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Adding fractions and subtracting fractions

Updated on December 31, 2012

Introduction to adding and subtracting fractions

It may seem difficult learning how to add fractions and how to subtract fractions at first, but once you get the hang of it, you will be amazed at how easy it is. Firstly you must know that a fraction is made up of a numerator and a denominator. The numerator tells the amount of parts used or remaining out of the whole, and the denominator tells the amount of equal parts an object is divided into.

There are three types of fractions:

  • proper fractions - These are fractions where the numerator is smaller than the denominator. Eg 1/3.
  • improper fractions - These are fractions whose numerators are larger than denominators. Eg 10/5
  • mixed fractions or mixed numbers - These fractions/numbers consist of a whole number accompanied by a fraction.


Adding fractions
Adding fractions


How to add fractions with shapes
How to add fractions with shapes

Adding fractions and subtracting fractions

Just like comparing fractions, adding fractions or subtracting fractions, the denominators must always be the same. Fifths can be subtracted from fiths and tenths can be subtracted from tenths, but fifths cannot be added or subtracted from tenths without doing some former calculations. The denominators must be changed first.

If the fractions to be addded or subtracted have the same denominator, then work with the numerators only. When I say work with the numerators only I mean add or subtract the numerator only.

E.g:5/11 + 2/11

Add the 5 to 2 and put the result 7 as the numerator, therefore 5/11 + 2/11 = 7/11.

E.g: 6/12 - 1/12

Subtract 1 from 6 and put the result 5 as the numerator, the answer 5/12.

Adding three fractions

How to add fractions
How to add fractions
Adding fractions and subtracting factions
Adding fractions and subtracting factions
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Adding fractions and subtracting fractions worksheet
Adding fractions and subtracting fractions worksheet
Adding fractions and subtracting fractions worksheet

How to add fractions with different denominator

With add fractions with different denominators, you must change the denominators to make them the same. To do so, you find something called, 'the lowest common multiple' of the denominators. To do this, you list about the first 10- 20 multiples of the denominators and then pick out the lowest common one. Multiples are the results you get when you multiply a given number by any other number. For example, the multiples of 2 are 2, 4, 6, 8, 10, etc. You get the multiples by multiplying 2 by 1, 2 by 2, 2 by 3, 2 by 4 and 2 by 5 respectively. After picking the lowest common multiply, this is the common denominator which you would use. Now you have to change the fractions to fractions which have denominators of the lowest common multiple you got, by dividing the lowest common multiple by the old denominator and then multiply the old numerator by the result you got.

For example:

1/5+ 2/3

Step 1: List the multiples of the denominators

5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50 etc

3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 etc

Step 2: Find the lowest common.

= 15

Step 3: Change the fractions into ones with denominators of 15.

To change 1/5 to a fraction with a denomiator of 15. Divide 15 by 5. Then multiply 1 by the result, which is 3. 1/5 = 3/15. To change 2/3 to a fraction with a denominator of 15. Divide 15 by 3 = 5, then multiply by 2, the old denomiator.

Now add 3/15 and 10/15 = 13/15

Subtracting fraction with different denomination

Follow the same process to subtract fractions with different, first change the fractions to fractions with common denomiators then subtract. Its as easy as that.

For example if asked to subtract 3/4 form 10/12

Step 1- List the multiples of the denominators, this would be multiples of 4 and multiples of 12.

Multiples of 4 - 4, 8,  12, 16, 18

Multiples of 12- 12, 24, 36, 48, 60

Step 2- Pick out the lowest common multiple

This would be 12.

Step 3- Change the fractions into fractions with the denominator of 12

To change 3/4 to a fraction with a denominator of 12.  Devide 12 by 4 = 3. Then mutiply 3 from the 3/4 by 3 (result from dividing 12 by 3). The other fraction already has a denominator of 12. There you can do your calculation.So the final answer would be 10/12 -9/12 = 1/12.

Adding mixed fractions and subtracting mixed fraction

Okay, to add mixed fractions (mixed numbers) you separate the addition of the whole numbers from the addition of the fraction. Add the whole number together first and then add the fractions.

For example: 1 1/3 + 2 1/3

The result is 3 2/3.

Do the samething to subtact mixed fractions. Subtract the whole numbers first then the fractions after.


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    • mathslover profile imageAUTHOR


      8 years ago from Barbados

      thankz alot

    • mathslover profile imageAUTHOR


      10 years ago from Barbados

      Thank you mathswizard I am glad that this hub helps you!

    • profile image


      10 years ago

      Hey mathslover your website realllly helped me .this hub rocks .tankz :-D

    • mathslover profile imageAUTHOR


      10 years ago from Barbados

      Thank you bayoulady, i am glad that my hub is of help to you.

    • mathslover profile imageAUTHOR


      10 years ago from Barbados

      I am greatful that you like this hub JKeiser. Thanks for your comment.

    • bayoulady profile image


      10 years ago from Northern Louisiana,USA

      Congrats!You just might get a LOT of outside traffic on this. I have to review fractions every once in a while , because I just plain old forget!Ha!

    • JKeiser profile image


      10 years ago from Halstead, KS

      I like this hub. I found math fascinating when I went to college -- it suddenly made sense! From then on, I have seen most things in a mathematical relationship.

      Congratulations on your well-earned hubnugget nomination!

    • mathslover profile imageAUTHOR


      10 years ago from Barbados

      I am glad you found this hub useful ripplemaker, thanks for the commment.

    • mathslover profile imageAUTHOR


      10 years ago from Barbados

      Thanks alot equealla.

    • ripplemaker profile image

      Michelle Simtoco 

      10 years ago from Cebu, Philippines

      Ripplemaker's News: This is a wonderful hub on teaching you how to add and subtract fractions. If you want to vote for this hub on the Hubnuggets, you are just one click away. :) Great job Mathslover!

    • equealla profile image


      10 years ago from Pretoria, South Africa

      This is a very well explained writing on how to do it!

      If my work was introduced to me like this, when I went to school, perhaps my scores would have been much higher.

      Congratulations on the hubnugget nomination.

    • mathslover profile imageAUTHOR


      10 years ago from Barbados

      thanks easyguyevo,thats a good thing, school is good.

    • easyguyevo profile image


      10 years ago from Barbados

      Very informative,but it reminds me of school.Arhhhhhh!


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