How to Add Fractions: Examples and Steps
Adding fractions is a usual math application that kids learn in school. It can look intimidating at first, but it turns simple with a bit of practice.
This blog post will take you through the process of adding two or more fractions and adding mixed fractions. We will also provide examples to demonstrate what must be done. Adding fractions is essential for various subjects as you move ahead in science and mathematics, so be sure to master these skills early!
The Procedures for Adding Fractions
Adding fractions is an ability that numerous students have difficulty with. However, it is a relatively easy process once you master the fundamental principles. There are three main steps to adding fractions: finding a common denominator, adding the numerators, and streamlining the results. Let’s carefully analyze every one of these steps, and then we’ll look into some examples.
Step 1: Look for a Common Denominator
With these helpful points, you’ll be adding fractions like a expert in a flash! 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 split uniformly.
If the fractions you desire to sum share the same denominator, you can avoid this step. If not, to find the common denominator, you can list out the factors of each number as far as you find a common one.
For example, let’s assume 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 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 next step is to change each fraction so that it has that denominator.
To convert these into an equivalent fraction with the same denominator, you will multiply both the denominator and numerator by the same 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 attain 2/6, while 1/6 will stay the same.
Since both the fractions share common denominators, we can add the numerators together to achieve 3/6, a proper fraction that we will continue to simplify.
Step Three: Simplifying the Answers
The final process is to simplify the fraction. As a result, it means we are required to lower the fraction to its minimum terms. To accomplish this, we find the most common factor of the numerator and denominator and divide them by it. In our example, the biggest common factor of 3 and 6 is 3. When we divide both numbers by 3, we get the concluding answer of 1/2.
You follow the same process 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 see that they share the same denominators. You are lucky, this means you can avoid the initial stage. At the moment, 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 try to simplify the fraction. We can notice that this is an improper fraction, as the numerator is higher than the denominator. This may suggest that you could simplify the fraction, but this is not necessarily the case 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 answer of 2 by dividing the numerator and denominator by 2.
Considering you follow 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
This process will require an additional 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 mentioned prior to 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 concentrate 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. Hence, we multiply each 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 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 ultimate result of 7/3.
Adding Mixed Numbers
We have talked about like and unlike fractions, but presently we will touch upon mixed fractions. These are fractions followed by whole numbers.
The Steps to Adding Mixed Numbers
To figure out addition sums with mixed numbers, you must start by changing 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 retain 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 solve 1 3/4 + 5/4.
Foremost, 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
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 conclude with this result:
7/4 + 5/4
By summing the numerators with the similar denominator, we will have a ultimate 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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