Adding Fractions with the Same Denominators
Adding fractions is easy when your addends already have the same denominator. All you have to do is add the numerators and use the same denominator.


Here are a few examples:

1/4 + 2/4 = 3/4



As you can see, the numerators 1, 2 and 3 were added and the sum has the same denominator as the addends.

20/41 + 8/41 = 28/41



31/101 + 11/101 + 14/101 = 46/101




Now, when the sum of the fractions you're adding is not in its simple form, you just need to simplify it.


3/20 + 7/20 = 10/20 or 1/2



17/200 + 3/200 + 30/200 = 50/200 or 1/4






Adding Mixed Fractions with the Same Denominators



When adding mixed fractions you need to convert the mixed fraction into an improper fraction. The equivalent improper fraction will have the same denominator. To get the numerator, multiply the denominator by the whole number and add the original numerator to it.

Here is an example of a mixed fraction converted into its equivalent improper fraction:

2 1/4 = (4 x 2) +1/4


(8)+1/4 = 9/4





Here's an example of adding mixed fractions:

1 1/4 + 2 3/4 = (4 x 1) +1/4 + (4 x 2) +3/4


(4)+1/4 + (8)+3/4 = 5/4 + 11/4


5/4 + 11/4 = 16/4 or 4





When adding a mixed fraction and a fraction, you convert the mixed fraction first and then proceed to adding the fractions:

1 3/4 + 3/4 = (4 x 1) +3/4 + 3/4


(4) +3/4 + 3/4 = 7/4 + 3/4


7/4 + 3/4 = 10/4 or 2 2/4 or 2 1/2




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