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Jun02

How to Find a Sum of Fractions

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In this post, we are going to learn how to find a sum of fractions.

Before you begin to add fractions, it is advisable that you know how to calculate the least common multiple (LCM) of two or more numbers.

To calculate a sum of fractions, the important thing is that the fractions have the same denominator.

Sum of fractions with the same denominator:

To add fractions with the same denominator you have to add the numerators and leave the same denominator.

For example:

sum of fractions

Since the 2 fractions have the same denominator, what we have to do is keep the same denominator, which is 4, and add the numerators.

3 + 2 = 5

And the result of the sum of fractions is:

sum of fractions

Sum of fractions with different denominators:

To add fractions with different denominators, the first thing that you have to do is find a common denominator: this is the least common multiple of the denominators that you have. Then we multiply each numerator by the number that we have multiplied the denominator by. Finally, we add the numerators that we have obtained and keep the same denominator.

For example,

sum of fractions

The first thing to do is find a common denominator between 3 and 5. To do this, we calculate the least common multiple between both numbers.

LCM(3,5) = 15

So 15 is the common denominator of the two fractions.

sum of fractions

Now we have to multiply each numerator by the number that we have multiplied the denominator by. To do this, we divide the LCM by the initial denominator and multiply the result by the numerator of that fraction.

For the first fraction:

15 / 3 = 5

5 x 2 = 10

So 10 is the numerator of the first fraction.

For the second fraction:

15 /  5 = 3

3 x 4 =12

So 12 is the numerator of the second fraction.

sum of fractions

Now all we have left to do is add the numerators:

10 + 12 = 22

And the result of the sum of fractions is:

sum of fractions

I hope that you have learned with this post how to to find a sum of fractions.

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