diff --git a/src/implementations/BigInt.jl b/src/implementations/BigInt.jl
index b2cfbb7..83d3d6f 100644
--- a/src/implementations/BigInt.jl
+++ b/src/implementations/BigInt.jl
@@ -27,6 +27,14 @@ function operate_to!(output::BigInt, ::typeof(+), a::BigInt, b::BigInt)
     return Base.GMP.MPZ.add!(output, a, b)
 end
 
+function operate_to!(output::BigInt, ::typeof(copy), a::BigInt)
+    return Base.GMP.MPZ.set!(output, a)
+end
+
+function operate_to!(output::BigInt, ::typeof(copy), a::Int)
+    return Base.GMP.MPZ.set_si!(output, a)
+end
+
 # -
 
 promote_operation(::typeof(-), ::Vararg{Type{BigInt},N}) where {N} = BigInt
@@ -35,6 +43,10 @@ function operate_to!(output::BigInt, ::typeof(-), a::BigInt, b::BigInt)
     return Base.GMP.MPZ.sub!(output, a, b)
 end
 
+function operate_to!(output::BigInt, ::typeof(-), a::BigInt)
+    return Base.GMP.MPZ.neg!(output, a)
+end
+
 # *
 
 promote_operation(::typeof(*), ::Vararg{Type{BigInt},N}) where {N} = BigInt
diff --git a/src/implementations/Rational.jl b/src/implementations/Rational.jl
index 8bdd6d5..0e0aa44 100644
--- a/src/implementations/Rational.jl
+++ b/src/implementations/Rational.jl
@@ -30,13 +30,29 @@ end
 # +
 
 function promote_operation(
-    ::typeof(+),
+    ::Union{typeof(+),typeof(-)},
     ::Type{Rational{S}},
     ::Type{Rational{T}},
 ) where {S,T}
     return Rational{promote_sum_mul(S, T)}
 end
 
+function promote_operation(
+    op::Union{typeof(+),typeof(-)},
+    ::Type{Rational{S}},
+    ::Type{I},
+) where {S,I<:Integer}
+    return promote_operation(op, Rational{S}, Rational{I})
+end
+
+function promote_operation(
+    op::Union{typeof(+),typeof(-)},
+    ::Type{I},
+    ::Type{Rational{S}},
+) where {S,I<:Integer}
+    return promote_operation(op, Rational{S}, Rational{I})
+end
+
 function operate_to!(output::Rational, ::typeof(+), x::Rational, y::Rational)
     xd, yd = Base.divgcd(promote(x.den, y.den)...)
     # TODO: Use `checked_mul` and `checked_add` like in Base
@@ -46,16 +62,28 @@ function operate_to!(output::Rational, ::typeof(+), x::Rational, y::Rational)
     return output
 end
 
-# -
+function operate_to!(output::Rational, ::typeof(+), x::Rational, y::Integer)
+    # TODO Use `checked_mul` and `checked_add` like in Base
+    operate_to!(output.num, *, x.den, y)
+    operate!(+, output.num, x.num)
+    operate_to!(output.den, *, x.den, oftype(x.den, 1))
+    return output
+end
 
-function promote_operation(
-    ::typeof(-),
-    ::Type{Rational{S}},
-    ::Type{Rational{T}},
-) where {S,T}
-    return Rational{promote_sum_mul(S, T)}
+function operate_to!(output::Rational, ::typeof(+), y::Integer, x::Rational)
+    return operate_to!(output, +, x, y)
+end
+
+# unary -
+
+function operate_to!(output::Rational, ::typeof(-), x::Rational)
+    operate_to!(output.num, -, x.num)
+    operate_to!(output.den, copy, x.den)
+    return output
 end
 
