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How To Add Mixed Fractions

Updated on June 15, 2013

This is Really Quite Easy

Mixed fractions are a combination of a whole number and a fraction. An example of a mixed fraction would be 1½ as in overtime pay is paid at the rate of 1½ times regular pay. Another example would be a recipe in which you are instructed to add 2 ¼ teaspoons of salt to the mixture.

Before going any further let's define the terms numerator and denominator. All fractions consist of two parts, a top part, which is called the numerator and the bottom part, which is called the denominator. Thus we have:

Numerator / Denominator

Next we have a couple of rules:

The First is: When adding any fractions we must first make sure that both fractions have the same denominator. If the fractions to be added do not have the same denominator then we must find a number into which the denominators of all the fractions to be added can be evenly divided into. While any number that can be evenly divided by each of the denominators will do, it is best if we find the smallest number that each can be evenly divided into – this is known as the least common denominator.

The Second is: we can either add fractions or whole numbers but not both together. To get around this, we convert the mixed number into a fraction by multiplying the whole number by the denominator and adding the result to the numerator. For example 1 ½ can be converted to a fraction by multiplying the whole number (1) by the denominator (2) to get the result of 2 which, when added to the numerator of 1 gives us 3. Our mixed number is now the fraction 3/2

An Example

Now that we know what is needed to add mixed numbers it is time for an example. Lets add:

1 ½ + 4 ¼ + 3 2/3

Since the denominators are all different, we will need to find the least common denominator which in this case is 12. Twelve is the smallest number that each denominator will divide into without leaving a fractional amount remaining. To give all of the fractions a 12 as the denominator we have to divide each denominator into 12 and multiply the result times the numerator to get our new numerator. Thus, to convert ½ to twelfths we change the denominator from 2 to 12 and divide two into twelve to get six. Multiplying the result which is six times the numerator which is 1 we get 6/12

Doing the same for the other fractions and leaving, for the moment, the numbers as mixed numbers we get:

1 6/12 + 4 3/ 12 +3 8/ 12

Next we convert the mixed numbers to fractions by multiplying the whole number by the denominator and adding it to the numerator to get:

18/ 12 + 51/ 12 + 44/ 12

Adding our numerators we get: 113/12

Finally, since the numerator is larger than the denominator, we convert this back to a mixed number by dividing the numerator 113 by the denominator 12 to get our answer which is: 9 5/12

This is how you add mixed fractions.

 

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    • eslob profile image

      Bandar F 

      6 years ago from Dammam

      math is interisting specialy with groups, if alone then its boring!

    • profile image

      Stuck 

      7 years ago

      So you say in this last "teaching".."Adding our numerators we get: 113/12

      Finally, since the numerator is larger than the denominator, we convert this back to a mixed number by dividing the numerator 113 by the denominator 12 to get our answer which is: 9 5/12

      This is how you add mixed fractions."

      ****IF YOU DIVIDE THE NUMERATOR (113) BY THE DENIMINAATOR (12)...HOW IS IT YOU GOT 9 5/12 FOR THE ANSWER?? WHERE DID 9 AND 5 COME FROM????? YOU REALLY NEED TO EXPLAIN MORE OF HOW YOU CAME TO 9 5/12...CUZ TO ME IT MAKES NO SENSE!!!!!!

    • profile image

      Nicole 

      7 years ago

      this is very confusing for a 6th grader tryin 2 get some info but i think i got it a little bit!!!!!

    • profile image

      Katherine 

      7 years ago

      This is actually Easy,now that I've read,tried,and solved this with the step by step.It seems very confusing but it is easy. Thank you Chuck,this was VERY hellppffuull!

    • profile image

      :) 

      7 years ago

      Yes this has helped lots!! Thank you!!!

    • profile image

      Mathwizard 

      7 years ago

      Wow i have to this website explains everything in a way that i can understand.:-) keep up the good work.thakz

    • profile image

      wow 

      7 years ago

      This was very helpful to me. Thank you!!

