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  2. Fraction - Wikipedia

    en.wikipedia.org/wiki/Fraction

    A simple fraction (also known as a common fraction or vulgar fraction, where vulgar is Latin for "common") is a rational number written as a / b or ⁠ ⁠, where a and b are both integers. [9] As with other fractions, the denominator (b) cannot be zero. Examples include ⁠ 1 2 ⁠, − ⁠ 8 5 ⁠, ⁠ −8 5 ⁠, and ⁠ 8 −5 ⁠.

  3. One half - Wikipedia

    en.wikipedia.org/wiki/One_half

    One half is the rational number that lies midway between 0 and 1 on the number line. 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 ...

  4. Ratio - Wikipedia

    en.wikipedia.org/wiki/Ratio

    As for fractions, the simplest form is considered that in which the numbers in the ratio are the smallest possible integers. Thus, the ratio 40:60 is equivalent in meaning to the ratio 2:3, the latter being obtained from the former by dividing both quantities by 20. Mathematically, we write 40:60 = 2:3, or equivalently 40:60∷2:3.

  5. Continued fraction - Wikipedia

    en.wikipedia.org/wiki/Continued_fraction

    Applying the fundamental recurrence formulas we find that the successive numerators A n are {1, 2, 3, 5, 8, 13, ...} and the successive denominators B n are {1, 1, 2, 3, 5, 8, ...}, the Fibonacci numbers. Since all the partial numerators in this example are equal to one, the determinant formula assures us that the absolute value of the ...

  6. Unit fraction - Wikipedia

    en.wikipedia.org/wiki/Unit_fraction

    In mathematics education, unit fractions are often introduced earlier than other kinds of fractions, because of the ease of explaining them visually as equal parts of a whole. [ 22 ] [ 23 ] A common practical use of unit fractions is to divide food equally among a number of people, and exercises in performing this sort of fair division are a ...

  7. Greedy algorithm for Egyptian fractions - Wikipedia

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

    The simplest fraction3 / y ⁠ with a three-term expansion is ⁠ 3 / 7 ⁠. A fraction ⁠ 4 / y ⁠ requires four terms in its greedy expansion if and only if y ≡ 1 or 17 (mod 24), for then the numerator −y mod x of the remaining fraction is 3 and the denominator is 1 (mod 6). The simplest fraction ⁠ 4 / y ⁠ with a four-term ...

  8. Irreducible fraction - Wikipedia

    en.wikipedia.org/wiki/Irreducible_fraction

    Two fractions ⁠ a / b ⁠ and ⁠ c / d ⁠ are equal or equivalent if and only if ad = bc.) For example, ⁠ 1 / 4 ⁠, ⁠ 5 / 6 ⁠, and ⁠ −101 / 100 ⁠ are all irreducible fractions. On the other hand, ⁠ 2 / 4 ⁠ is reducible since it is equal in value to ⁠ 1 / 2 ⁠, and the numerator of ⁠ 1 / 2 ⁠ is less than the numerator ...

  9. Farey sequence - Wikipedia

    en.wikipedia.org/wiki/Farey_sequence

    The latter means that, for Farey sequences of even order n, the number of fractions with numerators equal to ⁠ n / 2 ⁠ is the same as the number of fractions with denominators equal to ⁠ n / 2 ⁠, that is (/) = (/).

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