It's easy to add and subtract fractions when the pieces involved are the same size. Who doesn't like "easy"?
Sample Problem
Translation: "We have 1 piece out of 4 and add 1 more piece out of 4."
Sample Problem
"We have 3 pieces out of 5, take 1 away, and we're left with 2 pieces out of 5."
Sample Problem
"We have 3 pieces out of 5, try to take 4 away, are left owing 1 piece out of 5." Eh, put it on our tab.
Sample Problem
See what we did there? If the pieces are different sizes (i.e. if the denominators are different), we use the same trick we used when comparing fractions. We find the LCD, turn both fractions into something with the same denominator, and then add them up the easy way.
Sample Problem
When mixed numbers are involved, we turn the mixed numbers back into fractions and carry on as normal. Just act natural, and if anyone asks, deny everything. Remember that mixed numbers are themselves simply abbreviations for addition. But now that we've turned that mixed number into an improper fraction, how do we finish up the addition?
This will require one extra step, but we're up to the task. The LCD of these two fractions is 10, so now all we have to do is put the fractions over their LCD and then total 'em up:
If you want, you can now convert this back into a mixed number (8 1/10), but don't bother if you aren't asked to do so. You've got better things you can be doing with your time. Like painting rainbows on your fingernails.