How to Add Fractions: Examples and Steps
Adding fractions is a regular math application that students learn in school. It can appear scary initially, but it can be simple with a tiny bit of practice.
This blog post will take you through the steps of adding two or more fractions and adding mixed fractions. We will ,on top of that, provide examples to demonstrate how this is done. Adding fractions is necessary for a lot of subjects as you advance in math and science, so ensure to adopt these skills early!
The Procedures for Adding Fractions
Adding fractions is a skill that a lot of students have difficulty with. However, it is a relatively easy process once you grasp the essential principles. There are three main steps to adding fractions: determining a common denominator, adding the numerators, and simplifying the answer. Let’s take a closer look at each of these steps, and then we’ll work on some examples.
Step 1: Determining a Common Denominator
With these helpful points, you’ll be adding fractions like a pro in an instant! The first step is to look for a common denominator for the two fractions you are adding. The smallest common denominator is the lowest number that both fractions will split equally.
If the fractions you wish to sum share the equal 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 say we desire to add the fractions 1/3 and 1/6. The lowest common denominator for these two fractions is six for the reason that both denominators will divide evenly into that number.
Here’s a great tip: if you are not sure 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
Now that you have the common denominator, the next step is to change each fraction so that it has that denominator.
To convert these into an equivalent fraction with the exact denominator, you will multiply both the denominator and numerator by the identical number required to achieve the common denominator.
Subsequently the last example, six will become the common denominator. To change the numerators, we will multiply 1/3 by 2 to attain 2/6, while 1/6 would remain the same.
Since both the fractions share common denominators, we can add the numerators together to get 3/6, a proper fraction that we will be moving forward to simplify.
Step Three: Simplifying the Answers
The last step is to simplify the fraction. Doing so means we need to diminish 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 largest 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 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 utilizing the process shown above, you will notice that they share identical denominators. Lucky you, this means you can skip the first step. Now, all you have to do is add the numerators and allow it to be the same denominator as it was.
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 higher than the denominator. This may suggest that you can simplify the fraction, but this is not feasible when we work 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 ultimate 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 professional at adding fractions in a matter of time.
Adding Fractions with Unlike Denominators
The procedure will require an extra step when you add or subtract fractions with distinct denominators. To do this function with two or more fractions, they must have the same denominator.
The Steps to Adding Fractions with Unlike Denominators
As we have said before this, to add unlike fractions, you must follow all three steps mentioned prior to convert these unlike denominators into equivalent fractions
Examples of How to Add Fractions with Unlike Denominators
Here, we will focus on another example by summing up the following fractions:
1/6+2/3+6/4
As demonstrated, the denominators are different, and the smallest common multiple is 12. Thus, we multiply each fraction by a number to attain 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, coming to the ultimate result 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 figure out addition sums 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 result as a numerator and keep the denominator.
Now, you proceed 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.
First, let’s change 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 end up with this result:
7/4 + 5/4
By adding the numerators with the exact 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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