# How do you do add fractions

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

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To add fractions, you have to convert the fractions into the same family.  This is also called ‘finding the common denominator’ – the denominator is the bottom number (or family) and ‘common’ means they are the same.   If you have

½ + ¼

it is easy to convert, because ½ is the same as 2/4.  So, you get

2/4 + ¼

Now just add the numerators – you have 2 of something and add another 1 of the same thing, you have 3 of them all together.

2/4 + ¼ = ¾

What if you can’t change one of them to be the same as the other?  For example,

1/3 + ¼

You have to find a third number that they both CAN go into – this is called finding the ‘lowest common multiple’.  The new number has to be a multiple of both 3 and 4.  You want the smallest number that works.

3 x 1 = 3 no

3 x 2 = 6 no

3 x 3 = 9 no

3 x 4 = 12 yes!  4 goes into 12 evenly too

To convert 1/3, multiply TOP AND BOTTOM by how many times 3 goes into 12 -- which is 4.  You get 4/12.

To convert 1/4, multiply TOP AND BOTTOM by how many times 4 goes into 12 -- which is 3.  You get 3/12.

4/12 + 3/12 = 7/12

The key thing to remember is to multiply top and bottom by the same thing.

jennifer-taubenheim | Middle School Teacher | (Level 2) Assistant Educator

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In a fraction, the top number is called the numerator and the bottom number is called the denominator.

To add fractions together, the two denominators have to have the same number on the bottom (a common denominator). If they have a common denominator, add the top numbers together and keep the bottom number the same.

EG. 1/3 + 1/3 = 2/3

If the two fractions do not have a common denominator, you have to find one before you can add them. You do this by finding the lowest common multiple (or the smallest number that both can go into. You find equivalent fractions based on the new common denominator and then add.

EG. 1/6 + 1/3

The lowest common multiple would be 6. To change 1/3 into a fraction with a denominator of 6, you would have to multiply the denominator by 2. Then you multiply the numerator by the same number. You multiply the top and bottom by the same number so that the new fraction is an equivalent fraction. This is kind of the opposite of reducing.

1/3 = 2/6

Once you have common denominators, then you can add the two fractions together.

1/6 + 2/6 = 3/6

Then you would reduce the fraction to lowest terms by dividing both the numerator and denominator by the same number.

See one of the websites below for an explanation with images.

jess1999 | Student, Grade 9 | (Level 1) Valedictorian

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In order to add fractions, 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

atyourservice | Student, Grade 11 | (Level 3) Valedictorian

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You have to get a common denominator, for example if somebody tells you to

add 1/3 and 1/4 you have to find the lowest number that both 3 and 4 have in

common, which would be 12, so you multiply each number by a multiple so that

both bottom numbers would be 12.    1/3 by 4 and 1/4 by 3

4/12 + 3/12 now add them straight across and you would end up with 7/12

lakeltra | Student | eNotes Newbie

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t0 add you have to wel if the denumenator is the same you add the top number together and leave the bottom the denumenator stays the same.example~1/2 1/2 add 1+1=2/2

kevin0001 | Student, Grade 9 | (Level 1) Salutatorian

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To add fractions, their denominators have to be the same, also called having common denominators. After getting the common denominators, you just add the numerators together and you should get your sum. Here is an example :

1/2 + 5/12      The equation

1/2 (6/6) + 5/12  Get the denominators to be equal. 6 times 2 is 12 so that would get you a common denominator. Remember! What ever you do to the denominator, also do the same thing to the numerator.

nisarg | Student, Grade 11 | (Level 1) Valedictorian

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to add fractions first get them to have a common denominator

then simply add the top numbers together

1/2+1/4=

2/4+1/4=3/4

zumba96 | Student, Grade 11 | (Level 3) Valedictorian

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In math or in any case, if you are adding fractions you need to have common denominators. With two fractions with different denominators, get the fractions to have a common denominator by finding its LCM (Lowest Common Multiple) and adding them together. For example with same denominators

`(1/5)+(3/5)=4/5`

But if its not equal; `(1/5)+(1/2)=?`

``

`then multiply the denominator to get the LCM which in this case is 10. So if you multiply 1/5 by 2 and 1/2 by 5 and add the the answer would equal 7/10`

` <br data-mce-bogus="1"> `

zumba96 | Student, Grade 11 | (Level 3) Valedictorian

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If you multiply 1/5 by 2 and 1/2 by 5 and add them up you should get 7/10. I rewrote this because for some reason the explanation doesnt turn out normally

parama9000 | Student, Grade 11 | (Level 1) Valedictorian

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There are many ways.

You can try converting the denominator into the same one as the first fraction and add the numerators together.

You can simply multiply the denominators together to form a common denominator and add the numerators multiplied by their respective denominators.

For example, 1/2+3/8=(1x8+3x2)/16= 14/16=7/8

In the example above, you may also simply convert 1/2 to 4/8 , which will be more efficient.

acompanioninthetardis | Student, Undergraduate | (Level 1) Valedictorian

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To add fractions you simply try to get a common denominator or a common bottom number and then add the two numbers on the top together.

Jyotsana | Student, Grade 10 | (Level 1) Valedictorian

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Example: 2/3+3/4

cross multiply  2*4=8   3*3=9

multiply the denominator  3*4=12

8/12+9/12    you just have to add the numerators

17/12

You always have to make sure that both of the denominators are same when you are adding the fractions.

saransh2012 | Student | (Level 1) Honors

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In a fraction the top number is called a numerator & the bottom number is called denominator.Example-3/2

In the example 3 is the numerator & 2 is the denominator.If the denominators in the both terms are same then it can easily be added. For example

1/2+3/2 =4/2=2/1=2

If the denominators in the both terms are not same then we can do it by LCM (lowest common mutiple)

Example=LCM of 2,3 and 4

IF there is no number common while doing LCM we can multiply it.

Example=1/3+1/5+1/9

15/45+9/45+5/45=29/45

If the denominator is smaller than the numerator it can be converted to mixed fraction.

jackandchill | Student, Grade 10 | eNotes Newbie

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Adding fractions you  need to just make sure that all the fractions have the same denominator. Then you can simply add the numerators alone.For that you need to find a LCD.

revolution | College Teacher | (Level 1) Valedictorian

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First, get a common denominator, meaning find the lowest common multiple  like 2/3 +1/6= 4/6 +1/6

Then, you can add the numerator on top together 4/6+1/6=5/6

If need be, simplify to lowest terms. If not, leave it be.

dracomath | Student, Grade 11 | (Level 1) Honors

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In order to add fractions you must make sure that all fractions have same denominators.  First, find the LCD.  Then, add both numerators.