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  2. Irreducible fraction - Wikipedia

    en.wikipedia.org/wiki/Irreducible_fraction

    A fraction that is reducible can be reduced by dividing both the numerator and denominator by a common factor. It can be fully reduced to lowest terms if both are divided by their greatest common divisor. [5] In order to find the greatest common divisor, the Euclidean algorithm or prime factorization can be used. The Euclidean algorithm is ...

  3. Lowest common denominator - Wikipedia

    en.wikipedia.org/wiki/Lowest_common_denominator

    For example, the numerators of fractions with common denominators can simply be added, such that + = and that <, since each fraction has the common denominator 12. Without computing a common denominator, it is not obvious as to what 5 12 + 11 18 {\displaystyle {\frac {5}{12}}+{\frac {11}{18}}} equals, or whether 5 12 {\displaystyle {\frac {5 ...

  4. Farey sequence - Wikipedia

    en.wikipedia.org/wiki/Farey_sequence

    In mathematics, the Farey sequence of order n is the sequence of completely reduced fractions, either between 0 and 1, or without this restriction, [a] which when in lowest terms have denominators less than or equal to n, arranged in order of increasing size.

  5. Least common multiple - Wikipedia

    en.wikipedia.org/wiki/Least_common_multiple

    The least common multiple of the denominators of two fractions is the "lowest common denominator" (lcd), and can be used for adding, subtracting or comparing the fractions. The least common multiple of more than two integers a , b , c , . . . , usually denoted by lcm( a , b , c , . . .) , is defined as the smallest positive integer that is ...

  6. Fraction - Wikipedia

    en.wikipedia.org/wiki/Fraction

    In general, a common fraction is said to be a proper fraction if the absolute value of the fraction is strictly less than one—that is, if the fraction is greater than −1 and less than 1. [ 14 ] [ 15 ] It is said to be an improper fraction , or sometimes top-heavy fraction , [ 16 ] if the absolute value of the fraction is greater than or ...

  7. Algebraic fraction - Wikipedia

    en.wikipedia.org/wiki/Algebraic_fraction

    The numerator and denominator are called the terms of the algebraic fraction. A complex fraction is a fraction whose numerator or denominator, or both, contains a fraction. A simple fraction contains no fraction either in its numerator or its denominator. A fraction is in lowest terms if the only factor common to the numerator and the ...

  8. Partial fraction decomposition - Wikipedia

    en.wikipedia.org/wiki/Partial_fraction_decomposition

    In algebra, the partial fraction decomposition or partial fraction expansion of a rational fraction (that is, a fraction such that the numerator and the denominator are both polynomials) is an operation that consists of expressing the fraction as a sum of a polynomial (possibly zero) and one or several fractions with a simpler denominator. [1]

  9. Fractionation - Wikipedia

    en.wikipedia.org/wiki/Fractionation

    [1] [2] Fractions are collected based on differences in a specific property of the individual components. A common trait in fractionations is the need to find an optimum between the amount of fractions collected and the desired purity in each fraction. Fractionation makes it possible to isolate more than two components in a mixture in a single run.

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