# Adding and Subtracting Fractions

## Adding and Subtracting Fractions

To add and subtract fractions, first make sure that the denominators are the same. If they aren’t, like in 5/9 minus 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 the least common multiple is 18. We’re going to change both of our fractions, 5/9 to something over 18, and 1/6 to something over 18.

9 times 2 is 18. 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. We must also multiply our numerator times 3, and we get 3/18.

That means that 5/9 minus 1/6 is equal to 10/18 minus 3/18. Now we just subtract our numerators, and put that difference over our denominator of 18. 10 minus 3 is 7. Then, if you can simplify the result, you should.

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.

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. I’ll list the multiples: 3, 6, 9, 12, 15. My multiples for 5: 5, 10, 15. So my least common multiple is 15.

Which means I’m going to change both of my denominators to something over 15. 2/3 equals something over 15, and 4/5 equals something over 15. To get from 3 to 15, we have to multiply times 5.

We need to do the same to our numerator. 2 times 5 is 10, 5 to 15, we have to multiply 5 times 3. We do the same to our numerator, 4 times 3 is 12. Which means that 2/3 plus 4/5 is the same as 10/15 plus 12/15.

Again, we add the numerators, and put that result over our denominator. 10 plus 12 is 22. 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 divided by 15 is 1, since 15 goes in a 22 to 1 time with 7 leftover, out of, and the denominator stays the same. 1 7/15 is our result.