How to force Mathematica to show a rational with the denominator I specified?

Question

I want to write a function to force Mathematica to show a rational number in a denominator I specified. For example, the rational 2/3 with the specified denominator 6 should become 4/6.

I tried using HoldForm[] or Unevaluated[], but with no success.

In[1]:= setDenominator[x_, d_] := Unevaluated[Rational[x*d, d]];

In[2]:= setDenominator[2/3, 6]

        2
Out[2]= -
        3

Answer 1

You can use a FractionBox with DisplayForm:

setDenominator[x_, d_] := DisplayForm[FractionBox[x*d, d]]

Answer 2

HoldForm works but you have to be sneaky to get the numerical value of x*d in there

setDenominator[x_, d_] := HoldForm@Rational[foo, d] /. foo -> x*d

This can be improved by adding some checks for the suitability of d.

Answer 3

Here's a variation on sakra's idea that allows for addition and multiplication...

Format[setDenominator[x_, d_]] := DisplayForm@FractionBox[x*d, d]
setDenominator /: Plus[left___, setDenominator[x1_, d1_], right___] := left + x1 + right;
setDenominator /: Times[left___, setDenominator[x1_, d1_], right___] :=left*x1*right;

Trying it out:

a = setDenominator[3/5, 10];
Print[a, " + ", 2/3, " = " , a + 2/3]
Print[a, " + ", 2/3, " = " , setDenominator[a + 2/3, 30]]
Print[a, " × ", 2/3, " = " , a * 2/3]
Print[a, " × ", 2/3, " = " , setDenominator[a * 2/3, 30]]
Print[a, " ÷ ", 2/3, " = " , a /( 2/3)]