How to Add Fractions: Examples and Steps
Adding fractions is a usual math operation that students learn in school. It can seem scary at first, but it can be easy with a bit of practice.
This blog post will take you through the steps of adding two or more fractions and adding mixed fractions. We will then provide examples to show how it is done. Adding fractions is essential for several subjects as you move ahead in science and math, so be sure 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 somewhat hassle-free process once you understand the fundamental 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 do some examples.
Step 1: Look for a Common Denominator
With these helpful points, 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 smallest common denominator is the minimum number that both fractions will share uniformly.
If the fractions you wish to add share the identical denominator, you can skip 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 determine a common one.
For example, let’s say we wish to add the fractions 1/3 and 1/6. The lowest common denominator for these two fractions is six because both denominators will split equally 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 would be 18.
Step Two: Adding the Numerators
Once you acquired the common denominator, the next step is to turn each fraction so that it has that denominator.
To turn these into an equivalent fraction with the exact denominator, you will multiply both the denominator and numerator by the identical number needed to get the common denominator.
Following the last example, 6 will become the common denominator. To convert the numerators, we will multiply 1/3 by 2 to get 2/6, while 1/6 will remain the same.
Now that both the fractions share common denominators, we can add the numerators together to achieve 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. As a result, it means we are required to lower the fraction to its lowest terms. To achieve 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 ultimate answer of 1/2.
You follow 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 utilizing the steps above, you will notice that they share identical denominators. You are lucky, this means you can skip the initial stage. Now, 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 try 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 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.
Provided that 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 require an extra step when you add or subtract fractions with different 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 mentioned above, to add unlike fractions, you must obey 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 demonstrated, the denominators are dissimilar, and the least common multiple is 12. Hence, we multiply every 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 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 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 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 keep the denominator.
Now, you move forward by adding these unlike fractions as you normally would.
Examples of How to Add Mixed Numbers
As an example, we will solve 1 3/4 + 5/4.
Foremost, 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
Thereafter, 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 result:
7/4 + 5/4
By summing 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, ensuing in 3 as a conclusive answer.
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