September 29, 2022

How to Add Fractions: Examples and Steps

Adding fractions is a usual math operation that children learn in school. It can look daunting at first, but it turns simple with a shred of practice.

This blog post will walk you through the process of adding two or more fractions and adding mixed fractions. We will also provide examples to see how this is done. Adding fractions is crucial for several subjects as you advance in science and math, so be sure to adopt these skills early!

The Procedures for Adding Fractions

Adding fractions is an ability that many children struggle with. Nevertheless, it is a relatively easy process once you understand the essential principles. There are three major steps to adding fractions: finding a common denominator, adding the numerators, and streamlining the answer. Let’s take a closer look at each of these steps, and then we’ll look into some examples.

Step 1: Look for a Common Denominator

With these valuable points, you’ll be adding fractions like a professional 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 lowest number that both fractions will share equally.

If the fractions you want to sum share the same denominator, you can avoid this step. If not, to look for the common denominator, you can list out the factors of each number as far as you look for a common one.

For example, let’s assume we want to add the fractions 1/3 and 1/6. The lowest common denominator for these two fractions is six in view of the fact that both denominators will divide equally into that number.

Here’s a great tip: if you are not sure 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 acquired the common denominator, the immediate step is to convert each fraction so that it has that denominator.

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

Following the previous 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.

Since both the fractions share common denominators, we can add the numerators simultaneously to attain 3/6, a proper fraction that we will continue to simplify.

Step Three: Simplifying the Results

The final step is to simplify the fraction. Consequently, it means we need to lower the fraction to its minimum terms. To obtain this, we search 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 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 applying the process shown above, you will observe that they share identical denominators. You are lucky, this means you can avoid the first step. 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 see that this is an improper fraction, as the numerator is greater than the denominator. This might suggest that you could simplify the fraction, but this is not feasible when we work 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 result of 2 by dividing the numerator and denominator by two.

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

The procedure will require an supplementary step when you add or subtract fractions with distinct denominators. To do this function 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 mentioned prior to convert 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. Hence, we multiply each 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

Now that all the fractions have a common denominator, we will proceed 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 go through mixed fractions. These are fractions accompanied by whole numbers.

The Steps to Adding Mixed Numbers

To figure out addition exercises 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 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.

Foremost, let’s transform the mixed number into a fraction. You will need 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 be left with this operation:

7/4 + 5/4

By summing the numerators with the same denominator, we will have a ultimate result 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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