How to Add Fractions: Steps and Examples

Adding fractions is a usual math problem that students learn in school. It can appear scary at first, but it can be easy with a bit of practice.

This blog post will take you through the process of adding two or more fractions and adding mixed fractions. We will also provide examples to show how this is done. Adding fractions is essential for a lot of subjects as you progress in mathematics and science, so make sure to learn these skills initially!

The Procedures for Adding Fractions

Adding fractions is an ability that a lot of kids struggle with. However, it is a somewhat hassle-free process once you understand the basic principles. There are three primary steps to adding fractions: finding 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 professional in an instant! The first step is to find a common denominator for the two fractions you are adding. The least common denominator is the minimum number that both fractions will share uniformly.

If the fractions you wish to add share the equal denominator, you can avoid this step. If not, to look for the common denominator, you can list out the factors of each number until you find a common one.

For example, let’s say 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 quick tip: if you are not sure 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 possess the common denominator, the next step is to change each fraction so that it has that denominator.

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

Subsequently the prior 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 proceed to simplify.

Step Three: Simplifying the Results

The last step is to simplify the fraction. Consequently, it means we need to lower 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 greatest 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 exact 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 notice that they share identical denominators. Lucky you, this means you can skip the initial stage. At the moment, all you have to do is add the numerators and leave the same denominator as before.

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 higher than the denominator. This could suggest that you can 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.

Provided that you go by these steps when dividing two or more fractions, you’ll be a pro at adding fractions in matter of days.

Adding Fractions with Unlike Denominators

This process will need 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 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 stated above to transform these unlike denominators into equivalent fractions

Examples of How to Add Fractions with Unlike Denominators

Here, we will put more emphasis on another example by summing up the following fractions:

1/6+2/3+6/4

As shown, the denominators are distinct, and the least common multiple is 12. Thus, we multiply every fraction by a number 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 add the numerators:

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

We simplify the fraction by splitting the numerator and denominator by 4, concluding with a ultimate result 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 work out addition problems with mixed numbers, you must initiate 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

Write down your answer as a numerator and keep the denominator.

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

Examples of How to Add Mixed Numbers

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

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

4/4 + 3/4 = 7/4

You will be left with this result:

7/4 + 5/4

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

Use Grade Potential to Better Your Math Skills Now

If you're having problems understanding adding fractions, consider signing up for a tutoring class with Grade Potential. One of our expert instructors can help you grasp the material and nailcrack your next examination.