Q. How to Add Fractions with Different Denominators?

Ans.

Here's the main thing to remember about adding fractions with different denominators-you can't! Fractions with different denominators cannot be added.

So what do you do? If you want to add the fractions, you have to make the denominators the same.

Fortunately, this isn't hard to do. Take this, for example:

1/2 +5/6

The denominators are different, but we'll fix that.

Step 1. Factor the denominators

Step 2. Notice what the differences are .

Step 3. Figure out what extra factors are needed to make the denominators equal. If the left-hand denominator had a factor of 3, then they would be equal.

Step 4. Put in the extra factors. (Be sure to put them both in the numerator and denominator!) Here, we'll put the extra 3 factor in the left hand fraction, both top and bottom:

Remember, this is allowed, because multiplying the numerator and denominator of a fraction by the same number doesn't change the value of the fraction.

Step 5. Now the denominators are the same, and you can add. You can simplify the numerators, but don't simplify the denominators yet!

Step 6. Reduce (simplify) This is the reason you didn't simplify the denominators in the previous step: because it's nice to be able to see the factors 2 and 3. You know that 2 is also a factor of 8, so you can cancel out a 2:

And that's all!