Subtracting Fractions

Subtracting fractions is the second part of the fraction skillset you need to master before you can move into complicated math problems. However, this may require 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 subtract 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 Subtracting 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 subtracting the fractions. When subtracting fractions, you should only subtract 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 Subtracting Fractions (Non-Conversion)

Now we’ll talk about the non-conversion 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 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 subtract the numerators. If the second numerator is bigger than the first, you will need to borrow from the whole number. Then you can subtract the whole numbers. 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 yourself 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 Subtracting Fractions

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

Example 1

Let’s start with 1/31/2. Since there are no mixed numbers, there is only one procedure. We first multiply 1/3 by 2 on the top and bottom. Then we multiply the ½ by 3 on the top and bottom. The new problem is 3/62/6. We then subtract the numerators. Since we drag over the common denominator, that equals 1/6.

Subtracting fractions example 1

Example 2

Now let’s consider 34/5 – 11/3. Since there are mixed numbers, we’ll convert them so the problem looks like 19/5 – 4/3. 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 57/1520/15. Upon subtraction, that’s 37/15, which we then have to convert to a mixed number (see above). The final answer is 27/15.

If you want to use the non-conversion method on 34/5 – 11/3, 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 312/15 – 15/15. We then subtract the numerators numbers together and the whole numbers together. That gets us a final answer of 27/15.

Fraction subtraction example 2

Example 3

For our final example, let’s look at 71/23/5. We need to convert 71/2 to an improper fraction, 15/2. Then we multiply by the opposite bottom, turning the problem into 75/106/10. That comes to 69/10. From there, it’s converting back to a mixed number, 69/10.

For our final example, let’s look at 71/23/5 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 subtract the numerators, which requires borrowing from the 7 so that the new value looks like 615/10. Then we can subtract, bring out the final answer of 69/10.

Subtracting fractions example 3