How do I interpret a coefficient on a normalized sum of dummy variables?

I've got several dummy variables that I'm combining into two factors, so

FACT1 = DUM1 + DUM2 + DUM3
FACT2 = DUM4 + DUM5


Because there's a different number of dummies going into each factor, I thought I'd better normalize them so they're comparable on the same range.

FACT1_n = FACT1/3
FACT2_n = FACT2/2


Now I want to fit a model

y = a + b1(FACT1_n) + b2(FACT2_n)


and I'm not sure how to interpret the coefficients.