# How to add fractions together

Adding fractions may seem complicated at first, but it's really not that hard.

Here are three words that we should define at the beginning:

**1) Numerator **- the top part of the fraction

**2) Denominator **- the bottom part of the fraction

For example, for the fraction **2/3**:

**2**is the numerator**3**is the denominator.

**3) LCD - lowest common denominator** - the smallest number that all the different fractions' deminators will go into without giving you a remainder.

For example, for the fractions:

1/3 + 1/4 + 1/5

There are 3 denominators: 3, 4, and 5. **The LCD for these is 60**. 3, 4 and 5 all go into 60 without creating a remainder.

There are other common denominators for 3, 4 and 5, including 120 and 240, but these are larger than 60, so they are not the LCD.

__Hint:__ A quick way to find the LCD is to multiply the denominators together. However, sometimes this just creates a larger common denominator than the LCD, in which case you'll have to reduce the final fraction in your answer.

## When the denominators are all the same

When all the denominators are the same, it's easy: **Add up all the numerators, and put them over the same denominator.**

For example:

1/12 + 3/12 + 5/12

= (1+3+5)/12

= 9/12, which you can reduce to 3/4

Another example:

2/17 + 3/17 + 10/17

= (2+3+10)/17

= 15/17

Easy, right?

## Have 8 minutes? You can learn how to add fractions by watching this video

## When the denominators are different

Okay, here's where it gets a little trickier--but don't panic! Just follow this procedure. Let's start with an example:

1/3 + 2/9 + 3/10

**1) Find the LCD for all the denominators.**

For 3, 9 and 10, the LCD seems to be __90__. All 3 numbers go evenly into 90 without a remainder.

**2) For each of the denominators, find out how many times it goes into the LCD.**

__For 3:__ 3 goes into 90 *30 times*

__For 9:__ 9 goes into 90 *10 times*

__For 10:__ 10 goes into 90 *9 times*

**3) For each of the original fractions, multiply the numbers you get in (2) to both the numerator and the denominator.**

1/3 + 2/9 + 3/10 becomes

(1x30)/(3x30) + (2x10)/(9x10) + (3x9)/(10x9)

which, if you multiply out the numerators and denominators, becomes:

30/90 + 20/90 + 27/90

WAIT! Now they all have the same denominator! You can apply the procedure in the gray box above now:

= (30+20+27)/90

= **77/90**

There's your answer!