To add and subtract fractions, first, make sure that the denominators are the same. If they aren’t, like in 5/9 – 1/6, then we need to find the least common denominator.

The least common multiple of 9 and 6 can be found by listing the multiples 9, 18, 27, etc. 6, 12, 18. Our least common multiple is 18, so we’re going to change both of our fractions, 5/9 to something over 18, and 1/6 to something over 18.

The next lesson: Multiplying and Dividing Fractions

**The following transcript is provided for your convenience.**

9 times 2 is 18, so since we multiplied our denominator times 2, we must also multiply our numerator times 2, 5 times 2 is 10.

6 times 3 is 18, so we must also multiply our numerator times 3, and we get 3/18.

So, that means that 5/9 – 1/6 is equal to 10/18 – 3/18.

Now, we just subtract our numerators and put that difference over our denominator of 18. 10-3 is 7. Then, if you can simplify the result, you should, but in this case, 7/18 cannot be simplified, so that’s our answer.

Let’s look at an addition problem. Again, we’ve got to see if our denominators are the same, and if they aren’t, then we need to change them so that they are. So, we’re going to find the least common denominator for 3 and 5, which means we’re finding the least common multiple for 3 and 5. So, I’ll list the multiples, 3, 6, 9, 12, 15. And my multiples for 5 – 5, 10, 15. So, my least common multiple is 15, which means I’m going to change both my denominators to something over 15, 2/3 equals something over 15, and 4/5 equals something over 15.

So, to get from 3 to 15, we have multiply times 5, so we need to do the same to our numerator, 2 times 5 is 10.

5 to 15, we have to multiply 5 times 3, so we do the same to our numerator, 4 times 3 is 12, which means that 2/3 + 4/5 is the same as 10/15 + 12/15, and again, we add the numerators, and put that result over our denominator, 10+12 is 22.

And this is an improper fraction since our numerator is larger than our denominator, so we’d want to change it to a mixed number. To change this improper fraction to a mixed number, we’re going to divide our numerator by our denominator, 22/15 is 1, since 15 goes into 22 one time, with 7 leftover out of, and the denominator stays the same. So, 1 7/15 is our result.