Adding & Subtracting Improper Fractions

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  • 0:03 What Is an Improper Fraction?
  • 1:05 Rules for Adding & Subtracting
  • 3:11 Simplify
  • 4:29 Let's Try an Example
  • 5:53 Lesson Summary
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Lesson Transcript
Instructor: Kimberly Osborn
Improper fractions are those that have a larger number in the numerator and a smaller number in the denominator. This lesson will focus on showing you ways to easily and efficiently add and subtract improper fractions.

What Is an Improper Fraction?

Now I know the word fraction sometimes makes us feel a little nervous, especially when you start talking about the various rules that are associated with fractions. Let me assure you, however, that by the end of this lesson you will wonder exactly why you even felt anxious in the first place!

First off, it's important to understand the difference between the three types of fractions: proper, improper, and mixed number.

  • Proper Fractions: The numerator (top number) is smaller than the denominator (bottom number). For example: 1/3, 2/7, and 4/5.
  • Improper Fractions: The numerator is larger than the denominator. For example: 5/3, 9/2, and 7/4.
  • Mixed Numbers: This is a whole number combined with a proper fraction. For example: 3 1/2, 5 2/3, 21 5/6.

In the case of this lesson, we will be focusing our attention on improper fractions.

Rules for Adding & Subtracting Fractions

Before you get too worried about memorizing a new set of rules for improper fractions, let me begin by telling you that they involve the exact same rule set as those required for your standard proper fractions.

When adding and subtracting improper fractions you must first begin by finding a common denominator between your fractions. This means, you should find the smallest number that both of your denominators can go into evenly. As a simple rule of thumb, you can multiply both of your denominators together and use that as your new denominator.

Let's look at the improper fractions 5/3 and 7/5. We can multiply our denominators, 3 and 5 together to get a common denominator of 15. Now, to find our new numerators we must look at each fraction individually.

In our first improper fraction, 5/3 we can see that we multiplied our denominator 3 by a factor of 5 to get our new denominator of 15. What we do to the bottom, we must also do to the top to keep everything balanced. This means that we must multiply our numerator by a factor of 5 as well. This gives us a new numerator of 5 times 5, or 25. Our converted fraction is now 25/15.

We must do the same with our second improper fraction 7/5. We multiplied the denominator by a factor of 3 to get our new denominator of 15. We must then multiply our numerator by a factor of 3 as well to keep everything balanced. This gives us a new numerator of 7 times 3, or 21. Our converted fraction is now 21/15.

Now that we have a common denominator, our rules of fractions tell us that we can simply add or subtract our numerators, while keeping our denominator the same. Let's use our fractions from above to work out a concrete example of this rule.

Say you are given the problem:

5/3 - 7/5 = ?

Using the common denominators we converted above, we can rewrite the problem as:

25/15 - 21/15 = ?

Our rule tells us that we can then simply subtract our numerators (25 minus 21) and then keep our denominator of 15 the same. This means that our solution would then be 4/15.


It is super important to always check your answer to make sure that it is in its simplest form. Say you get a solution of 28/8 after working through an addition problem. You can't stop here and say that your final solution is 28/8 because your answer is not in simplest form. To simplify a fraction, we must determine if there are any numbers that can evenly go into both our numerator and denominator.

In this case, 28 and 8 are both divisible by a factor of 4. When you divide 28 by 4, you get the whole number 7. When you divide 8 by 4, you get the whole number 2. This means that our fraction in simplest form is then 7/2.

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