How to Add Fractions: Steps and Examples
Adding fractions is a common math application that students learn in school. It can look daunting initially, but it can be easy with a bit of practice.
This blog post will walk you through the process of adding two or more fractions and adding mixed fractions. We will then give examples to see how this is done. Adding fractions is necessary for various subjects as you advance in mathematics and science, so ensure to master these skills initially!
The Procedures for Adding Fractions
Adding fractions is a skill that a lot of kids struggle with. Nevertheless, it is a moderately hassle-free process once you master the fundamental principles. There are three main steps to adding fractions: determining a common denominator, adding the numerators, and streamlining the results. Let’s take a closer look at each of these steps, and then we’ll look into some examples.
Step 1: Finding a Common Denominator
With these valuable tips, you’ll be adding fractions like a pro in an instant! The first step is to determine a common denominator for the two fractions you are adding. The least common denominator is the lowest number that both fractions will split evenly.
If the fractions you desire to sum share the identical denominator, you can avoid this step. If not, to determine the common denominator, you can list out the factors of respective 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 smallest common denominator for these two fractions is six for the reason that both denominators will split uniformly into that number.
Here’s a quick tip: if you are uncertain 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 have the common denominator, the immediate step is to change each fraction so that it has that denominator.
To change these into an equivalent fraction with the exact denominator, you will multiply both the denominator and numerator by the identical number needed to attain the common denominator.
Subsequently the prior example, 6 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.
Since both the fractions share common denominators, we can add the numerators together to attain 3/6, a proper fraction that we will be moving forward to simplify.
Step Three: Streamlining the Answers
The last process is to simplify the fraction. Consequently, it means we are required to reduce 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 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 continue to add these two fractions:
2/4 + 6/4
By using the steps above, you will notice that they share equivalent 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 attempt to simplify the fraction. We can notice that this is an improper fraction, as the numerator is higher than the denominator. This might indicate that you could simplify the fraction, but this is not necessarily the case 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 two.
Provided that you go by these steps when dividing two or more fractions, you’ll be a pro 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 mentioned above, 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
At this point, we will focus on another example by summing up the following fractions:
1/6+2/3+6/4
As you can see, the denominators are dissimilar, and the least common multiple is 12. Therefore, 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
Now that all the fractions have a common denominator, we will go forward to add 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 revise through mixed fractions. These are fractions followed by whole numbers.
The Steps to Adding Mixed Numbers
To solve addition problems 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 go ahead by adding these unlike fractions as you generally would.
Examples of How to Add Mixed Numbers
As an example, we will work out 1 3/4 + 5/4.
First, let’s transform 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 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 adding the numerators with the similar denominator, we will have a conclusive result of 12/4. We simplify the fraction by dividing both the numerator and denominator by 4, resulting in 3 as a final result.
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