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Showing content from https://timsong-cpp.github.io/cppwp/n4140/ratio.arithmetic below:

[ratio.arithmetic]

Each of the alias templates ratio_add, ratio_subtract, ratio_multiply, and ratio_divide denotes the result of an arithmetic computation on two ratios R1 and R2. With X and Y computed (in the absence of arithmetic overflow) as specified by Table [tab:ratio.arithmetic], each alias denotes a ratio<U, V> such that U is the same as ratio<X, Y>::num and V is the same as ratio<X, Y>::den.

If it is not possible to represent U or V with intmax_t, the program is ill-formed. Otherwise, an implementation should yield correct values of U and V. If it is not possible to represent X or Y with intmax_t, the program is ill-formed unless the implementation yields correct values of U and V.

Table

58

— Expressions used to perform ratio arithmetic


Type Value of X Value of Y ratio_add<R1, R2> R1::num * R2::den + R1::den * R2::den R2::num * R1::den ratio_subtract<R1, R2> R1::num * R2::den - R1::den * R2::den R2::num * R1::den ratio_multiply<R1, R2> R1::num * R2::num R1::den * R2::den ratio_divide<R1, R2> R1::num * R2::den R1::den * R2::num

[ Example:

static_assert(ratio_add<ratio<1,3>, ratio<1,6>>::num == 1, "1/3+1/6 == 1/2");
static_assert(ratio_add<ratio<1,3>, ratio<1,6>>::den == 2, "1/3+1/6 == 1/2");
static_assert(ratio_multiply<ratio<1,3>, ratio<3,2>>::num == 1, "1/3*3/2 == 1/2");
static_assert(ratio_multiply<ratio<1,3>, ratio<3,2>>::den == 2, "1/3*3/2 == 1/2");

  static_assert(ratio_add<ratio<1,INT_MAX>, ratio<1,INT_MAX>>::num == 2,
  "1/MAX+1/MAX == 2/MAX");
static_assert(ratio_add<ratio<1,INT_MAX>, ratio<1,INT_MAX>>::den == INT_MAX,
  "1/MAX+1/MAX == 2/MAX");
static_assert(ratio_multiply<ratio<1,INT_MAX>, ratio<INT_MAX,2>>::num == 1,
  "1/MAX * MAX/2 == 1/2");
static_assert(ratio_multiply<ratio<1,INT_MAX>, ratio<INT_MAX,2>>::den == 2,
  "1/MAX * MAX/2 == 1/2");

 — end example ]

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