    • profile image

      cupcake  

      8 years ago

      thanks for helping me out . i mean im 30 and still go to school!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!well any way thanks bye!!!

    • adorababy profile image

      adorababy 

      8 years ago from Syracuse, NY

      To make it easy to add and subtract them, just convert to Improper Fractions first. This is what I do whenever I encounter them.

    • profile image

      chris 

      8 years ago

      Well i wanted to know how to do adding mix fractions with unlike denominators

    • rose06 profile image

      rose06 

      8 years ago

      u r syntist ,haha.................pls don't tell others pl...s..................pl...............s

    • profile image

      diva dancer 

      8 years ago

      This really helped I got a good grade on a quiz

    • profile image

      angelli 

      8 years ago

      thanks !! this website is very helpful !!

    • profile image

      undertaker 

      8 years ago

      vvvvvvvvvveeeeeeeeeerrrrrrrrrrrryyyyyyyyy HELPFUL

    • profile image

      ok 

      8 years ago

      this is very confusing for a 1st grader haha

    • jayb23 profile image

      jayb23 

      9 years ago from India

      wow..this is nostalgic, it makes me remember my school days. Great expalanation

    • profile image

      Babbiiy Gurl 

      9 years ago

      This Could Never Get Any More Confusing...!!  

    • profile image

      hi.. 

      9 years ago

      there is a shorter way of doing this... ex. 1 1/2 + 4 1/4 + 3 2/3..

      first add whole numbers we should get 8...get the lcd of 1/2, 1/4, 2/3..we get 12 as denominator..

      we should get this

      8 6+3+8/12..... 8 17/12..now we simplify.. 17/12=1 r. 5 .....add the whole number to the mix, 8+1 =9 we have 9 as whole number, then subtract the remainder for the mix's numerator... 17 - 12=5 we have 5 as numerator, and the denominator is the lcd which is 12..we now have 9 5/12

    • profile image

      mssuccess2000 

      9 years ago

      This was a great tool. Thank you. I needed a refresher course on mixed fractions to help my 5th grade daughter.

      I will be back for more lessons :-)

      Thanx from a happy mom!

    • profile image

      um ya im beast 

      9 years ago

      yea this iz wow nice job chuck =]

    • profile image

      carlo90 

      9 years ago

      thanks for it it help me in my assinment but it's a little bit hard to understand

    • profile image

      sharie 

      9 years ago

      this website is so beautiful it help my grade high

    • profile image

      jessica 

      9 years ago

      thank you so much! im trying to review my son for his math quarter exams. this has been very very helpful!!!

    • profile image

      Jackie 

      9 years ago

      I'm in nursing school and of course there is math involved and this really helped refresh my memory on how to add mixed fractions, Thank you!

    • profile image

      elizabeth 

      10 years ago

      wow this website really helped me. just read carefully and do the examples in a paper to memorize.

    • profile image

      goodboy 

      10 years ago

      this was rubish i dint even understand this was crap

    • profile image

      karlene 

      10 years ago

      If all teachers would take this approach to teaching math and other subjects there wouldn't be so many students struggling in college. Take a note teachers learn how to teach effectively or go back to teaching school. Thanks Karlene

    • profile image

      josenna 

      10 years ago

      wow that was pretty easy its great that they go through it step by step i understand now. Now

    • profile image

      tman 

      10 years ago

      it is real hard to do it but once you got the hang of it it is so easy

    • profile image

      juan34u 

      10 years ago

      i hate this website it is hard to understand the things written down.

    • profile image

      tinkerbell 

      10 years ago

      well i must say i never new how to do that

    • johnr54 profile image

      Joanie Ruppel 

      10 years ago from Texas

      I'll have to print this one out and save it for my 5th grader.

    • profile image

      Anna 

      10 years ago

      This website is very helpful

    • Bug Mee profile image

      Bug Mee 

      10 years ago from Great Midwest

      Never hurts to review a little math from time to time!!!!

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