Adding Three or More Fractions

In this video you will learn to add three or more fractions with different denominators.

Transcript

Welcome to MooMooMath where we upload a ne Math video everyday. In this video I would like to work on adding more than one fraction. In particular adding three fractions. For instance, how would you add 1/2 + 1/3 + 3/4. We will start with an easy one.

I line the fractions up in a vertical line. Put 1/2 + 1/3 + 3/4 in a vertical line. I then find a common denominator for all three fractions. I know 12 will be the common denominator. I know 2 will go into 12 6 times and 6 x 1 =6 so we have 6/12. I keep them in this vertical line. 3 goes into 12 4 times and 4 x 1 = 4, and 4 goes into 12 3 times, and 3 times 9 = 9.

I next just add them up and when I add them I get 19/12

I then can convert to a mixed fraction by dividing 19 by 12 which equals 1 7/12.

Lets look at another example. Lets add 1/2 + 3/4 + 7/8

I line them up in a vertical column, and then I start thinking about a common denominator of 2.4.and 8. 8 will be the common denominator. 2 goes into 2 times, so we have 2/8's, oops 2 goes into 8 4 times.

Next 4 goes into 8 2 times and 2 times 3 = 6 and 8 goes into 8 1 time so that equals 7/8.

Next I add them, 4/8 + 6/8+7/8 = 17/8.

I have an improper fraction and 8 will go into 17 two times which is 16 and that leaves 2 1/8.

Let me go over how I created the mixed fraction.

17 divided by 8 equals 2 and 17 -16 =1 so it becomes 2 1/8

On this last one I have mixed fractions.

What if you have the following?

1 1/2 + 21/6 + 3 1/4

You can line them up vertically.

Lets line them up and you have, 1 1/2 + 2 1/6 + 3 1/4

Next you can add the whole numbers, and 1 + 2 + 3 = 6

and you will add the fractions. I'm going to rewrite them

1/2 + 1/6 + 1/4

Find a common denominator, which is 12, and 2 goes into 12 6 times, 6 goes into 12 2 times, and 4 goes into 12 3 times. I next add them up and I get 6 + 2 + 3 = 11/12

Now I combine these two and end up with 6 11/12, and I can't simplify anymore.

Thanks for watching and we upload a new Math video everyday.

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How to add three or more fractions

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.
16/12

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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