Understanding Fractions

Fractions are ways to show a portion.

Fractions are divided into two parts: the numerator and the denominator.  The numerator goes on top and tells you the part or portion you are interested in.  The denominator goes on the bottom, and it tells you the total number of possible parts or pieces.

$\displaystyle{\frac{\text{Numerator}}{\text{Denominator}}=\frac{\text{The part you are interested in}}{\text{The total number of parts}}}$

Example:

If you look at the figure below, you can see there is a rectangle broken into 6 equal pieces (fractions always assume that size of the pieces is equal).

If we wanted to know the shaded fraction of the shape, we would set up the following fraction:

$\displaystyle{\frac{\text{The part you are interested in}}{\text{The total number of parts}}=\frac{\text{Shaded parts}}{\text{Total parts}}=\frac{1}{6}}$

You could also be interested in the unshaded pieces.  If a question asked you what fraction of the shape is UNSHADED, you would set up the following fraction:

$\displaystyle{\frac{\text{The part you are interested in}}{\text{The total number of parts}}=\frac{\text{Unshaded parts}}{\text{Total parts}}=\frac{5}{6}}$

As you can see, fractions are quite flexible.  As long as items are broken into equal sized parts, you can talk about them in terms of fractions.

Of course, fractions do not only apply to shapes.  You can find a fraction of just about anything (as long as that thing is divided into basically equal or equivalent portions).

Example:

You visit the local animal shelter. You expect to find a lot of cats and dogs but are surprised to find a lot of rabbits and birds too!  At the shelter there are 16 dogs, 11 cats, 4 birds, 9 rabbits, and 1 lizard.  

What fraction of the animals is birds?

$\displaystyle{\frac{\text{The part you are interested in}}{\text{The total number of parts}}=\frac{\text{Birds}}{\text{Total animals}}=\frac{4}{41}}$

What fraction of the animals is cats?

$\displaystyle{\frac{\text{The part you are interested in}}{\text{The total number of parts}}=\frac{\text{Cats}}{\text{Total animals}}=\frac{11}{41}}$

What fraction of the animals is lizards?

$\displaystyle{\frac{\text{The part you are interested in}}{\text{The total number of parts}}=\frac{\text{Lizards}}{\text{Total animals}}=\frac{1}{41}}$

Fractions are easy, just remember, part you care about on top, total number on the bottom.

Note: Fractions are also ways to write division problems.  $\displaystyle{\frac{5}{6}}$ also means $5 \div 6 =$.  If you do the division problem you get a decimal -- and that's how you convert fractions to decimals (more in the lesson on that topic!).  $5\div6=.8\overline{33}$.