ratio.h

#include <ratio>

namespace detail {

template <class... Args>
struct RatioAdd;

template <class R1, class R2>
struct RatioAdd<R1, R2> {
  using Type = std::ratio_add<R1, R2>;
};

template <class R1, class R2, class... Args>
struct RatioAdd<R1, R2, Args...> {
  using Type = typename RatioAdd<
    std::ratio_add<R1, R2>,
    Args...
  >::Type;
};

template <class... Args>
struct RatioSubtract;

template <class R1, class R2>
struct RatioSubtract<R1, R2> {
  using Type = std::ratio_subtract<R1, R2>;
};

template <class R1, class R2, class... Args>
struct RatioSubtract<R1, R2, Args...> {
  using Type = typename RatioSubtract<
    std::ratio_subtract<R1, R2>,
    Args...
  >::Type;
};

template <class... Args>
struct RatioMultiply;

template <class R1, class R2>
struct RatioMultiply<R1, R2> {
  using Type = std::ratio_multiply<R1, R2>;
};

template <class R1, class R2, class... Args>
struct RatioMultiply<R1, R2, Args...> {
  using Type = typename RatioMultiply<
    std::ratio_multiply<R1, R2>,
    Args...
  >::Type;
};

template <class... Args>
struct RatioDivide;

template <class R1, class R2>
struct RatioDivide<R1, R2> {
  using Type = std::ratio_divide<R1, R2>;
};

template <class R1, class R2, class... Args>
struct RatioDivide<R1, R2, Args...> {
  using Type = typename RatioDivide<
    std::ratio_divide<R1, R2>,
    Args...
  >::Type;
};

}  // namespace detail

template <class... Args>
using RatioAdd = typename detail::RatioAdd<Args...>::Type;

template <class... Args>
using RatioSubtract = typename detail::RatioSubtract<Args...>::Type;

template <class... Args>
using RatioMultiply = typename detail::RatioMultiply<Args...>::Type;

template <class... Args>
using RatioDivide = typename detail::RatioDivide<Args...>::Type;