How to Add and Subtract Fractions with Unlike Denominators

When you're adding fractions with an unlike denominator you make a common denominator by multiplying it with each other or if one denominator is the answer to the other denominator you multiply the factor and don't change the other fraction it stays like that until you add. So when you multiply the denominator you multiply the numerator with that multiple. Then you add it but you don't add your denominator because that tells you how many equal pieces make a whole. You only add the numerator. After you put it into lowest terms, if there are any. When you're subtracting its the exact same but you just have to subtract instead of add.

Examples: 

2  x4 +  1 x3
3 x4      4 x3

 8    +    3      =   11
12         12          12


7       +      7 x3   
12             4 x3

7       +       21      =   28
12              12            12

Adding fractions and Subtracting fractions with like denominators

Adding fractions and subtracting fractions with like denominators (bottom number) is easy, because all you have to do is add or subtract the numerators together (top number) . You only add or subtract the numerators because the denominators have the same number, which means they have the same number to make a whole. So you don't worry about adding the denominators. Lastly, if you fraction isn't in lowest terms (simplified) then make it in lowest terms. But how? Divide the fractions with it's biggest common multiple.

Example:

21/30 - 11/30 = 10/30 divided by 10 (biggest common multiple) = 1/3

Adding fractions & subtracting fractions (without lowest terms):

1/4 + 2/4 = 3/4    (1 + 2 = 3 --> then just put the denominator in the fraction.)
                                                                      ^ (3/4)
3/4 - 2/4 = 1/4    (3 - 2 = 1 --> then just put the denominator in the fraction.)
                                                                      ^ (1/4)

Adding And Subtracting Fractions With Like And Unlike Denominators

Addition:

Like Denominators: To add with like denominators, you add the numerators only. 

For example, 
5/12 + 2/12 = 7/12
Notice how I only added 5+2? That's because you do not add denominators. It's the equal pieces the whole is cut into, you do not change the whole.

Try these:
6/10 + 2/10, 3/8 + 1/8, 3/9 + 4/9.

Unlike Denominators: To add with unlike denominators, you find a common denominator.
Once you find one, simply add the numerators of both the fractions to get your answer. 

For example,
4/12 + 1/4 = 7/12
1/4 can be changed into 3/12 by multiplying 1/4 by 3/3. 1/4 x 3/3 = 3/12. 
Re-write the question, 4/12 + 3/12 = 7/12. It's easier now, right? 

Try these:
5/7 + 2/14, 6/10 + 1/5, 2/6 + 1/3. 


Subtraction:

Like Denominators: To subtract fractions with like denominators, all you need to do is subtract the numerators. Then figure out your answer. It's the same with adding fractions with like denominators, except you subtract. 

For example, 
7/12 - 4/12 = 3/12  
Do not subtract denominators. (Because those are the equal pieces your whole is cut into, your whole does not change! As said before!)  

Try these:
14/20 - 8/20, 9/13 - 7/13, 4/5 - 3/5.

Unlike Denominators: To subtract fractions with unlike denominators, you have to find a common denominator. You can do it without finding a common denominator, but that would take more work. (E.g. Diagrams, etc.) 

For example, 
9/12 -  2/6 = 5/12 
You can change 2/6 into 4/12 by multiplying the fractions, 2/6 x 2/2 = 4/12. 
Then, re-write the question and simply subtract the numerators again for your answer. 
9/12 - 4/12 = 5/12 

Try these:
4/10 - 1/5, 7/16 - 2/8, 6/14 - 2/7. 

(Put answers into lowest terms if asked to. This applies to both adding and subtracting.) 

adding and subtracting fractions

4/10 + 6/10 = 10/10
4/6 + 3/6 = 1/6