A = b and c = d, then a x c = b x d

what kind of reasong is used here

A = b is given to us

Multiply both sides by c to get

a = b

a*c = b*c

The rule to multiply both sides by c is the multiplicative property of equality

Then on the right side, replace c with d. This replacement is possible due to the fact that c = d. This is using the substitution property.

So we go from

a*c = b*c

to this

a*c = b*d