How to Add Fractions: Steps and Examples
Adding fractions is a common math operation that students study in school. It can seem scary initially, but it turns simple with a shred of practice.
This blog post will walk you through the procedure of adding two or more fractions and adding mixed fractions. We will ,on top of that, provide examples to demonstrate how this is done. Adding fractions is crucial for several subjects as you advance in mathematics and science, so ensure to master these skills initially!
The Steps of Adding Fractions
Adding fractions is an ability that many children struggle with. Nevertheless, it is a moderately simple process once you master the fundamental principles. There are three main steps to adding fractions: looking for a common denominator, adding the numerators, and simplifying the answer. Let’s take a closer look at every one of these steps, and then we’ll look into some examples.
Step 1: Determining a Common Denominator
With these helpful points, you’ll be adding fractions like a pro 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 split equally.
If the fractions you desire to sum share the same denominator, you can skip this step. If not, to find the common denominator, you can determine the number of the factors of respective number until you determine a common one.
For example, let’s say we want to add the fractions 1/3 and 1/6. The smallest common denominator for these two fractions is six for the reason that both denominators will divide equally 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
Once you possess the common denominator, the immediate step is to turn each fraction so that it has that denominator.
To turn these into an equivalent fraction with the same denominator, you will multiply both the denominator and numerator by the same number required to get the common denominator.
Subsequently the previous 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 will remain the same.
Considering 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: Streamlining the Results
The final step is to simplify the fraction. As a result, it means we are required to diminish 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 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 go by the exact steps 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 using the procedures mentioned above, you will see that they share equivalent denominators. Lucky you, this means you can avoid the first stage. Now, all you have to do is add 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 greater than the denominator. This might suggest that you could 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 ultimate result of 2 by dividing the numerator and denominator by two.
Provided that you follow these procedures when dividing two or more fractions, you’ll be a professional at adding fractions in no time.
Adding Fractions with Unlike Denominators
This process will require an additional step when you add or subtract fractions with different denominators. To do this function with two or more fractions, they must have the exact denominator.
The Steps to Adding Fractions with Unlike Denominators
As we mentioned before this, to add unlike fractions, you must obey all three procedures mentioned above to transform these unlike denominators into equivalent fractions
Examples of How to Add Fractions with Unlike Denominators
At this point, we will focus on another example by summing up the following fractions:
1/6+2/3+6/4
As demonstrated, the denominators are different, and the least common multiple is 12. Thus, 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, concluding with a 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 accompanied by whole numbers.
The Steps to Adding Mixed Numbers
To solve addition exercises 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
Take down your answer as a numerator and retain the denominator.
Now, you proceed by summing 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.
First, 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 exact denominator, we will have a ultimate result of 12/4. We simplify the fraction by dividing both the numerator and denominator by 4, resulting in 3 as a conclusive result.
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