# Distributive Propery with Fractions

I have several problems in this format and I don't know where to start. I understand the distributive property until I get to some fractions. The directions say write each fraction as a sum or difference. Here is an example of one of them:

$$\displaystyle\frac{2m-5}{9}$$

Any help is appreciated

• What do you mean by $\underline{2m-5}$? (If that's what you actually want.) – mrf Sep 7 '15 at 21:28
• Hint: Consider $\frac {1}{9}=9^{-1}$ – Karl Sep 7 '15 at 21:29

Another way to write $$\frac{2m-5}{9}$$ is $$\frac{1}{9}(2m-5)$$ From this it is much easier to see how the distributive property applies. We get $$\frac{1}{9}(2m)-\frac{1}{9}(5)=\frac{2m}{9}-\frac{5}{9}$$
$${2m-5\over 9} = \frac19(2m-5)=\frac{2m}9-\frac59$$
You have distributed the fraction $$\frac19$$ in order to write the original expression as a difference.