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How do I add fractions with uncommon denominators?

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prdmomof4 | eNotes Newbie

Posted March 9, 2009 at 5:11 AM via web

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How do I add fractions with uncommon denominators?

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cburr | Middle School Teacher | (Level 2) Associate Educator

Posted March 9, 2009 at 6:31 AM (Answer #1)

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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

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kborgeson | Middle School Teacher | (Level 2) Adjunct Educator

Posted March 9, 2009 at 10:23 AM (Answer #2)

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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.

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singer0011 | Student , Grade 9 | eNotes Newbie

Posted March 11, 2009 at 6:33 AM (Answer #4)

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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).

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atyourservice | Student , Grade 10 | eNoter

Posted April 17, 2014 at 10:57 PM (Answer #5)

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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 `

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