September 29, 2022

How to Add Fractions: Examples and Steps

Adding fractions is a usual math problem that kids study in school. It can appear scary initially, but it can be simple with a bit of practice.

This blog article will take you through the steps of adding two or more fractions and adding mixed fractions. We will then provide examples to show how this is done. Adding fractions is necessary for a lot of subjects as you progress in math and science, so be sure to master these skills early!

The Process of Adding Fractions

Adding fractions is a skill that many students have difficulty with. Despite that, it is a moderately simple process once you master the basic principles. There are three major steps to adding fractions: finding a common denominator, adding the numerators, and simplifying the results. Let’s carefully analyze every one of these steps, and then we’ll do some examples.

Step 1: Finding a Common Denominator

With these valuable points, you’ll be adding fractions like a pro in no time! The first step is to determine a common denominator for the two fractions you are adding. The smallest common denominator is the lowest number that both fractions will divide evenly.

If the fractions you wish to sum share the identical denominator, you can avoid this step. If not, to find the common denominator, you can determine the amount of the factors of respective number until you find a common one.

For example, let’s assume we want to add the fractions 1/3 and 1/6. The smallest common denominator for these two fractions is six in view of the fact that both denominators will split equally into that number.

Here’s a great tip: if you are unsure about this process, you can multiply both denominators, and you will [[also|subsequently80] get a common denominator, which would be 18.

Step Two: Adding the Numerators

Now that you acquired the common denominator, the following step is to convert each fraction so that it has that denominator.

To turn these into an equivalent fraction with the same denominator, you will multiply both the denominator and numerator by the exact number needed to attain the common denominator.

Subsequently the prior example, six will become the common denominator. To change the numerators, we will multiply 1/3 by 2 to get 2/6, while 1/6 will stay the same.

Considering that both the fractions share common denominators, we can add the numerators collectively to achieve 3/6, a proper fraction that we will be moving forward to simplify.

Step Three: Simplifying the Results

The final step is to simplify the fraction. Consequently, it means we need to diminish the fraction to its minimum terms. To achieve this, we find the most common factor of the numerator and denominator and divide them by it. In our example, the biggest common factor of 3 and 6 is 3. When we divide both numbers by 3, we get the ultimate result of 1/2.

You go by the same steps to add and subtract fractions.

Examples of How to Add Fractions

Now, let’s move forward to add these two fractions:

2/4 + 6/4

By applying the procedures mentioned above, you will notice that they share identical denominators. Lucky you, this means you can skip the initial stage. Now, all you have to do is add the numerators and let it be the same denominator as before.

2/4 + 6/4 = 8/4

Now, let’s try to simplify the fraction. We can notice that this is an improper fraction, as the numerator is larger than the denominator. This may suggest that you could simplify the fraction, but this is not necessarily the case with proper and improper fractions.

In this instance, the numerator and denominator can be divided by 4, its most common denominator. You will get a final result of 2 by dividing the numerator and denominator by 2.

Provided that you go by these procedures when dividing two or more fractions, you’ll be a professional at adding fractions in a matter of time.

Adding Fractions with Unlike Denominators

This process will require an supplementary step when you add or subtract fractions with different denominators. To do these operations with two or more fractions, they must have the same denominator.

The Steps to Adding Fractions with Unlike Denominators

As we mentioned prior to this, to add unlike fractions, you must obey all three procedures stated above to change these unlike denominators into equivalent fractions

Examples of How to Add Fractions with Unlike Denominators

Here, we will concentrate on another example by adding the following fractions:


As demonstrated, the denominators are distinct, and the smallest common multiple is 12. Thus, we multiply every fraction by a number to achieve the denominator of 12.

1/6 * 2 = 2/12

2/3 * 4 = 8/12

6/4 * 3 = 18/12

Once all the fractions have a common denominator, we will proceed to add the numerators:

2/12 + 8/12 + 18/12 = 28/12

We simplify the fraction by dividing the numerator and denominator by 4, finding a final result of 7/3.

Adding Mixed Numbers

We have talked about like and unlike fractions, but now we will touch upon mixed fractions. These are fractions followed by whole numbers.

The Steps to Adding Mixed Numbers

To figure out addition problems with mixed numbers, you must start by converting the mixed number into a fraction. Here are the procedures and keep reading for an example.

Step 1

Multiply the whole number by the numerator

Step 2

Add that number to the numerator.

Step 3

Note down your answer as a numerator and retain the denominator.

Now, you proceed by adding these unlike fractions as you generally would.

Examples of How to Add Mixed Numbers

As an example, we will solve 1 3/4 + 5/4.

Foremost, let’s convert the mixed number into a fraction. You will need to multiply the whole number by the denominator, which is 4. 1 = 4/4

Thereafter, add the whole number represented as a fraction to the other fraction in the mixed number.

4/4 + 3/4 = 7/4

You will conclude with this operation:

7/4 + 5/4

By summing the numerators with the exact denominator, we will have a ultimate answer of 12/4. We simplify the fraction by dividing both the numerator and denominator by 4, resulting in 3 as a conclusive answer.

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