# Adding Fractions

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## Introduction: Adding Fractions

Adding fractions may seem difficult but it is really fairly easy.

## Step 1: Finding the Lowest Common Denominator (LCD)

The first step of adding fractions is to find the Lowest Common Denominator (LCD). To find the LCD you must find the multiples of each of your denominators. To find a multiple you take one of you denominators and multiply it by: 1,2,3,4,etc... You then repeat this with the other denominator. The first numeral that is a multiple of both denominators is your LCD.

For this instructable we will be using a simple equation 4/5+6/15= x.
Multiples of 5 are 5, 10, 15, 20, 25,...
Multiples of 15 are 15, 30, 45,...
But wait! 15 is a multiple of both 5 and 15!

Our LCD is 15

## Step 2: I Found My LCD, Now What?

Now we need to change our denominators to the LCD. In our example we already have one example over 15 (6/15). So, now we just have to set our other fraction (4/5) to be over 15. To do this we have to figure out what number we must multiple the denominator by to get our LCD. In terms of an algebraic expression for our equation it would be: 5x=15; solving for x. Assuming you know how to handle an equation this is very easy. Divide both sides by 5 to get x = 3. Now that we know what we need to multiple the denominator by to get to the LCD we must multiply the numerator by that number also.

4/5 * 3/3 = 12/15
for help on multiplying fractions see step 3 of this instructable by meeze

Why can we do this? Wouldn't that change the equation?
No.
If the numerator and the denominator are the same it is equivalent to one (1). As we all know multiplying anything by one causes the number to stay the same.

## Step 3: Now You Have the Two Parts of Your Equation Finished. What Now?

Now we have one fraction plus another fraction (with both denominators the same) equals x
a/b + c/b = x
To find out what x equals we add across the numerators and carry our denominator across.
a+c/b=x

Going back to our example before:
12/15 + 6/15 = 18/15
Uh Oh!!!
18/15??? how does that work?

This is called an improper fraction. An improper fraction is one in which the numerator is greater than the denominator.
To simplify an improper fraction we need to find out how many times the denominator goes into the numerator.

18/15, how many times does 15 go into 18?
1

Now we take this number multiply it by the denominator and subtract it from the numerator.
This will give us a whole number usually followed by a fraction.

15*1=15
18-15=3
we get 1 3/15(one and three-fifteenths)

If we want to put this fraction in simplest form we need to simplify the fraction.

divide the top and bottom by 3
and we get 1/5(one-fifth)

put this back into our answer and our final solution is...
1 1/5(one and one-fifth)
4/5 + 6/15 = 1 1/5

## Step 4: But What If You Have More Than Two Fractions to Add???

Simple. The only step that changes is step 1(Finding the LCD).
For a equation with more than two fractions you must find the LCD of all the fractions.

For example:
6/5 + 3/6 + 2/15 =x

For this we need to find the LCD of: 5, 6, and 15
5= 5,10,15,20,25,30,35,...
6= 6,12,18,24,30, 26,...
15= 15, 30 , 45,...
But wait! 30 is a multiple of 5, 6, and 15!!!

Our LCD is 30

After finding the LCD of all of your fractions you follow steps 2 and 3 the same way. Participated in the
Burning Questions Round 6.5