2/15+(-3/10)

$$\frac{2}{15}+\frac{-3}{10}$$ is probably what you mean. Being that, lets solve it.

Firstly what we need to do is find the LCM of 15 and 10. What we can do is $${\mathtt{15}}{\mathtt{\,\times\,}}{\mathtt{10}}$$... and it will work.. but there is a smaller number that both of us can think of. It's 30. Now we make the two denominator into 30, while following the rule of what you do to the denominator you must do the same to the numerator.So being this I'll take you through it slowly.

Lets make the denominator 30 by multiplying 15 by 2 and 10 by 3.

$$\frac{2}{15*2}+\frac{-3}{10*3}$$

Now lets do that to the numerator as well.

$$\frac{2*2}{15*2}+\frac{-3*3}{10*3}$$

This becomes:

$$\frac{4}{30}+\frac{-9}{30}$$

Now that we have the denominator the same, we just do simple addition with the numerator.

$$\frac{4+(-9)}{30}$$

That will be the answer.

$$\frac{-5}{30}$$

We can simplify that by dividing the denominator and the numerator. Remember! If we do something to the numerator we must do the same to the denominator!

So we Divide both the numerator and the denominator by 5.

$$\frac{-5/5}{30/5}$$

Which is:

$$\frac{-1}{6}$$

.

Great explanation, TM! (oh great, now im using CPhill's abbreviations)

I gave you a thumbs up. :)