Finding lowest number to multiply a fraction and get a wholeI am trying to find the multiplier for a fraction that will let me get a whole number.So trying to solve c = a × bWhere a is a number like 1.6 or 0.7 or 5.24Where b is the lowest number that a can be multiplied by to make c a whole number.The use case is in a game I am programming the currency is only in whole numbers of a single denomination (single gold coins) if the player wants to sell a quantity of items that are worth a fractional value like 1.6, how many must they sell so they can receive a whole number without throwing out the fractions.

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Finding lowest number to multiply a fraction and get a wholeI am trying to find the multiplier for a fraction that will let me get a whole number.So trying to solve   c  =  a  ×  bWhere   a is a number like   1.6 or   0.7 or   5.24Where   b is the lowest number that   a can be multiplied by to make   c a whole number.The use case is in a game I am programming the currency is only in whole numbers of a single denomination (single gold coins) if the player wants to sell a quantity of items that are worth a fractional value like   1.6, how many must they sell so they can receive a whole number without throwing out the fractions.

Brooks Hogan · Accepted Answer

Multiply   a  =            8      5       by   b  =  5 to get  c  =      8    5    ⋅  5  =  8When a rational number is expressed as a fraction             n      d       that is fully reduced meaning   gcd  (  n  ,  d  )  =  1, with (n, numerator; d, denominator, each an integer,) then we have  a  =      n    d       so we put     b  =  d  ,and so  c  =      n    d    ⋅  d  =  nThat is, any rational number expressed as a fully reduced fraction where the numerator and denominator are co-prime, then the lowest integer value for   b is given by   b  d, where   d is the denominator of the fully reduced fraction =   a

Mark Elliott · Accepted Answer

I&#039;d suggest this algorithm: multiply by   10 repeatedly until you have an integer. You can now write your decimal as a fraction:       k          10      n      . Then, use any factorization algorithm to find the greatest common divisor of   k and       10    n  , and divide both the numerator and denominator by that. This puts the fraction in lowest terms, and now the denominator is the number you wanted.For the record: This is a horribly inefficient algorithm. If you need it to be fast (for example, if you&#039;re trying to do billions of these calculations) you&#039;ll want to do something else. But it&#039;ll work if you&#039;re only trying to do it a hundred times a second, or something like that.

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