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  2. Fraction - Wikipedia

    en.wikipedia.org/wiki/Fraction

    A ratio is often converted to a fraction when it is expressed as a ratio to the whole. In the above example, the ratio of yellow cars to all the cars on the lot is 4:12 or 1:3. We can convert these ratios to a fraction, and say that ⁠ 4 / 12 ⁠ of the cars or ⁠ 1 / 3 ⁠ of the cars in the lot are yellow.

  3. 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 ...

  4. Irreducible fraction - Wikipedia

    en.wikipedia.org/wiki/Irreducible_fraction

    The final result, ⁠ 4 / 3 ⁠, is an irreducible fraction because 4 and 3 have no common factors other than 1. The original fraction could have also been reduced in a single step by using the greatest common divisor of 90 and 120, which is 30. As 120 ÷ 30 = 4, and 90 ÷ 30 = 3, one gets = Which method is faster "by hand" depends on the ...

  5. Continued fraction - Wikipedia

    en.wikipedia.org/wiki/Continued_fraction

    where c 1 = ⁠ 1 / a 1 ⁠, c 2 = ⁠ a 1 / a 2 ⁠, c 3 = ⁠ a 2 / a 1 a 3 ⁠, and in general c n+1 = ⁠ 1 / a n+1 c n ⁠. Second, if none of the partial denominators b i are zero we can use a similar procedure to choose another sequence {d i} to make each partial denominator a 1:

  6. Clearing denominators - Wikipedia

    en.wikipedia.org/wiki/Clearing_denominators

    The simplified equation is not entirely equivalent to the original. For when we substitute y = 0 and z = 0 in the last equation, both sides simplify to 0, so we get 0 = 0 , a mathematical truth. But the same substitution applied to the original equation results in x /6 + 0/0 = 1 , which is mathematically meaningless .

  7. Mathematics - Wikipedia

    en.wikipedia.org/wiki/Mathematics

    The apparent plural form in English goes back to the Latin neuter plural mathematica , based on the Greek plural ta mathēmatiká (τὰ μαθηματικά) and means roughly "all things mathematical", although it is plausible that English borrowed only the adjective mathematic(al) and formed the noun mathematics anew, after the pattern of ...

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