diff --git a/src/primitive.jl b/src/primitive.jl
index f3fd0c2..9bb3bb9 100644
--- a/src/primitive.jl
+++ b/src/primitive.jl
@@ -106,6 +106,8 @@ end
     ex = :($ex; TaylorScalar($([Symbol('v', i) for i in 1:N]...)))
     return :(@inbounds $ex)
 end
+@inline *(a::TaylorScalar{T1, N}, b::TaylorScalar{T2, N}) where {T1,T2,N} = *(promote(a,b)...)
+@inline /(a::TaylorScalar{T1, N}, b::TaylorScalar{T2, N}) where {T1,T2,N} = *(promote(a,b)...)
 
 @generated function ^(t::TaylorScalar{T, N}, n::S) where {S <: Number, T, N}
     ex = quote
diff --git a/src/scalar.jl b/src/scalar.jl
index e69c950..53fae9f 100644
--- a/src/scalar.jl
+++ b/src/scalar.jl
@@ -72,6 +72,9 @@ function promote_rule(::Type{TaylorScalar{T, N}},
                       ::Type{S}) where {T, S, N}
     TaylorScalar{promote_type(T, S), N}
 end
+function promote_rule(::Type{TaylorScalar{T1, N}}, ::Type{TaylorScalar{T2,N}}) where {T1, T2, N}
+TaylorScalar{promote_type(T1,T2), N}
+end
 
 # Number-like convention (I patched them after removing <: Number)
 
@@ -79,6 +82,9 @@ convert(::Type{TaylorScalar{T, N}}, x::TaylorScalar{T, N}) where {T, N} = x
 function convert(::Type{TaylorScalar{T, N}}, x::S) where {T, S, N}
     TaylorScalar{T, N}(convert(T, x))
 end
+function convert(::Type{TaylorScalar{T1,N}},x::TaylorScalar{T2,N}) where {T1,T2,N}
+    TaylorScalar{T1,N}(convert.(T1,value(x)))
+end
 @inline +(a::Number, b::TaylorScalar) = TaylorScalar((a + value(b)[1]), value(b)[2:end]...)
 @inline -(a::Number, b::TaylorScalar) = TaylorScalar((a - value(b)[1]), .-value(b)[2:end]...)
 @inline *(a::Number, b::TaylorScalar) = TaylorScalar((a .* value(b))...)