# std::ratio_subtract

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< cpp‎ | numeric‎ | ratio

Defined in header `<ratio>` |  |
template< class R1, class R2 > using ratio_subtract = /* see below */; |  |

The alias template `std::ratio_subtract` denotes the result of subtracting two exact rational fractions represented by the std::ratio specializations `R1` and `R2`.

The result is a std::ratio specialization std::ratio<U, V>, such that given Num == R1::num * R2::den - R2::num * R1::den and Denom == R1::den * R2::den (computed without arithmetic overflow), `U` is std::ratio<Num, Denom>::num and `V` is std::ratio<Num, Denom>::den.

### Notes

If `U` or `V` is not representable in `std::intmax_t`, the program is ill-formed. If `Num` or `Denom` is not representable in `std::intmax_t`, the program is ill-formed unless the implementation yields correct values for `U` and `V`.

The above definition requires that the result of std::ratio_subtract<R1, R2> be already reduced to lowest terms; for example, std::ratio_subtract<std::ratio<1, 2>, std::ratio<1, 6>> is the same type as std::ratio<1, 3>.

### Example

Run this code

    #include <iostream>
    #include <ratio>

    int main()
    {
        typedef std::ratio<2, 3> two_third;
        typedef std::ratio<1, 6> one_sixth;

        typedef std::ratio_subtract<two_third, one_sixth> diff;
        std::cout << "2/3 - 1/6 = " << diff::num << '/' << diff::den << '\n';
    }

Output:

    2/3 - 1/6 = 1/2

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