+# binary -
+
 function operate_to!(output::Rational, ::typeof(-), x::Rational, y::Rational)
     xd, yd = Base.divgcd(promote(x.den, y.den)...)
     # TODO: Use `checked_mul` and `checked_sub` like in Base
@@ -65,6 +93,22 @@ function operate_to!(output::Rational, ::typeof(-), x::Rational, y::Rational)
     return output
 end
 
+function operate_to!(output::Rational, ::typeof(-), x::Rational, y::Integer)
+    # TODO Use `checked_mul` and `checked_sub` like in Base
+    operate_to!(output.num, *, x.den, y)
+    operate!(-, output.num)
+    operate!(+, output.num, x.num)
+    operate_to!(output.den, copy, x.den)
+    return output
+end
+
+function operate_to!(output::Rational, ::typeof(-), y::Integer, x::Rational)
+    # TODO Use `checked_mul` and `checked_sub` like in Base
+    operate_to!(output, -, x, y)
+    operate_to!(output, -, output)
+    return output
+end
+
 # *
 
 function promote_operation(
@@ -75,6 +119,22 @@ function promote_operation(
     return Rational{promote_operation(*, S, T)}
 end
 
+function promote_operation(
+    ::typeof(*),
+    ::Type{Rational{S}},
+    ::Type{I},
+) where {S,I<:Integer}
+    return promote_operation(*, Rational{S}, Rational{I})
+end
+
+function promote_operation(
+    ::typeof(*),
+    ::Type{I},
+    ::Type{Rational{S}},
+) where {S,I<:Integer}
+    return promote_operation(*, Rational{S}, Rational{I})
+end
+
 function operate_to!(output::Rational, ::typeof(*), x::Rational, y::Rational)
     xn, yd = Base.divgcd(promote(x.num, y.den)...)
     xd, yn = Base.divgcd(promote(x.den, y.num)...)
@@ -83,6 +143,69 @@ function operate_to!(output::Rational, ::typeof(*), x::Rational, y::Rational)
     return output
 end
 
+function operate_to!(output::Rational, ::typeof(*), x::Rational, y::Integer)
+    xn = x.num
+    xd, yn = Base.divgcd(promote(x.den, y)...)
+    operate_to!(output.num, *, xn, yn)
+    operate_to!(output.den, copy, x.den)
+    return output
+end
+
+function operate_to!(output::Rational, ::typeof(*), y::Integer, x::Rational)
+    return operate_to!(output, *, x, y)
+end
+
+# //
+
+function operate_to!(
+    output::Rational,
+    op::Union{typeof(/),typeof(//)},
+    x::Rational,
+    y::Rational,
+)
+    xn, yn = Base.divgcd(promote(x.num, y.num)...)
+    xd, yd = Base.divgcd(promote(x.den, y.den)...)
+    operate_to!(output.num, *, xn, yd)
+    operate_to!(output.den, *, xd, yn)
+    return output
+end
+
+function operate_to!(
+    output::Rational,
+    op::Union{typeof(/),typeof(//)},
+    x::Rational,
+    y::Integer,
+)
+    xn, yn = Base.divgcd(promote(x.num, y)...)
+    operate_to!(output.num, copy, xn)
+    operate_to!(output.den, *, x.den, yn)
+    return output
+end
+
+function operate_to!(
+    output::Rational,
+    op::Union{typeof(/),typeof(//)},
+    x::Integer,
+    y::Rational,
+)
+    xn, yd = Base.divgcd(promote(x, y.den)...)
+    operate_to!(output.num, *, xn, yd)
+    operate_to!(output.den, copy, y.num)
+    return output
+end
+
+function operate_to!(
+    output::Rational,
+    op::Union{typeof(/),typeof(//)},
+    x::Integer,
+    y::Integer,
+)
+    n, d = Base.divgcd(promote(x, y)...)
+    operate_to!(output.num, copy, n)
+    operate_to!(output.den, copy, d)
+    return output
+end
+
 # gcd
 
 function promote_operation(
diff --git a/src/interface.jl b/src/interface.jl
index fc1c5f5..dc24275 100644
--- a/src/interface.jl
+++ b/src/interface.jl
@@ -20,28 +20,22 @@ function promote_operation_fallback(
 end
 
 function promote_operation_fallback(
-    ::typeof(/),
+    op::Function,
     ::Type{S},
     ::Type{T},
 ) where {S,T}
-    return typeof(zero(S) / oneunit(T))
+    U = Base.promote_op(op, S, T)
+    return return U == Union{} ? typeof(op(oneunit(S), oneunit(T))) : U
 end
 
