How many 75 ml bottles can be filled by 7 1/2 litres

First we transform all the units into litres:

We know that milli means "one thousandth", i.e. 1/1000. Therefore 75 mL = 75L * 1/1000 = 75/1000 L = 0,075L

Also:

$$7 \frac{1}{2}L= 7L + \frac{1}{2}L =\frac{14}{2}L + \frac{1}{2}L = \frac{15}{2}L$$

So, how many times can you pour 75 mL in order to fill 7 1/2 L ?

Remember that when we divide one fraction by another, we multiply the first one by the multiplicative inverse of the last one, we get:

$$\frac{15}{2}L/\frac{75}{1000}L=\frac{15}{2}/\frac{75}{1000}= \frac{15}{2}*\frac{1000}{75}= 100$$

We see that the units cancels out and we get a dimentionless quantity, which is what is expected in this case.