diff --git a/base/mpfr.jl b/base/mpfr.jl
index ee1e4eac39145..cb51d21aa5bc5 100644
--- a/base/mpfr.jl
+++ b/base/mpfr.jl
@@ -392,12 +392,18 @@ BigFloat(x::Union{Float16,Float32}, r::MPFRRoundingMode=rounding_raw(BigFloat);
     BigFloat(Float64(x), r; precision=precision)
 
 function BigFloat(x::Rational, r::MPFRRoundingMode=rounding_raw(BigFloat); precision::Integer=_precision_with_base_2(BigFloat))
+    r_den = _opposite_round(r)
     setprecision(BigFloat, precision) do
         setrounding_raw(BigFloat, r) do
-            BigFloat(numerator(x))::BigFloat / BigFloat(denominator(x))::BigFloat
+            BigFloat(numerator(x))::BigFloat / BigFloat(denominator(x), r_den)::BigFloat
         end
     end
 end
+function _opposite_round(r::MPFRRoundingMode)
+    r == MPFRRoundUp && return MPFRRoundDown
+    r == MPFRRoundDown && return MPFRRoundUp
+    return r
+end
 
 function tryparse(::Type{BigFloat}, s::AbstractString; base::Integer=0, precision::Integer=_precision_with_base_2(BigFloat), rounding::MPFRRoundingMode=rounding_raw(BigFloat))
     !isempty(s) && isspace(s[end]) && return tryparse(BigFloat, rstrip(s), base = base)
diff --git a/test/mpfr.jl b/test/mpfr.jl
index 8a537d1d4acd8..48477fc4dbcb7 100644
--- a/test/mpfr.jl
+++ b/test/mpfr.jl
@@ -35,6 +35,9 @@ import Base.MPFR
 
     @test typeof(BigFloat(1//1)) == BigFloat
     @test typeof(BigFloat(one(Rational{BigInt}))) == BigFloat
+    rat = 1 // (big(2)^300 + 1)
+    @test BigFloat(rat, RoundDown) < rat < BigFloat(rat, RoundUp)
+    @test BigFloat(-rat, RoundUp) < -rat < BigFloat(-rat, RoundDown)
 
     # BigFloat constructor respects global precision when not specified
     let prec = precision(BigFloat) < 16 ? 256 : precision(BigFloat) ÷ 2