How do I add fractions with uncommon denominators?

Expert Answers
cburr eNotes educator| Certified Educator

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

kborgeson eNotes educator| Certified Educator

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 it is fun!  ;)

Hope this helps.  :)  Good luck.

malkaam | Student

Adding fractions with uncommon denominators isn't hard all you have to do is find the Least Common Multiple (LCM) to make both the denominators same. Here's an example, add 2/5 and 6/2 --- to solve this we need to find the LCM.

List out the multiples of 2 and 5

2 = 2  4  6  8  10

5 = 5  10

10 is The least common multiple here, therefore (2/5) * 2 and (6/2) * 5

4/10 + 30/10


Another example is  (2/10) + 4, since over here 4 doesn't have a denominator then all we have to do is multiply (4/1) by 10, therefore,

2/10 + 40/10


crystaltu001 | Student

You should find a common multiple for the denominators. If something doesn't exactly pop into your head at first, you can just multiply both the denominators for a common denominator. Then you multiply the numerators by the numbers you multiplied the denominators. Well, numerator a with denominator a's number multiplied and numerator b with denominator b's number multiplied. This explanation is a bit, hard to understand. . .

fashionableb1 | Student

 find the lowest common multiple for the denominators 

nisarg | Student

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.``

` `

jess1999 | Student

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

zumba96 | Student

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


atyourservice | Student

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 `

singer0011 | Student

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).