# std::ratio_add

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< cpp‎ | numeric‎ | ratio

Defined in header `<ratio>` |  |
template< class R1, class R2 > using ratio_add = /* see below */; |  | (since C++11)

The alias template `std::ratio_add` denotes the result of adding 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_add<R1, R2> be already reduced to lowest terms; for example, std::ratio_add< std::ratio <1, 3>, std::ratio <1, 6>> is the same type as std::ratio <1, 2>.

### 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_add<two_third, one_sixth> sum;
        std::cout << "2/3 + 1/6 = " << sum::num << '/' << sum::den << '\n';
    }

Output:

    2/3 + 1/6 = 5/6

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