diff --git a/base/rational.jl b/base/rational.jl
index 05b4a062d8711..0462554664fcc 100644
--- a/base/rational.jl
+++ b/base/rational.jl
@@ -61,16 +61,16 @@ julia> (3 // 5) // (2 // 1)
 //(n::Integer,  d::Integer) = Rational(n,d)
 
 function //(x::Rational, y::Integer)
-    xn, yn = divgcd(x.num,y)
+    xn, yn = divgcd(promote(x.num, y)...)
     checked_den(xn, checked_mul(x.den, yn))
 end
 function //(x::Integer,  y::Rational)
-    xn, yn = divgcd(x,y.num)
+    xn, yn = divgcd(promote(x, y.num)...)
     checked_den(checked_mul(xn, y.den), yn)
 end
 function //(x::Rational, y::Rational)
-    xn,yn = divgcd(x.num,y.num)
-    xd,yd = divgcd(x.den,y.den)
+    xn,yn = divgcd(promote(x.num, y.num)...)
+    xd,yd = divgcd(promote(x.den, y.den)...)
     checked_den(checked_mul(xn, yd), checked_mul(xd, yn))
 end
 
@@ -280,7 +280,7 @@ end
 for (op,chop) in ((:+,:checked_add), (:-,:checked_sub), (:rem,:rem), (:mod,:mod))
     @eval begin
         function ($op)(x::Rational, y::Rational)
-            xd, yd = divgcd(x.den, y.den)
+            xd, yd = divgcd(promote(x.den, y.den)...)
             Rational(($chop)(checked_mul(x.num,yd), checked_mul(y.num,xd)), checked_mul(x.den,yd))
         end
 
@@ -305,16 +305,16 @@ for (op,chop) in ((:rem,:rem), (:mod,:mod))
 end
 
 function *(x::Rational, y::Rational)
-    xn, yd = divgcd(x.num, y.den)
-    xd, yn = divgcd(x.den, y.num)
+    xn, yd = divgcd(promote(x.num, y.den)...)
+    xd, yn = divgcd(promote(x.den, y.num)...)
     unsafe_rational(checked_mul(xn, yn), checked_mul(xd, yd))
 end
 function *(x::Rational, y::Integer)
-    xd, yn = divgcd(x.den, y)
+    xd, yn = divgcd(promote(x.den, y)...)
     unsafe_rational(checked_mul(x.num, yn), xd)
 end
 function *(y::Integer, x::Rational)
-    yn, xd = divgcd(y, x.den)
+    yn, xd = divgcd(promote(y, x.den)...)
     unsafe_rational(checked_mul(yn, x.num), xd)
 end
 /(x::Rational, y::Union{Rational, Integer, Complex{<:Union{Integer,Rational}}}) = x//y
diff --git a/test/rational.jl b/test/rational.jl
index 4b2d48305660b..81a9ab16c5ff7 100644
--- a/test/rational.jl
+++ b/test/rational.jl
@@ -575,3 +575,22 @@ end
     @test -Int32(1) // typemax(Int32) - Int32(1) == typemin(Int32) // typemax(Int32)
     @test 1 // (typemax(Int128) + BigInt(1)) - 2 == (1 + BigInt(2)*typemin(Int128)) // (BigInt(1) + typemax(Int128))
 end
+
+@testset "Promotions on binary operations with Rationals (#36277)" begin
+    inttypes = (Base.BitInteger_types..., BigInt)
+    for T in inttypes, S in inttypes
+        U = Rational{promote_type(T, S)}
+        @test typeof(one(Rational{T}) + one(S)) == typeof(one(S) + one(Rational{T})) == typeof(one(Rational{T}) + one(Rational{S})) == U
+        @test typeof(one(Rational{T}) - one(S)) == typeof(one(S) - one(Rational{T})) == typeof(one(Rational{T}) - one(Rational{S})) == U
+        @test typeof(one(Rational{T}) * one(S)) == typeof(one(S) * one(Rational{T})) == typeof(one(Rational{T}) * one(Rational{S})) == U
+        @test typeof(one(Rational{T}) // one(S)) == typeof(one(S) // one(Rational{T})) == typeof(one(Rational{T}) // one(Rational{S})) == U
+    end
+    @test (-40//3) // 0x5 == 0x5 // (-15//8) == -8//3
+    @test (-4//7) // (0x1//0x3) == (0x4//0x7) // (-1//3) == -12//7
+    @test -3//2 + 0x1//0x1 == -3//2 + 0x1 == 0x1//0x1 + (-3//2) == 0x1 + (-3//2) == -1//2
+    @test 0x3//0x5 - 2//3 == 3//5 - 0x2//0x3 == -1//15
+    @test rem(-12//5, 0x2//0x1) == rem(-12//5, 0x2) == -2//5
+    @test mod(0x3//0x1, -4//7) == mod(0x3, -4//7) == -3//7
+    @test -1//5 * 0x3//0x2 == 0x3//0x2 * -1//5 == -3//10
+    @test -2//3 * 0x1 == 0x1 * -2//3 == -2//3
+end