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Putting The Pieces Together: How To Add Fractions

Updated on July 15, 2008
Fractions can be a bother, no matter what form of math you are studying. In order to successfully add two or more fractions together, you must first find a common denominator. The denominator is the bottom number of a fraction and serves as a base. The numerator goes above the denominator, and can be added or subtracted from a numerator of a different fraction. However, before the numerators can be added or subtracted from each other, the fractions must share the same denominator. For example, if you added 1/4 and 2/4, you would end up with 3/4. This equation is true because both fractions have a denominator of 4. The difficult part is, not all fractions share similar denominators. An example of this would be: 1/4 + 1/2. However, there is a simple way to solve this. By multiplying both the numerator and denominator of 1/2 by 2, you would end up with 2/4. Then you can simply add 2/4 and 1/4 together to get 3/4, just like in the first example. Some fractions may have large numbers, and will take a while to find a common denominator. Take this example: 3/24 + 1/54 = ? Neither of these denominators will fit into each other, so you'll have to find a least common denominator (LCD) between them. A least common denominator is the lowest multiple that each number shares. Multiples of 24 would be 48, 72, 96, 120, 144, 168, 192, 216, 240, etc. Multiples of 54 would be 108, 162, 216, etc. Both numbers share 216 as their LCD. 24 goes into 216 nine times, so you would multiply top and bottom of 3/24 by 9 to get 27/216. 54 goes into 216 four times, so you would multiply 1/54 by 4 to get 4/216. Now, add 27/216 to 4/216 to get 31/216. Problem solved!

An example of the numerator and denominator


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    • profile image

      toya 7 years ago

      how do i do this problem 6 5/9 + 6 5/12 + 2 5/18

    • Sith Penguin profile image

      Sith Penguin 8 years ago

      Vamp: Same way. You just need to make sure the denominators on all three match. If they don't, you'll have to find a common denominator that all three fit into by using the method above. Hope that helps!

    • profile image

      Vamp 8 years ago

      Um...How do you add three fraction together? please tell me! :'(

    • profile image

      George 8 years ago

      I am so sorry, I made a mistake....this is the correct one1) first u need to change the mixed fraction

      ie, 4 5/9 to be (4*9+5)/9 = (36+5)9 = 41/9

      then, 71/6 + 41/9

      here u have to find the LCM of 6,9

      which is 18you have to multiply each fractional number with 18 and then divide complete with with LCM

      so (71/6 * 18 + 41/9 *18)/18= (71*3+41*2)/18= (213+82)/18=295/18=16.39

    • profile image

      George 8 years ago

      1) first u need to change the mixed fraction

      ie, 4 5/9 to be (4*5+9)/9 = (20+9)9 = 29/9

      then, 71/6 + 29/9

      here u have to find the LCM of 6,9

      which is 18

    • profile image

      tray 11 years ago

      i was wondering how to solve two math problems:

      1. 71/6 - 4 5/9

      2. 13/5 + 29/10 + 3

    • Chuck profile image

      Chuck Nugent 11 years ago from Tucson, Arizona

      Good Hub. I'm sure this will help many people.