Weighted Averages an multiple columns

I have tried uploading the worksheet and it won't let me for whatever reason so I will try to be as clear as possible.
I have the following formula to give me a weighted average.
=SUMPRODUCT(A8:A14,B8:B14)/SUM(B8:B14)

I also have data in E8:E14,F8:F18 which has its own weighted average formula that it covers, and the same for
I8:I18,J8:J18. What I want to do is to write a formula that will give me one large weighted average that encompasses all of these data fields.

Can you do something like this?

=(SUMPRODUCT(A8:A14,B8:B14)+SUMPRODUCT(E8:E14,F8:F14)+SUMPRODUCT(I8:I14,J8:J14))/SUM(B8:B14,F8:F14,J8:J14)

That worked without any errors, as far as I can tell that is the right formula then. Thank you.

You're welcome.