Performing Fraction Operations in Math

Instructor: Deborah Schell

Deborah teaches college Accounting and has a master's degree in Educational Technology.

There are some special rules when completing basic operations with fractions. In this lesson, you will learn how to add, subtract, multiply and divide fractions.

Why Are Operations with Fractions Different?

Let's meet Jeff who is confused about how to work with fractions. His teacher and his friends have tried explaining it to him, but he is getting frustrated because he still doesn't understand it. Let's see if we can help Jeff with this problem.

A fraction is a number that is not a whole number and has a numerator and a denominator. A numerator is the upper part in a fraction that is above the line, and the denominator is the lower part of the fraction. Let's look at an example:


fraction example


In this example, 2 is the numerator and 5 is the denominator. Like whole numbers, we can add, subtract, multiply and divide fractions. Let's look at how we can complete these operations.

Adding Fractions

If we want to add fractions, we must make sure that the fractions have a common denominator or denominators that are the same. Let's assume that Jeff is trying to solve the following problem:


fraction addition ds


We can see that the denominators are not the same: one fraction has a denominator of 4 and the other has a denominator of 2. We need to find a denominator that both 2 and 4 go into. In this case, Jeff would want to make the denominator of each fraction 4.

Since 3/4 already has a denominator of 4, we will leave it as is. We will need to change 1/2 so it has a denominator of 4. To change the denominator, we need to determine how many times 2 (the existing denominator) goes into 4. The answer would be 2 (4 / 2). Therefore, we need to multiply both the numerator and the denominator by 2.


fraction addition common


Now we can add the fractions:


fraction addition answer


When the two fractions are added together, the answer is 3/4.

Subtracting Fractions

Just like adding fractions, subtracting fractions requires that we find a common denominator for the fractions. Let's look at the following example:


fraction sub example


We can see that the denominators in each fraction are different, so we must figure out the lowest number that each of the denominators will go into. In this case, both 2 and 3 go into 6 evenly, so we will have to change each fraction to have a denominator of 6.

Let's start with 1/2 first. We have to determine what we need to multiply 2 by to get the new denominator of 6. In this case, we need to multiply the numerator and the denominator by 3.


fraction sub common 1


Now let's look at 1/3. This time, we need to determine what we need to multiply the denominator of 3 by to turn it into 6. In this case, we need to multiply the numerator and the denominator by 2.


fraction sub common 2


Let's put it all together:


fraction sub answer


We can see that the answer is 1/6.

Multiplying Fractions

When we multiply fractions, we don't need to find a common denominator. We just multiply numerators together and then denominators together. Let's help Jeff work through the following problem:


fraction mult example


Remember that when we multiply fractions, we multiply numerator by numerator and denominator by denominator.


fraction mult answer


Therefore, the answer to the problem is 2/6, which we know we can reduce to 1/3 by dividing both the numerator and the denominator by 2.

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