Question

How do you use the distributive property with fractions?

Answer 1

Distributive property of multiplication relative to addition is universal for all numbers - integers, rational, real, complex - and states that
`a*(b+c)=a*b+a*c`

In particular, if we deal with fractions, when each member of the above formula can be represented in the form `x/y` where both `x` and `y` are integers, the distributive law works in exactly the same way:
`m/n*(p/q+r/s)=m/n*p/q+m/n*r/s`
where `m,n,p,q,r,s` are integers and denominators of each fraction `n,q,s` are not zeros.

If we know the distributive law for integer numbers and understand that a rational number `x/y` is, by definition, a new number that, if multiplies by `y`, produces `x`, the above formula for fractions can be easily proved by transforming fractions on the left and on the right to a common denominator `n*q*s`:
`(m*(p*s+r*q))/(n*q*s)=(m*p*s+m*r*q)/(n*q*s)`.
In this form the distributive law for fractions is a simple consequence of the distributive law for integers.