How to Add Fractions: Examples and Steps
Adding fractions is a common math problem that students learn in school. It can seem intimidating at first, but it can be simple with a bit of practice.
This blog article will guide the process of adding two or more fractions and adding mixed fractions. We will then give examples to show what must be done. Adding fractions is crucial for several subjects as you advance in math and science, so be sure to master these skills initially!
The Procedures for Adding Fractions
Adding fractions is an ability that numerous students struggle with. Nevertheless, it is a somewhat simple process once you grasp the essential principles. There are three primary steps to adding fractions: finding a common denominator, adding the numerators, and streamlining 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 valuable points, you’ll be adding fractions like a professional in no time! The initial 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 divide equally.
If the fractions you want to add share the equal denominator, you can avoid this step. If not, to determine the common denominator, you can determine the number of the factors of each number until you determine a common one.
For example, let’s assume 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 divide equally into that number.
Here’s a quick 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 possess the common denominator, the next step is to turn 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 necessary to get the common denominator.
Subsequently the last example, 6 will become the common denominator. To change the numerators, we will multiply 1/3 by 2 to achieve 2/6, while 1/6 would remain the same.
Now that both the fractions share common denominators, we can add the numerators together to get 3/6, a proper fraction that we will proceed to simplify.
Step Three: Streamlining the Answers
The last step is to simplify the fraction. Consequently, it means we are required to lower the fraction to its lowest 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 result 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 utilizing the process shown above, you will observe that they share the same denominators. Lucky for you, this means you can avoid the first stage. Now, all you have to do is add the numerators and leave the same denominator as before.
2/4 + 6/4 = 8/4
Now, let’s try to simplify the fraction. We can perceive that this is an improper fraction, as the numerator is larger than the denominator. This might indicate that you can simplify the fraction, but this is not possible when we deal 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 two.
Considering you go by these steps when dividing two or more fractions, you’ll be a pro at adding fractions in a matter of time.
Adding Fractions with Unlike Denominators
The procedure will need an extra step when you add or subtract fractions with dissimilar 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 stated before this, to add unlike fractions, you must obey all three procedures stated 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 adding the following fractions:
1/6+2/3+6/4
As you can see, the denominators are different, and the smallest common multiple is 12. Therefore, we multiply every 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
Since 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 splitting the numerator and denominator by 4, coming to the ultimate answer of 7/3.
Adding Mixed Numbers
We have talked about like and unlike fractions, but presently we will go through 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 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 retain the denominator.
Now, you go ahead by adding these unlike fractions as you usually would.
Examples of How to Add Mixed Numbers
As an example, we will work with 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
Then, add the whole number represented 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 exact denominator, we will have a final result of 12/4. We simplify the fraction by dividing both the numerator and denominator by 4, ensuing in 3 as a conclusive result.
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