September 29, 2022

How to Add Fractions: Examples and Steps

Adding fractions is a common math operation that children learn in school. It can seem scary initially, but it can be simple with a shred of practice.

This blog post will walk you through the procedure of adding two or more fractions and adding mixed fractions. We will also provide examples to demonstrate what must be done. Adding fractions is crucial for various subjects as you move ahead in science and mathematics, so make sure to master these skills early!

The Procedures for Adding Fractions

Adding fractions is an ability that numerous students have difficulty with. However, it is a moderately easy process once you understand the fundamental principles. There are three main steps to adding fractions: determining a common denominator, adding the numerators, and simplifying the answer. Let’s closely study each of these steps, and then we’ll work on some examples.

Step 1: Finding a Common Denominator

With these helpful points, you’ll be adding fractions like a professional in an instant! The first step is to find a common denominator for the two fractions you are adding. The smallest common denominator is the minimum number that both fractions will share uniformly.

If the fractions you want to sum share the equal denominator, you can avoid this step. If not, to find the common denominator, you can list out the factors of respective number as far as you find a common one.

For example, let’s assume we wish 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 uniformly into that number.

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

Step Two: Adding the Numerators

Now that you possess the common denominator, the following step is to change 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 identical number necessary to attain the common denominator.

Subsequently the last example, six will become the common denominator. To convert the numerators, we will multiply 1/3 by 2 to achieve 2/6, while 1/6 would remain the same.

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

Step Three: Simplifying the Results

The final process is to simplify the fraction. Doing so means we are required to reduce the fraction to its minimum terms. To accomplish this, we look for the most common factor of the numerator and denominator and divide them by it. In our example, the greatest common factor of 3 and 6 is 3. When we divide both numbers by 3, we get the final result of 1/2.

You follow the exact procedure to add and subtract fractions.

Examples of How to Add Fractions

Now, let’s proceed to add these two fractions:

2/4 + 6/4

By applying the process shown above, you will see that they share the same denominators. Lucky you, this means you can avoid the first step. Now, all you have to do is sum of the numerators and let it be the same denominator as before.

2/4 + 6/4 = 8/4

Now, let’s attempt to simplify the fraction. We can notice that this is an improper fraction, as the numerator is higher than the denominator. This may indicate that you could simplify the fraction, but this is not feasible when we work 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 ultimate result of 2 by dividing the numerator and denominator by 2.

As long as you go by these steps when dividing two or more fractions, you’ll be a expert at adding fractions in no time.

Adding Fractions with Unlike Denominators

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

The Steps to Adding Fractions with Unlike Denominators

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

Examples of How to Add Fractions with Unlike Denominators

At this point, we will focus on another example by adding the following fractions:


As you can see, the denominators are distinct, and the smallest common multiple is 12. Therefore, we multiply every fraction by a value to get 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 move ahead 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 answer of 7/3.

Adding Mixed Numbers

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

The Steps to Adding Mixed Numbers

To solve addition exercises 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 result as a numerator and keep the denominator.

Now, you move forward by adding these unlike fractions as you usually would.

Examples of How to Add Mixed Numbers

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

First, 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 described as a fraction to the other fraction in the mixed number.

4/4 + 3/4 = 7/4

You will end up with this result:

7/4 + 5/4

By adding the numerators with the exact denominator, we will have a ultimate result of 12/4. We simplify the fraction by dividing both the numerator and denominator by 4, ensuing in 3 as a final result.

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