How to Add Fractions: Steps and Examples

Adding fractions is a common math application that students study in school. It can look daunting initially, but it turns easy 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 show how this is done. Adding fractions is crucial for a lot of subjects as you advance in science and math, so ensure to learn these skills early!

The Process of Adding Fractions

Adding fractions is a skill that many students have difficulty with. However, it is a moderately hassle-free process once you grasp the essential principles. There are three main steps to adding fractions: finding a common denominator, adding the numerators, and streamlining the answer. Let’s closely study each of these steps, and then we’ll do some examples.

Step 1: Determining a Common Denominator

With these valuable tips, you’ll be adding fractions like a expert in no time! The initial step is to find a common denominator for the two fractions you are adding. The smallest common denominator is the minimum number that both fractions will share equally.

If the fractions you wish to sum share the identical denominator, you can avoid this step. If not, to look for the common denominator, you can determine the amount of the factors of each number as far as you find a common one.

For example, let’s say we want to add the fractions 1/3 and 1/6. The smallest common denominator for these two fractions is six for the reason that both denominators will split evenly into that number.

Here’s a great tip: if you are unsure 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 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 an identical denominator, you will multiply both the denominator and numerator by the identical number necessary to achieve the common denominator.

Following the prior example, 6 will become the common denominator. To change the numerators, we will multiply 1/3 by 2 to achieve 2/6, while 1/6 would remain the same.

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

Step Three: Simplifying the Answers

The final process is to simplify the fraction. Consequently, it means we need to diminish the fraction to its lowest 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 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 same procedure to add and subtract fractions.

Examples of How to Add Fractions

Now, let’s proceed to add these two fractions:

2/4 + 6/4

By applying the procedures mentioned above, you will see that they share equivalent denominators. Lucky you, this means you can skip the initial stage. At the moment, all you have to do is sum of the numerators and allow it to be 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 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 final answer of 2 by dividing the numerator and denominator by 2.

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

Adding Fractions with Unlike Denominators

The procedure will need 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 identical denominator.

The Steps to Adding Fractions with Unlike Denominators

As we stated before 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

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

1/6+2/3+6/4

As demonstrated, the denominators are dissimilar, and the lowest common multiple is 12. Therefore, 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

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, coming to the final result of 7/3.

Adding Mixed Numbers

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

The Steps to Adding Mixed Numbers

To work out addition sums with mixed numbers, you must start by turning 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

Note down your result 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 out 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

Then, add the whole number represented as a fraction to the other fraction in the mixed number.

4/4 + 3/4 = 7/4

You will end up with this operation:

7/4 + 5/4

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

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