How do you add fractions with different numerators?

Expert Answers
litteacher8 eNotes educator| Certified Educator

In order to add fractions with different numerators, you have to find the lowest common denominator if they have different denominators.  Otherwise, you just add!

When it comes to fractions, it’s all about the denominator.  The denominator is the number on the bottom.  It is basically telling you how many pieces a fraction has been broken into.  In order to add two fractions, you need to have the same denominator, but it does not matter what the numerators are.  Numerators are the number on the top, or how many pieces you have of the whole.

Imagine you have 1/4 + 2/4.  The numerators are 1 and 2.  You can add these together and get 3.   It does not matter that they are different.  The denominators are both 4.  That’s all you need to add.  You leave the denominator the same, and just add the two numerators.  You end up with 3/4.

If you have two different denominators, you will need to find the lowest common denominator.  If you have 1/2 + 3/4, for example, you would use 4 as the lowest common denominator.  Then you would have 2/4 + 3/4 = 5/4.  This fraction can be left this way or written like a mixed number. 

To make a mixed number out of a fraction like this, you need to divide the top number (the numerator) by the bottom number (the denominators).  In this case 4 goes into 5 4 times, and 4/4 is 1.  We have 1/4 left, so our mixed number becomes 1 1/4.


jenasherry eNotes educator| Certified Educator

The numerator is "the top number" so yes, just add, leaving the denominator or "bottom number" the same. I say to use it like a label. "One fourth plus two fourths equals three fourths." Just like 1 banana plus two bananas equals three bananas.

I love math but am not a fan of finding common denominators. If (more like when) you run into this situation, you may use what I call "The Zorro Method." (Doesn't that make it sound really fun?) I've attached a photo of an example that I've done to help you see how it works. 

The one thing about this "zorro" method is that you will many times have to put your answer in lowest terms. 

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atyourservice | Student

You have to multiply so that the denominators are the same. For example if someone tells you to add or minus `1/2` and `1/7`

you have to find a common multiplier, both 2 and 7 have a common multiplier of 14 so we have to multiply the whole fraction to get them to 14.

so 2 and 7 and 7 and 2

`1/2 xx 7/7 = 7/14 `

`1/7 xx 2/2 = 2/14 `

add them up:

`7/ (14) + 2/ (14) = 9/(14) `