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  2. Collatz conjecture - Wikipedia

    en.wikipedia.org/wiki/Collatz_conjecture

    The number is taken to be 'odd' or 'even' according to whether its numerator is odd or even. Then the formula for the map is exactly the same as when the domain is the integers: an 'even' such rational is divided by 2; an 'odd' such rational is multiplied by 3 and then 1 is added.

  3. Continued fraction - Wikipedia

    en.wikipedia.org/wiki/Continued_fraction

    The story of continued fractions begins with the Euclidean algorithm, [4] a procedure for finding the greatest common divisor of two natural numbers m and n.That algorithm introduced the idea of dividing to extract a new remainder – and then dividing by the new remainder repeatedly.

  4. Odd greedy expansion - Wikipedia

    en.wikipedia.org/wiki/Odd_greedy_expansion

    However, a simpler greedy algorithm has successfully found Egyptian fractions in which all denominators are odd for all instances / (with odd ) on which it has been tested: let be the least odd number that is greater than or equal to /, include the fraction / in the expansion, and continue in the same way (avoiding repeated uses of the same ...

  5. Fraction - Wikipedia

    en.wikipedia.org/wiki/Fraction

    A compound fraction is a fraction of a fraction, or any number of fractions connected with the word of, [22] [23] corresponding to multiplication of fractions. To reduce a compound fraction to a simple fraction, just carry out the multiplication (see § Multiplication).

  6. Egyptian fraction - Wikipedia

    en.wikipedia.org/wiki/Egyptian_fraction

    An obvious necessary condition is that the starting fraction ⁠ x / y ⁠ have an odd denominator y, and it is conjectured but not known that this is also a sufficient condition. It is known [20] that every ⁠ x / y ⁠ with odd y has an expansion into distinct odd unit fractions, constructed using a different method than the greedy algorithm.

  7. Multiplication algorithm - Wikipedia

    en.wikipedia.org/wiki/Multiplication_algorithm

    In arbitrary-precision arithmetic, it is common to use long multiplication with the base set to 2 w, where w is the number of bits in a word, for multiplying relatively small numbers. To multiply two numbers with n digits using this method, one needs about n 2 operations.

  8. Greedy algorithm for Egyptian fractions - Wikipedia

    en.wikipedia.org/wiki/Greedy_algorithm_for...

    In mathematics, the greedy algorithm for Egyptian fractions is a greedy algorithm, first described by Fibonacci, for transforming rational numbers into Egyptian fractions. An Egyptian fraction is a representation of an irreducible fraction as a sum of distinct unit fractions , such as ⁠ 5 / 6 ⁠ = ⁠ 1 / 2 ⁠ + ⁠ 1 / 3 ⁠ .

  9. Arithmetic - Wikipedia

    en.wikipedia.org/wiki/Arithmetic

    Common tools in early arithmetic education are number lines, addition and multiplication tables, counting blocks, and abacuses. [186] Later stages focus on a more abstract understanding and introduce the students to different types of numbers, such as negative numbers, fractions, real numbers, and complex numbers.

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