How do I add fractions with uncommon denominators?

### 8 Answers | Add Yours

First, I have to apologize for the fact that the formatting here will be hard to follow. It is not possible to set it up properly in here. I have had to show the fractions like this 1/2. I hope that isn't too confusing.

The first step in adding fractions with *different* denominators is to convert them to fractions with the **same** denominator.

Sometimes this is really easy, because one of the denominators is a multiple of the other. So, for example,

½ + ¼ is simple to do, because ½ is the same as 2/4. That's one you probably knew, but often it's hard to guess the equivalent fraction. So, just multiply **both the top and bottom** of the fraction by the same number.

numerator 1 x 2 = 2

denominator 2 x 2 = 4

so, the equivalent fraction is 2/4

Now the addition is straightforward:

2/4 + 1/4 = 3/4

It’s a little harder when neither number goes evenly into the other one. Then you have to find the **lowest common denominator**. All this means is the **lowest **(or smallest) number that is **common** to both (it is a **multiple** of **both** numbers).

Let’s look at an example:

1/3 + 2/5

We know that 3 doesn’t go evenly into 5, and 5 doesn’t go evenly into 3. So, we have to look for the *smallest* number that is a *multiple* of *both* 3 and 5.

The 3 table: 3 6 9 12 **15** 18 21 ….

The 5 table: 5 10 **15** 20 25 . . .

The smallest number that is a multiple of *both* 3 and 5 is 15.

Now to convert the fractions. The main thing to remember here is that you have to multiply **top and bottom** of the fraction by the same number to keep the fraction equivalent.

numerator: 1 x 5 = 5

denominator: 3 x 5 = 15

So, 1/3 is equivalent to 5/15

Now we'll do the same thing for 2/5.numerator: 2 x 3 = 6

denominator: 5 x 3 = 15

So, 2/5 is equivalent to 6/15

Now to do the addition:

5/15 + 6/15 = 11/15

Your son is not alone with the confussion. He simply needs to remember that when two fractions have uncommon denomiators they can easily have the same denomiator by choosing a number that both denomiators go into. For example: Problem: 1/5 + 1/6

Step 1: look at 5 and 6, they can both go into 30.

Step 2: muliply the first fraction (1/5) by a new fraction of 6/6 (which really equals 1) The product of this is 6/30.

Step 3: muliply the second fraction (1/6) by a second new fraction of 5/5 (which again equals 1). The product of this is 5/30.

Step 4: add 6/30 + 5/30 = 11/30

Step 5: check 11/30 to make sure it does not reduce. (this step can be eliminated by using the LCM of both denomiators)

Some times there is a problem where one of the two fractions has a denominator that the other fraction can easily convert to. For example: 1/2 + 1/8

Step 1: 2 can go into 8, so we only need to change the faction 1/2.

Step 2: we can change 1/2 to have a denominator of 8 by muliplying this fraction by 4/4.

Step 3: 4/4 times 1/2 = 4/8

Step 4: add 4/8 + 1/8 = 5/8

Step 5: check to see if 5/8 can be reduced. If not then 5/8 is the answer.

Try the website below for a way to help with fractions and other math...plus it is fun! ;)

Hope this helps. :) Good luck.

Its a little harder when neither number goes evenly into the other one. Then you have to find the lowest common denominator. All this means is the lowest (or smallest) number that is common to both (it is a multiple of both numbers).

You have to find the lowest common multiple for the denominators such as:

when you are told to add 1/2 and 1/3 together, the first is to find a multiple that both 2 and 3 have together.

The easiest way is to set up a table. Once you find the common multiple (6) you have to multiple the whole fraction by the number that would allow it to have 6 as a denominators:

for example you will multiply 1/2 by 3 and 1/3 by 2. This would turn 1/2 into 3/6 and 1/3 into 2/6

then it is easier to add

`3/6 + 2/6 = 5/6 `

You have to find the Least Common Multiple and then add

For example

2/3+3/5 = ?

Since the least common factor 3 and 5 share is 15 it would become

10/15+9/15=19/15

In order to add fractions with different denominator, you need to find a common denominator.

For example, 3/4 + 2/9

In order to add this fraction you need to find the common denominator for these two fractions. So basically find a number that both of the denominators are able to be divisible by. The common denominator can be 36 for this example. If you change the denominator though you have to change the numerator

3/4 would have to be multiplied by 9/9 = 27/36

2/9 would have to be multiplied by 4/4 = 8/36

Now, you can add the two fraction together, but remember **don't **add the denominator

27/36 + 8/36 = 35/36

To add fractions they need to have the same denominator.

For example 1/3+1/8

so the lowest common denominator of 3 and 8 is 24. An easier way to find a common number is to just multiply the denominators

Now you the denominators of both are 24 but to get 24 you have to multiply 3 by 8 so the fraction 1/3 turns into 8/24.

To get 24 you have to multiply 8 by 3 so 1/8 turns into 3/24

so now`8/24+3/24=11/24`

That is how you add fractions with uncommon denominators.``

` `

find the lowest common multiple for the denominators

### Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes