) sign. When the fraction is written horizontally, a space is added between the integer and ...

  5. Cross-multiplication - Wikipedia

    en.wikipedia.org/wiki/Cross-multiplication

    Pike's System of arithmetick abridged: designed to facilitate the study of the science of numbers, comprehending the most perspicuous and accurate rules, illustrated by useful examples: to which are added appropriate questions, for the examination of scholars, and a short system of book-keeping., 1827 - facsimile of the relevant section

  6. Multiplication - Wikipedia

    en.wikipedia.org/wiki/Multiplication

    The multiplication of whole numbers may be thought of as repeated addition; that is, the multiplication of two numbers is equivalent to adding as many copies of one of them, the multiplicand, as the quantity of the other one, the multiplier; both numbers can be referred to as factors.

  7. Arithmetic - Wikipedia

    en.wikipedia.org/wiki/Arithmetic

    For example, in the method addition with carries, the two numbers are written one above the other. Starting from the rightmost digit, each pair of digits is added together. The rightmost digit of the sum is written below them. If the sum is a two-digit number then the leftmost digit, called the "carry", is added to the next pair of digits to ...