 # Julia v1.0.x has trouble with inference with the `Vararg` method, see
 # https://travis-ci.org/jump-dev/JuMP.jl/jobs/617606373
-function promote_operation_fallback(
-    op::F,
-    ::Type{S},
-    ::Type{T},
-) where {F<:Function,S,T}
-    return typeof(op(zero(S), zero(T)))
-end
-
 function promote_operation_fallback(
     op::F,
     args::Vararg{Type,N},
 ) where {F<:Function,N}
-    return typeof(op(zero.(args)...))
+    U = Base.promote_op(op, args...)
+    return return U == Union{} ? typeof(op(oneunit.(args)...)) : U
 end
 
 promote_operation_fallback(::typeof(*), ::Type{T}) where {T} = T
@@ -172,9 +166,7 @@ function operate(
 ) where {N}
     return op(x, y, args...)
 end
-
-operate(op::Union{typeof(-),typeof(/)}, x, y) where {N} = op(x, y)
-
+operate(op::Union{typeof(-),typeof(/),typeof(//)}, x, y) = op(x, y)
 operate(::typeof(convert), ::Type{T}, x) where {T} = convert(T, x)
 
 operate(::typeof(convert), ::Type{T}, x::T) where {T} = copy_if_mutable(x)
diff --git a/test/broadcast.jl b/test/broadcast.jl
index 37ea93b..5be1836 100644
--- a/test/broadcast.jl
+++ b/test/broadcast.jl
@@ -28,7 +28,7 @@ end
     if VERSION >= v"1.5"
         # FIXME This should not allocate but I couldn't figure out where these
         #       240 come from.
-        alloc_test(() -> MA.broadcast!!(+, a, b), 240)
+        alloc_test(() -> MA.broadcast!!(+, a, b), 80)
         alloc_test(() -> MA.broadcast!!(+, a, c), 0)
     end
 end
diff --git a/test/rational.jl b/test/rational.jl
new file mode 100644
index 0000000..9fb00e6
--- /dev/null
+++ b/test/rational.jl
@@ -0,0 +1,21 @@
+for op in (+, -, *, //)
+    for (a,b) in (
+        (2 // 3, 5),
+        (2, 3 // 5),
+        (2 // 3, 5 // 7),
+        (big(2) // 3, 5),
+        (big(2), 3 // 5),
+        (big(2) // 3, 5 // 7),
+    )
+        @test MA.operate_to!!(MA.copy_if_mutable(op(a, b)), op, a, b) ==
+              op(a, b)
+        @test MA.operate_to!!(MA.copy_if_mutable(op(b, a)), op, b, a) ==
+              op(b, a)
+    end
+end
+
+op = //
+for (a, b) in ((2, 3), (big(2), 3), (2, big(3)))
+    @test MA.operate_to!!(MA.copy_if_mutable(op(a, b)), op, a, b) == op(a, b)
+    @test MA.operate_to!!(MA.copy_if_mutable(op(b, a)), op, b, a) == op(b, a)
+end
diff --git a/test/runtests.jl b/test/runtests.jl
index 442c208..c45d22d 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -14,6 +14,11 @@ end
 @testset "BigInt" begin
     include("big.jl")
 end
+
+@testset "Rational" begin
+    include("rational.jl")
+end
+
 @testset "Broadcast" begin
     include("broadcast.jl")
 end