Extracting common factor

Reading from right to left the equality given by the distributive property, we have the expression$${\displaystyle \frac{a}{b}\cdot \frac{c}{d}+\frac{a}{b}\cdot \frac{n}{m}}$$which can be written:$${\displaystyle \frac{a}{b}\cdot (\frac{c}{d}+\frac{n}{m})}$$

We call this process extracting common factor since we have found a factor, that is a number that is multiplying, common to both addends of the expression.

Namely$${\displaystyle \frac{a}{b}\cdot \frac{c}{d}+\frac{a}{b}\cdot \frac{n}{m}=\frac{a}{b}\cdot (\frac{c}{d}+\frac{n}{m})=\frac{a}{b}\cdot (\frac{c}{d}+\frac{n}{m})}$$which means that the sum of two products has been converted into the product of a number by a sum.