Originally Posted by

**craig** All the different kind of fractions...that could take a while. Could you let us know what level/school year your are at, this could help when people try to answer your questions. Anyway onto the answer:

Improper (or top heavy fractions) are, as the name suggests, fractions where the numerator (number at the top), is larger than the denominator (number at the bottom).

$\displaystyle \frac{11}{4}$ is an example of an improper fractions. To convert what I suggest doing is dividing 11 by 4. You will notice that that 4 goes into 11 2 times, with remainder 3. Therefore we can write $\displaystyle \frac{11}{4}$ as $\displaystyle 2+\frac{3}{4}$.

Now you try one, convert $\displaystyle \frac{17}{8}$ into mixed numbers (a whole number and a fraction, as above).

Multiplying fractions is easy, you simply multiply the two numerators and the two denominators, for example:

$\displaystyle \frac{3}{4} \times \frac{7}{8} = \frac{3 \times 7}{4 \times 8} = \frac{21}{32}$, simple enough?

Now dividing fractions is just as easy as multiplying them, as long as you remember the little trick.

To multiply two fractions, you take the reciprocal of one, and multiply it by the other. The reciprocal simply means one over the number, or the fractions upside down. The reciprocal of 2 for example would be $\displaystyle \frac{1}{2}$ and the reciprocal of $\displaystyle \frac{8}{3}$ would be $\displaystyle \frac{3}{8}$.

For example:

$\displaystyle \frac{5}{12} \div \frac{1}{2} = \frac{5}{12} \times \frac{2}{1} = \frac{10}{12}$ or $\displaystyle \frac{5}{6}$.

Hope this helps, make sure you let us know if there is anything you are unsure about.