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  2. Partial fraction decomposition - Wikipedia

    en.wikipedia.org/wiki/Partial_fraction_decomposition

    Using the preceding decomposition inductively one gets fractions of the form , with ⁡ < ⁡ = ⁡, where G is an irreducible polynomial. If k > 1 , one can decompose further, by using that an irreducible polynomial is a square-free polynomial , that is, 1 {\displaystyle 1} is a greatest common divisor of the polynomial and its derivative .

  3. Fraction - Wikipedia

    en.wikipedia.org/wiki/Fraction

    (For example, two-fifths is the fraction ⁠ 2 / 5 ⁠ and two fifths is the same fraction understood as 2 instances of ⁠ 1 / 5 ⁠.) Fractions should always be hyphenated when used as adjectives. Alternatively, a fraction may be described by reading it out as the numerator over the denominator, with the denominator expressed as a cardinal ...

  4. Number Forms - Wikipedia

    en.wikipedia.org/wiki/Number_Forms

    3 ⁄ 5: 0.6 Vulgar Fraction Three Fifths 2157 8535 ⅘ 4 ⁄ 5: 0.8 Vulgar Fraction Four Fifths 2158 8536 ⅙ 1 ⁄ 6: 0.166... Vulgar Fraction One Sixth 2159 8537 ⅚ 56: 0.833... Vulgar Fraction Five Sixths 215A 8538 ⅛ 1 ⁄ 8: 0.125 Vulgar Fraction One Eighth 215B 8539 ⅜ 3 ⁄ 8: 0.375 Vulgar Fraction Three Eighths 215C 8540 ⅝ 5 ...

  5. Farey sequence - Wikipedia

    en.wikipedia.org/wiki/Farey_sequence

    Thus F 6 consists of F 5 together with the fractions ⁠ 1 / 6 ⁠ and ⁠ 5 / 6 ⁠. The middle term of a Farey sequence F n is always ⁠ 1 / 2 ⁠, for n > 1. From this, we can relate the lengths of F n and F n−1 using Euler's totient function φ(n): | | = | | + ().

  6. Solving quadratic equations with continued fractions - Wikipedia

    en.wikipedia.org/wiki/Solving_quadratic...

    By applying the fundamental recurrence formulas we may easily compute the successive convergents of this continued fraction to be 1, 3/2, 7/5, 17/12, 41/29, 99/70, 239/169, ..., where each successive convergent is formed by taking the numerator plus the denominator of the preceding term as the denominator in the next term, then adding in the ...

  7. Irreducible fraction - Wikipedia

    en.wikipedia.org/wiki/Irreducible_fraction

    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 of ⁠ 2 / 4 ⁠. A fraction that is reducible can be reduced by dividing both the numerator ...

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