Why doesn't the distributive property always work for division?

Answer 1

The distributive property works is defined for multiplication and addition:

a (b + c) = ab + ac

also:

(a + b)c = ac + bc

For a division, it works if you can convert it into a multiplication, in a form similar to the above. For example:

(10 + 2) / 2

can be converted into a multiplication; in this case, dividing by 2 is equivalent to multiplying by 1/2:

(10 + 2) (1/2) = (10 x 1/2) + (2 x 1/2)

If the sum is in the divisor, for example:

15 / (1 + 2)

then there is no way you can convert it into an equivalent multiplication, which conforms to the forms used for the distributive property.