Fractions have lots of different names, and renaming is often needed to add or subtract fractions.
Here's how you'd add [beautiful math coming... please be patient] $\displaystyle\,\frac{1}{2}\,$ and [beautiful math coming... please be patient] $\displaystyle\,\frac{1}{3}\,$:
[beautiful math coming... please be patient] $\displaystyle \frac12 + \frac13 \ \ =\ \ \frac12\cdot\frac33 + \frac13\cdot \frac22 \ \ =\ \ \frac36 + \frac26 \ \ =\ \ \frac56 $
Notice that
[beautiful math coming... please be patient]
$\,\frac{3}{6}\,$
is just another name for
$\,\frac{1}{2}\,$, and
$\,\frac{2}{6}\,$
is just another name for
$\,\frac{1}{3}\,$.
However, these are the names that are needed for addition!
The next few paragraphs discuss the ideas in this example.
When fractions have the same denominator (called a common denominator),
then it's easy to add them:
When fractions to be added don't have a common denominator,
you need to find one, and then
rewrite the fractions with this common denominator.
In general, you'll want to use the least common multiple of the individual denominators
as the new denominator.
This is called the least common denominator.
Subtraction works the same way, because subtraction is just a special kind of addition.
Use the least common denominator.
You must input your answer as a diagonal fraction (like “2/5”), since you can't input horizontal fractions.
You'll probably want to use paper-and-pencil to solve each problem; key in your answer when you're done.