September 29, 2022

How to Add Fractions: Steps and Examples

Adding fractions is a common math operation that students study in school. It can appear daunting at first, but it can be simple with a shred of practice.

This blog article will take you through the procedure of adding two or more fractions and adding mixed fractions. We will then provide examples to see how it is done. Adding fractions is necessary for several subjects as you advance in mathematics and science, so ensure to adopt these skills initially!

The Process of Adding Fractions

Adding fractions is an ability that numerous students struggle with. Nevertheless, it is a relatively simple process once you grasp the basic principles. There are three primary steps to adding fractions: finding a common denominator, adding the numerators, and simplifying the results. Let’s carefully analyze each of these steps, and then we’ll look into some examples.

Step 1: Look for a Common Denominator

With these helpful points, you’ll be adding fractions like a expert in no time! The first 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 share equally.

If the fractions you want to add share the identical 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 find a common one.

For example, let’s assume 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 divide equally into that number.

Here’s a great tip: if you are uncertain regarding this process, 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 convert 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 necessary to achieve the common denominator.

Subsequently the last example, six will become the common denominator. To convert the numerators, we will multiply 1/3 by 2 to attain 2/6, while 1/6 would stay the same.

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

Step Three: Streamlining the Results

The final process is to simplify the fraction. Consequently, it means we need to reduce the fraction to its minimum terms. To achieve 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 result of 1/2.

You go by the exact procedure 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 see that they share equivalent denominators. You are lucky, this means you can avoid the first stage. At the moment, 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 perceive 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 possible when we deal 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.

Considering you go by these steps when dividing two or more fractions, you’ll be a expert at adding fractions in no time.

Adding Fractions with Unlike Denominators

The procedure will need an additional 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 have said prior to this, to add unlike fractions, you must obey all three procedures stated prior to convert 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 adding the following fractions:

1/6+2/3+6/4

As you can see, the denominators are different, and the least common multiple is 12. Thus, we multiply each fraction by a value 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 move ahead to total the numerators:

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

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

Adding Mixed Numbers

We have talked about 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 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 retain the denominator.

Now, you move forward by summing these unlike fractions as you usually would.

Examples of How to Add Mixed Numbers

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

First, 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 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 adding the numerators with the similar denominator, we will have a final result 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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