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The reciprocal function: y = 1/x.For every x except 0, y represents its multiplicative inverse. The graph forms a rectangular hyperbola.. In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x −1, is a number which when multiplied by x yields the multiplicative identity, 1.
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.
The reciprocal of a proper fraction is improper, and the reciprocal of an improper fraction not equal to 1 (that is, numerator and denominator are not equal) is a proper fraction. When the numerator and denominator of a fraction are equal (for example, 7 / 7 ), its value is 1, and the fraction therefore is improper.
The harmonic mean of a set of positive integers is the number of numbers times the reciprocal of the sum of their reciprocals. The optic equation requires the sum of the reciprocals of two positive integers a and b to equal the reciprocal of a third positive integer c. All solutions are given by a = mn + m 2, b = mn + n 2, c = mn.
This, for cyclic fractions with long repetends, allows us to easily predict what the result of multiplying the fraction by any natural number n will be, as long as the repetend is known. A proper prime is a prime p which ends in the digit 1 in base 10 and whose reciprocal in base 10 has a repetend with length p − 1.
In mathematics, Thiele's interpolation formula is a formula that defines a rational function from a finite set of inputs and their function values ().The problem of generating a function whose graph passes through a given set of function values is called interpolation.
It is also observed that 1 gram of chlorine reacts with 1.19 g of iodine. This ratio of 1.19 obeys the law because it is a simple fraction (1/3) of 3.58. (This is because it corresponds to the formula ICl 3, which is one known compound of iodine and chlorine.) Similarly, hydrogen, carbon, and oxygen follow the law of reciprocal proportions.
Rules for calculating the periods of repeating decimals from rational fractions were given by James Whitbread Lee Glaisher in 1878. [5] For a prime p, the period of its reciprocal divides p − 1. [6] The sequence of recurrence periods of the reciprocal primes (sequence A002371 in the OEIS) appears in the 1973 Handbook of Integer Sequences.