Subtraction of Fractions

πŸ†Practice subtraction of fractions

To subtract fractions, we must find the common denominator by simplifying, expanding, or multiplying the denominators.
Then, we only need to subtract the numerators to get the result.

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Solve the following exercise:

\( \frac{3}{2}-\frac{1}{2}=\text{?} \)

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Subtraction of Fractions

In this article, we will learn how to subtract fractions in a simple and quick way.
By the way, subtracting fractions is very similar to adding fractions, therefore, if you know how to add them, you will know how to subtract them without any problem.
Shall we start?

The first step to solving fraction subtractions is to find the common denominator.
This way, we will have two fractions with the same denominator.
We will do this by simplifying, expanding, or multiplying the denominators.
After finding the common denominator, ensuring that both fractions have the same denominator, we will move on to the second step of the resolution.
The second step to solve a subtraction of fractions is to subtract the numerators.
We will encounter different cases of subtractions that we will study below:

First case:

One of the denominators that appears in the initial exercise will be the common denominator.

Sometimes, we will have exercises in which it will be enough to carry out a single operation on a single fraction to achieve a common denominator.

Let's look at an example


Upon observing these denominators, we will immediately realize that, if we multiply the denominator 33 by 22, we will reach the denominator 66.
This way, we will reach the common denominator and will be able to solve the exercise easily.

Observe - When multiplying the denominator to transform it into a common denominator, we must also multiply the numerator by the same number so that the value of the fraction does not change.

We will do this by multiplying by 22 and we will obtain:


Now let's move to the second step and subtract the numerators.
Attention – We do not subtract the denominators.
When we obtain an identical common denominator only the numerators are subtracted and, from now on, the denominator is written only once.

Let's see it in an exercise


We subtract 5βˆ’25-2 and leave the denominator only once.

If we wish, we can simplify the result and write it this way 121 \over 2 Another exercise:

We will realize that, if we multiply 22 by 22 we will get 44 this will be the common denominator.

We will obtain:


Let's subtract the numerators and we will get:

343 \over 4

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Second case

The common denominator will be the product of the given denominators.

Sometimes we will come across exercises in which it will not be enough to expand a single fraction to obtain the common denominator, but rather, we must intervene in both fractions.
In such a case, simply, we multiply the first fraction by the denominator of the second and the second fraction by the denominator of the first.

Let's look at an example

Let's multiply the denominators:
We will multiply 474 \over 7 by 33 (the denominator of the second fraction) and 131 \over 3Β by 77 (the denominator of the first fraction).
We will obtain:


Let's subtract the numerators and we will arrive at the solution:
5215 \over 21

Tip - This method is technical and does not require us to think about how to find the common denominator.
Therefore, we recommend using it in all fraction subtraction exercises.

Third case

Subtraction of 3 Fractions

In case there were in the exercise 33 fractions with different denominators, we will first find the common denominator for 22 of them (the simplest ones), then we will find the common denominator between the obtained one and the third given fraction.

Let's see an example and you will understand how simple this is:

Let's look at the denominators and ask ourselves - Among the three denominators, which 22 is it easier to find a common denominator for?
The answer is 55 and 1010, since 1010 is the common denominator for both.
Therefore, we will multiply 151 \over 5 by 22 and obtain:
Now we can subtract the numerators that already have a common denominator to arrive at a clearer and more orderly exercise (this step is not mandatory, but it will help us later):

Now we just need to find the common denominator between 1010, the new denominator we found, and 33 the third denominator of the exercise.
We will do it with the method of multiplying denominators and obtain:
Let's subtract the numerators and we will obtain:
1301 \over 30

Do you know what the answer is?
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