How to Add Fractions: Steps and Examples

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

This blog post will walk you through the steps of adding two or more fractions and adding mixed fractions. We will then provide examples to show how it is done. Adding fractions is crucial for a lot of subjects as you advance in math and science, so ensure to learn these skills initially!

The Steps of Adding Fractions

Adding fractions is a skill that numerous students have difficulty with. Nevertheless, it is a somewhat simple process once you understand the fundamental principles. There are three main steps to adding fractions: finding a common denominator, adding the numerators, and streamlining the results. Let’s closely study every one of these steps, and then we’ll look into some examples.

Step 1: Finding a Common Denominator

With these valuable points, you’ll be adding fractions like a pro in no time! The initial step is to look for a common denominator for the two fractions you are adding. The least common denominator is the minimum number that both fractions will split evenly.

If the fractions you wish to add share the same denominator, you can avoid this step. If not, to find the common denominator, you can determine the amount of the factors of each number until 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 in view of the fact that both denominators will divide 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

Once you possess the common denominator, the next step is to convert 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 identical number required to attain the common denominator.

Following the prior example, 6 will become the common denominator. To convert the numerators, we will multiply 1/3 by 2 to achieve 2/6, while 1/6 will 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: Simplifying the Results

The final step is to simplify the fraction. As a result, it means we need to lower 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 largest common factor of 3 and 6 is 3. When we divide both numbers by 3, we get the ultimate answer of 1/2.

You go by the exact procedure 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 utilizing the procedures mentioned above, you will see that they share equivalent denominators. Lucky you, this means you can avoid the first step. Now, all you have to do is add the numerators and let it be the same denominator as it was.

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 greater than the denominator. This could 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 conclusive answer of 2 by dividing the numerator and denominator by 2.

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

Adding Fractions with Unlike Denominators

This process will require an additional 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 have said above, to add unlike fractions, you must obey all three steps mentioned prior to transform 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 summing up the following fractions:

1/6+2/3+6/4

As shown, the denominators are distinct, and the smallest common multiple is 12. Hence, 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

Now that 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, concluding with a ultimate result of 7/3.

Adding Mixed Numbers

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

The Steps to Adding Mixed Numbers

To solve addition problems 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

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

Now, you move forward by summing 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.

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

Next, add the whole number described 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 similar 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 final answer.

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