Summary:

- Adding fractions is easy if the denominators are the same - just add the numerators

- WATCH OUT if the denominators are different - you HAVE to make them the same!!

- You can change the denominator of a fraction (without changing the fraction) by multiplying new factors on both top and bottom

- You shouldn't make the common denominator any bigger than you have to - so only multiply by the factors you need

- Adding fractions is easy if the denominators are the same - just add the numerators

- WATCH OUT if the denominators are different - you HAVE to make them the same!!

- You can change the denominator of a fraction (without changing the fraction) by multiplying new factors on both top and bottom

- You shouldn't make the common denominator any bigger than you have to - so only multiply by the factors you need

## The Math Tutor - Austin

Adding (and Subtracting) Fractions

The Easy Part - When The Denominators Are The Same

Couldn't be simpler - if the denominators are the same, just add (or subtract) the numerators!

In fact, the only thing you need to worry about is to make sure you put the final answer in lowest terms.

Examples:

2/9 + 5/9 = (2+5)/9 = 7/9

11/21 - 4/21 = (11-4)/21 = 7/21. But don't forget lowest terms! 7/21 = (1*7)/(3*7) = 1/3

A Little Harder (But Not Much) - When The Denominators Are Different

IMPORTANT - if the denominators are different, then you are NOT ready to add the fractions!!

Instead, you have to change the denominators to be the same first. In addition, you should try not to make the denominators any bigger than they need to be.

Still - this isn't too hard - and it's probably easiest to get by example.

Example:

Add 8/45 + 3/15

Now, you could get a common denominator by multiplying 45*15=(something huge), but you really don't need to. (And plus, if you do, you're going to have to add bigger numbers than you need - and who wants to do more work than necessary?)

Instead - notice that, when you look at their factors, the two denominators are ALMOST the same!

45 = 3*3*5

15 = 3*5

The only trouble is that the 15 needs an extra 3, so let's multiply it in (multiply top and bottom by the same number):

3/15 = (3*3)/(15*3) = 9/45

Cool! Now the problem is easy:

8/45 +3/15 = 8/45 + 9/45 = (8+9)/45 = 17/45

(And since 17 is prime, it's already in lowest terms...)