How to Add Fractions: Steps and Examples
Adding fractions is a common math operation that students learn in school. It can appear intimidating initially, but it becomes simple with a bit of practice.
This blog post will take you through the procedure of adding two or more fractions and adding mixed fractions. We will also give examples to demonstrate how this is done. Adding fractions is necessary for various subjects as you progress in science and mathematics, so be sure to adopt these skills initially!
The Procedures for Adding Fractions
Adding fractions is a skill that a lot of students struggle with. Nevertheless, it is a relatively hassle-free process once you grasp the fundamental principles. There are three primary steps to adding fractions: finding a common denominator, adding the numerators, and simplifying the results. Let’s closely study each of these steps, and then we’ll look into some examples.
Step 1: Finding a Common Denominator
With these useful tips, you’ll be adding fractions like a expert in no time! The first step is to find a common denominator for the two fractions you are adding. The least common denominator is the lowest number that both fractions will divide uniformly.
If the fractions you desire to add share the identical 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 desire to add the fractions 1/3 and 1/6. The lowest common denominator for these two fractions is six in view of the fact that both denominators will split evenly into that number.
Here’s a quick tip: if you are not sure about 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
Now that you acquired the common denominator, the immediate step is to turn each fraction so that it has that denominator.
To change these into an equivalent fraction with an identical denominator, you will multiply both the denominator and numerator by the exact number required 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 get 2/6, while 1/6 will remain the same.
Now that both the fractions share common denominators, we can add the numerators collectively to achieve 3/6, a proper fraction that we will proceed to simplify.
Step Three: Simplifying the Results
The last process is to simplify the fraction. Consequently, it means we need to reduce the fraction to its minimum terms. To obtain 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 concluding answer 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 applying the procedures mentioned above, you will observe that they share identical denominators. Lucky you, this means you can avoid the initial stage. Now, all you have to do is sum of the numerators and let it be the same denominator as before.
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 larger than the denominator. This could indicate that you can simplify the fraction, but this is not possible when we deal 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 ultimate answer of 2 by dividing the numerator and denominator by 2.
Provided that you go by these steps when dividing two or more fractions, you’ll be a expert 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 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 before this, to add unlike fractions, you must obey all three steps stated above to transform these unlike denominators into equivalent fractions
Examples of How to Add Fractions with Unlike Denominators
At this point, we will put more emphasis on another example by summing up the following fractions:
1/6+2/3+6/4
As shown, the denominators are dissimilar, and the lowest 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
Once 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 dividing the numerator and denominator by 4, coming to the ultimate answer of 7/3.
Adding Mixed Numbers
We have discussed 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 work out addition problems with mixed numbers, you must initiate 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
Note down your result as a numerator and retain the denominator.
Now, you move forward by summing these unlike fractions as you usually would.
Examples of How to Add Mixed Numbers
As an example, we will work out 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
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 end up with this result:
7/4 + 5/4
By adding the numerators with the exact 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 result.
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