How to add three or more fractions

Monday, January 18, 2016

Adding more than two fractions at a time is just like adding two fractions, but slightly different at the same time.
Before you add the fractions ,you need to make sure all of the denominators are the same, but instead of just two fractions you will be looking at several fractions.
Also, if you have to find a least common denominator, you will need to find a common denominator for several numbers.
Follow these simple steps for adding three or more fractions.

Step 1: Check to see if the denominators (bottom numbers) are the same.

Step 2.  If they are not the same find a least common denominator for all of the fractions.
The least common denominator is the smallest positive integer that is a multiple of each denominator in the set of fractions.
For example, say you are adding the following fractions, 1/3 + 2/4 + 1 /2.
The least common denominator (LCD)  would be 12 because all three of the numbers divide evenly into 12.

Divide the denominator into the least common denominator, and multiply this number by the numerator for each fraction.
For example:  2/4
12 ÷ 4 = 3
3 x 2 = 6
So the fraction becomes   6/12
Repeat this for each fraction.

1/3 becomes 12 ÷3 = 4
4 x 1 = 4
The fraction becomes 4/12
And 1 /2 becomes 6/12

Step 3. Add the top numerators (top numbers)
6 + 4 + 6 = 16

Step 4. Place the answer over the denominator from step 2.

Step 5. Simplify the fraction if possible.
16 ÷ 12 = 2 4/12

2 4/12 can be simplified to   2 1/3

Remember, you can add the fractions in any order and get the same answer.
For example, 2/3 + 1/4 + 5/6 will equal 5/6 + 1/4 + 2/3.

Here is a link to a helpful fraction calculator so you can check your work.

This least common denominator calculator may come in handy also.

Follow moomoomath's board Math Resources and helpful information on Pinterest.


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