Adding Fractions

Adding fractions is the first of the fraction skillset you need to master before you can move into complex math problems. However, this may require a significant amount of practice before you feel comfortable.

Necessary Skills

Depending on the problem, the below skills may be necessary. You will need them on an actual math GED® exam.

The Idea of a Common Denominator

A common denominator is a necessity for adding and subtracting fractions. The denominator is the lower number on a fraction. It indicates how many pieces the metaphorical pie is cut into. If we try to add two different denominators, we’re talking about two different size pieces of pie. That gets confusing quickly.

The solution is changing the denominator before you do math on it. The trick is multiplying the top and bottom of the fraction by the same number. This maintains the fraction at equivalency and will make your math problem turn out correct.

So, in summation, the goal is to reach the same denominator with the two fractions involved in the math problem. To do this, you treat each fraction as an individual and only multiply that numerator and denominator by the same number. Then we’re all talking about the same size pieces of metaphorical pie.

Important note: Adding or subtracting does not affect the common denominator. The answer will also share the common denominator until you reduce it.

mixed number structure

The Steps for Adding Fractions (Conversion)

There are two primary ways to handle fractions, and we’ll start with the conversion method. This method works reliably for all manner of problems. However, you will probably need the calculator provided for your exam once you get to double digit fractions.

The first step for this method is converting the mixed numbers, if there are any, to improper fractions. This allows you to manipulate the numbers on a level playing field.

The next step is finding the common denominator. You can find lower common denominator, but it requires knowledge of your times tables. The simplest method, however, is multiplying by the opposite bottom. Make sure you multiply both the numerator and denominator by the same number while you’re finding the common denominator.

Once you have a common denominator, you can proceed with adding the fractions. When adding fractions, you should only add the numerators (tops). The denominator will stay the same. Don’t worry if the numerator become bigger than the denominator.

If the numerator is bigger than the denominator, convert the improper fraction to a mixed number. If the denominator is bigger, see if you can reduce the fractions. See the necessary skills section on how to do this.

The Steps for Adding Fractions (Non-Conversion)

Now we’ll talk about the borrowing method. For this method, you do not convert any mixed numbers into improper fractions. Instead, you’ll only deal with them if you need to borrow (see subtraction) or when you have an improper fraction in the answer.

While you’re seeking a common denominator, remember to only drag the whole number around, do not multiply it like you would the fraction parts. Instead, focus on the fraction. The same trick of multiplying by the opposite fraction’s bottom number does work.

Once you have a common denominator, you are going to add the whole numbers. Then you can add the numerators. With common denominators, you simply move the denominator value into the answer, no math required.

If the numerator is bigger than the denominator, you have an improper fraction. You can follow the procedure outlined in the necessary skills section or ask your self how many times the denominator fits in the numerator. You can add the answer to that to the whole number. If the numerator is smaller than the denominator, make sure you reduce it as outlined above.

Example Problems for Adding Fractions

Let’s work on a few example problems so you can get a good feeling for adding fractions.

Example 1

Let’s start with ½ + 1/3. Since there are no mixed numbers, there is only one procedure. We will multiply the ½ by 3 on the top and bottom. Then we multiply 1/3 by 2 on the top and bottom. The new problem is 3/6 + 2/6. We then add the numerators. Since we drag over the common denominator, that equals 5/6.

Adding fractions example 1

Example 2

Now let’s consider 11/3 + 34/5. Since there are mixed numbers, we’ll convert them so the problem looks like 4/3 + 19/5. This is where calculators are handy, since we must multiply both parts of 4/3 by 5 and both parts of 19/5 by 3. This makes the problem 20/15 + 57/15. Upon addition, that’s 77/15, which we then have to convert to a mixed number (see above). The final answer is 52/15.

If you want to use the non-conversion method on 11/3 + 34/5, it goes like this. We’ll drag the whole numbers along with the fractions as we multiply for the common denominator. Multiplying be the opposite bottom gets us 15/15 + 312/15. We then add the whole numbers together and the numerators together. That gets us 417/15. We then determine 15 goes int 17 once with 2 left over. That makes our final answer 52/15.

Faction addition example 2

Example 3

For our final example, let’s look at 71/2 + 3/5. We need to convert 71/2 to an improper fraction, 15/2. The we multiply by the opposite bottom, turning the problem into 75/10 + 6/10. That comes to 81/10. From there, it’s converting back to a mixed number, 81/10.

For our final example, let’s look at 71/2 + 3/5 from a non-conversion perspective. We jump right into multiplying the opposite bottoms against the respective fractions. That gets us 75/10 + 6/10. Then we add the numerators for a total of 711/10. After figuring out 10 goes into 11 once and adding the whole, we end up with 81/10.

Adding fractions example 3