# std::ratio_multiply

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< cpp‎ | numeric‎ | ratio

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

The alias template `std::ratio_multiply` denotes the result of multiplying 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::num 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_multiply<R1, R2> be already reduced to lowest terms; for example, std::ratio_multiply< std::ratio <1, 6>, std::ratio <4, 5>> is the same type as std::ratio <2, 15>.

### 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_multiply<two_third, one_sixth> r;
        std::cout << "2/3 * 1/6 = " << r::num << '/' << r::den << '\n';
    }

Output:

    2/3 * 1/6 = 1/9

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