How to Add Fractions: Steps and Examples

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

This blog post will walk you through the procedure of adding two or more fractions and adding mixed fractions. We will also give examples to show how it is done. Adding fractions is necessary for a lot of subjects as you progress in math and science, so make sure to adopt these skills initially!

The Process of Adding Fractions

Adding fractions is an ability that many students struggle with. Nevertheless, it is a somewhat easy process once you understand the fundamental principles. There are three primary steps to adding fractions: determining a common denominator, adding the numerators, and streamlining the answer. Let’s closely study every one of these steps, and then we’ll work on some examples.

Step 1: Finding a Common Denominator

With these valuable points, you’ll be adding fractions like a expert in a flash! The first step is to find a common denominator for the two fractions you are adding. The least common denominator is the lowest number that both fractions will divide uniformly.

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

For example, let’s say we desire to add the fractions 1/3 and 1/6. The smallest common denominator for these two fractions is six for the reason that both denominators will divide 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

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

To change these into an equivalent fraction with an identical denominator, you will multiply both the denominator and numerator by the exact number required to get the common denominator.

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

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

Step Three: Streamlining the Answers

The final process is to simplify the fraction. Doing so means we need to reduce the fraction to its minimum terms. To accomplish this, we search for 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 concluding 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 utilizing the steps above, you will observe that they share equivalent denominators. You are lucky, this means you can skip the initial stage. 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 see that this is an improper fraction, as the numerator is higher than the denominator. This might indicate that you could simplify the fraction, but this is not necessarily the case with proper and improper fractions.

In this example, the numerator and denominator can be divided by 4, its most common denominator. You will get a ultimate answer of 2 by dividing the numerator and denominator by 2.

As long as you follow these procedures when dividing two or more fractions, you’ll be a professional at adding fractions in matter of days.

Adding Fractions with Unlike Denominators

The procedure will require an supplementary step when you add or subtract fractions with distinct 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 above, to add unlike fractions, you must follow all three procedures 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:

1/6+2/3+6/4

As shown, the denominators are dissimilar, and the least common multiple is 12. Hence, we multiply every fraction by a value to attain the denominator of 12.

1/6 * 2 = 2/12

2/3 * 4 = 8/12

6/4 * 3 = 18/12

Since all the fractions have a common denominator, we will move ahead to total the numerators:

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

We simplify the fraction by splitting the numerator and denominator by 4, coming to the final answer of 7/3.

Adding Mixed Numbers

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

The Steps to Adding Mixed Numbers

To figure out addition sums with mixed numbers, you must start by turning 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

Note down your answer as a numerator and retain 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 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

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

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