September 29, 2022

How to Add Fractions: Examples and Steps

Adding fractions is a common math operation that children study in school. It can appear daunting initially, but it can be simple with a tiny bit of practice.

This blog article will take you through the process of adding two or more fractions and adding mixed fractions. We will then give examples to see how this is done. Adding fractions is essential for a lot of subjects as you progress in science and mathematics, so be sure to adopt these skills early!

The Process of Adding Fractions

Adding fractions is a skill that numerous students struggle with. Nevertheless, it is a somewhat easy process once you master the fundamental principles. There are three primary steps to adding fractions: finding a common denominator, adding the numerators, and streamlining the results. Let’s carefully analyze every one of these steps, and then we’ll do some examples.

Step 1: Determining a Common Denominator

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

If the fractions you desire to add share the identical denominator, you can skip this step. If not, to find the common denominator, you can determine the number of the factors of each number until you determine a common one.

For example, let’s say 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 divide uniformly into that number.

Here’s a great tip: if you are uncertain regarding 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

Once you have the common denominator, the immediate step is to convert each fraction so that it has that denominator.

To turn these into an equivalent fraction with an identical denominator, you will multiply both the denominator and numerator by the exact number necessary to achieve the common denominator.

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

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

Step Three: Streamlining the Answers

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

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

Examples of How to Add Fractions

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

2/4 + 6/4

By utilizing the process shown above, you will observe that they share the same denominators. Lucky you, this means you can skip the first step. At the moment, all you have to do is sum of the numerators and leave the same denominator as it was.

2/4 + 6/4 = 8/4

Now, let’s attempt to simplify the fraction. We can perceive that this is an improper fraction, as the numerator is greater than the denominator. This could suggest 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 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 expert at adding fractions in no time.

Adding Fractions with Unlike Denominators

The procedure will require 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 above, 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 focus on another example by adding the following fractions:


As shown, 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 go forward to total the numerators:

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

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

Adding Mixed Numbers

We have mentioned like and unlike fractions, but now we will go through mixed fractions. These are fractions followed by whole numbers.

The Steps to Adding Mixed Numbers

To figure out addition sums with mixed numbers, you must start by converting the mixed number into a fraction. Here are the steps 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

Take down your result as a numerator and keep the denominator.

Now, you proceed by summing these unlike fractions as you usually would.

Examples of How to Add Mixed Numbers

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

Foremost, let’s change 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 end up with this operation:

7/4 + 5/4

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

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