I am getting a little confused with different answers to my fractions, any advice welcome. I have,

3/5 + 1/6 - 2/3 = ?

My understanding is to do the addition first, but change the demonitors so,

3/5 + 1/6 = (3/5 x 6/6) + (1/6 x 5/5) = 18/30 + 5/30 = 23/30 - 2/3 = 21/27 = 7/9

My problem is that the calculator gives an answer of 1/10 in its simplest form which is not equivalent to 7/9.

I can't see where I am going wrong?

Any help greatly appreciated