How to Add Fractions: Examples and Steps
Adding fractions is a common math operation that children learn in school. It can look daunting at first, but it turns simple with a tiny bit of practice.
This blog post will take you through the procedure of adding two or more fractions and adding mixed fractions. We will then give examples to demonstrate how it is done. Adding fractions is essential for several subjects as you progress in math and science, so be sure to master these skills initially!
The Process of Adding Fractions
Adding fractions is a skill that numerous students struggle with. Nevertheless, it is a relatively easy process once you grasp the basic principles. There are three main steps to adding fractions: finding 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 do some examples.
Step 1: Determining a Common Denominator
With these valuable tips, you’ll be adding fractions like a professional in no time! The first step is to determine a common denominator for the two fractions you are adding. The least common denominator is the minimum number that both fractions will divide evenly.
If the fractions you desire to sum share the same denominator, you can skip this step. If not, to look for the common denominator, you can determine the number of the factors of respective number as far as you determine 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 because both denominators will split uniformly 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 should be 18.
Step Two: Adding the Numerators
Once you have the common denominator, the following step is to convert each fraction so that it has that denominator.
To convert these into an equivalent fraction with an identical denominator, you will multiply both the denominator and numerator by the exact number needed to get 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 achieve 2/6, while 1/6 will stay the same.
Since both the fractions share common denominators, we can add the numerators collectively to get 3/6, a proper fraction that we will proceed to simplify.
Step Three: Streamlining the Answers
The final process is to simplify the fraction. Doing so means we need to diminish the fraction to its lowest terms. To achieve this, we find 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 ultimate answer of 1/2.
You go by the same procedure to add and subtract fractions.
Examples of How to Add Fractions
Now, let’s move forward to add these two fractions:
2/4 + 6/4
By applying 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 might indicate 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 conclusive result of 2 by dividing the numerator and denominator by 2.
As long as 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
The procedure 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 exact denominator.
The Steps to Adding Fractions with Unlike Denominators
As we have said above, to add unlike fractions, you must follow all three steps mentioned above to change these unlike denominators into equivalent fractions
Examples of How to Add Fractions with Unlike Denominators
Here, we will focus on another example by adding the following fractions:
1/6+2/3+6/4
As you can see, the denominators are different, and the lowest common multiple is 12. Therefore, 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
Since all the fractions have a common denominator, we will move ahead to add 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 presently 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
Note down your result as a numerator and keep the denominator.
Now, you move forward 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.
First, 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 described 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 same denominator, we will have a conclusive answer of 12/4. We simplify the fraction by dividing both the numerator and denominator by 4, resulting in 3 as a final answer.
Use Grade Potential to Better Your Math Skills Now
If you're struggling to understand adding fractions, think about signing up for a tutoring class with Grade Potential. One of our expert instructors can assist you grasp the topic and nailcrack your next exam.
