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  2. Fraction - Wikipedia

    en.wikipedia.org/wiki/Fraction

    While the Persian mathematician Jamshīd al-Kāshī claimed to have discovered decimal fractions himself in the 15th century, J. Lennart Berggren notes that he was mistaken, as decimal fractions were first used five centuries before him by the Baghdadi mathematician Abu'l-Hasan al-Uqlidisi as early as the 10th century. [41] [n 3]

  3. Egyptian fraction - Wikipedia

    en.wikipedia.org/wiki/Egyptian_fraction

    The Rhind Mathematical Papyrus. An Egyptian fraction is a finite sum of distinct unit fractions, such as + +. That is, each fraction in the expression has a numerator equal to 1 and a denominator that is a positive integer, and all the denominators differ from each other.

  4. Fractional part - Wikipedia

    en.wikipedia.org/wiki/Fractional_part

    The fractional part or decimal part [1] of a non‐negative real number is the excess beyond that number's integer part. The latter is defined as the largest integer not greater than x , called floor of x or ⌊ x ⌋ {\displaystyle \lfloor x\rfloor } .

  5. Unit fraction - Wikipedia

    en.wikipedia.org/wiki/Unit_fraction

    Slices of approximately 1/8 of a pizza. A unit fraction is a positive fraction with one as its numerator, 1/ n.It is the multiplicative inverse (reciprocal) of the denominator of the fraction, which must be a positive natural number.

  6. Irreducible fraction - Wikipedia

    en.wikipedia.org/wiki/Irreducible_fraction

    An equivalent definition is sometimes useful: if a and b are integers, then the fraction ⁠ a / b ⁠ is irreducible if and only if there is no other equal fraction ⁠ c / d ⁠ such that | c | < | a | or | d | < | b |, where | a | means the absolute value of a. [4] (Two fractions ⁠ a / b ⁠ and ⁠ c / d ⁠ are equal or equivalent if and ...

  7. Positional notation - Wikipedia

    en.wikipedia.org/wiki/Positional_notation

    Decimal fractions were first developed and used by the Chinese in the form of rod calculus in the 1st century BC, and then spread to the rest of the world. [ 6 ] [ 7 ] J. Lennart Berggren notes that positional decimal fractions were first used in the Arab by mathematician Abu'l-Hasan al-Uqlidisi as early as the 10th century. [ 8 ]

  8. Field of fractions - Wikipedia

    en.wikipedia.org/wiki/Field_of_fractions

    The field of fractions of an integral domain is sometimes denoted by ⁡ or ⁡ (), and the construction is sometimes also called the fraction field, field of quotients, or quotient field of . All four are in common usage, but are not to be confused with the quotient of a ring by an ideal , which is a quite different concept.

  9. Continued fraction - Wikipedia

    en.wikipedia.org/wiki/Continued_fraction

    Continued fractions can also be applied to problems in number theory, and are especially useful in the study of Diophantine equations. In the late eighteenth century Lagrange used continued fractions to construct the general solution of Pell's equation, thus answering a question that had fascinated mathematicians for more than a thousand years. [9]

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