How to Add Fractions: Examples and Steps

Adding fractions is a regular math application that children study in school. It can appear intimidating at first, but it becomes easy with a shred of practice.

This blog article will walk you through the steps of adding two or more fractions and adding mixed fractions. We will ,on top of that, give examples to demonstrate what must be done. Adding fractions is necessary for a lot of subjects as you move ahead in math and science, so be sure to learn these skills initially!

The Steps of Adding Fractions

Adding fractions is an ability that a lot of students have difficulty with. Despite that, it is a somewhat hassle-free process once you master the basic principles. There are three major steps to adding fractions: looking for a common denominator, adding the numerators, and simplifying the answer. Let’s carefully analyze each of these steps, and then we’ll look into some examples.

Step 1: Finding a Common Denominator

With these useful tips, you’ll be adding fractions like a professional in an instant! The initial 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 share equally.

If the fractions you want to add share the identical denominator, you can skip 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 desire to add the fractions 1/3 and 1/6. The smallest common denominator for these two fractions is six because both denominators will split equally into that number.

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

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

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

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

Step Three: Streamlining the Results

The last step is to simplify the fraction. Consequently, it means we need to lower 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 same process 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 procedures mentioned above, you will see that they share identical denominators. You are lucky, this means you can avoid the initial step. Now, all you have to do is sum of 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 see that this is an improper fraction, as the numerator is larger than the denominator. This might suggest that you could simplify the fraction, but this is not necessarily the case 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 conclusive answer of 2 by dividing the numerator and denominator by 2.

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

Adding Fractions with Unlike Denominators

This process will need an extra 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 prior to this, to add unlike fractions, you must follow all three procedures stated prior to convert these unlike denominators into equivalent fractions

Examples of How to Add Fractions with Unlike Denominators

At this point, we will concentrate on another example by summing up the following fractions:

1/6+2/3+6/4

As demonstrated, the denominators are different, and the least common multiple is 12. Hence, we multiply every fraction by a value to achieve 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 go forward to total the numerators:

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

We simplify the fraction by dividing the numerator and denominator by 4, finding a ultimate answer of 7/3.

Adding Mixed Numbers

We have mentioned like and unlike fractions, but now we will touch upon mixed fractions. These are fractions accompanied by whole numbers.

The Steps to Adding Mixed Numbers

To solve addition problems with mixed numbers, you must start by converting the mixed number into a fraction. Here are the procedures 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 generally would.

Examples of How to Add Mixed Numbers

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

Foremost, 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 represented as a fraction to the other fraction in the mixed number.

4/4 + 3/4 = 7/4

You will conclude with this result:

7/4 + 5/4

By summing 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, ensuing in 3 as a conclusive result.

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