How to Add Fractions: Steps and Examples
Adding fractions is a regular math application that students learn in school. It can look intimidating initially, but it becomes simple with a bit of practice.
This blog post will guide the process of adding two or more fractions and adding mixed fractions. We will then provide examples to demonstrate what must be done. Adding fractions is essential for several subjects as you progress in mathematics and science, so be sure to adopt these skills early!
The Procedures for Adding Fractions
Adding fractions is an ability that many children struggle with. However, it is a relatively hassle-free process once you grasp the fundamental principles. There are three major steps to adding fractions: determining a common denominator, adding the numerators, and simplifying the results. Let’s carefully analyze each of these steps, and then we’ll do some examples.
Step 1: Finding a Common Denominator
With these helpful tips, you’ll be adding fractions like a pro in a flash! 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 equally.
If the fractions you wish to add share the same denominator, you can avoid this step. If not, to find the common denominator, you can determine the number of the factors of each number until you determine a common one.
For example, let’s say we desire 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 evenly into that number.
Here’s a great tip: if you are unsure 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
Now that you have 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 the same denominator, you will multiply both the denominator and numerator by the identical number needed to attain the common denominator.
Subsequently 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 would stay 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 Results
The last process is to simplify the fraction. Doing so means we are required to diminish the fraction to its minimum 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 largest common factor of 3 and 6 is 3. When we divide both numbers by 3, we get the ultimate result of 1/2.
You follow the same steps 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 using the procedures mentioned above, you will notice that they share the same denominators. Lucky you, this means you can skip the first step. Now, all you have to do is add the numerators and leave the same denominator as it was.
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 greater than the denominator. This could suggest that you could simplify the fraction, but this is not feasible when we work 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 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 a matter of time.
Adding Fractions with Unlike Denominators
The procedure will need an supplementary step when you add or subtract fractions with different 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 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 concentrate on another example by adding the following fractions:
1/6+2/3+6/4
As shown, the denominators are dissimilar, and the smallest common multiple is 12. Thus, we multiply each fraction by a number to achieve 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 dividing the numerator and denominator by 4, concluding with a final result of 7/3.
Adding Mixed Numbers
We have discussed like and unlike fractions, but now we will go through mixed fractions. These are fractions accompanied by whole numbers.
The Steps to Adding Mixed Numbers
To solve addition exercises with mixed numbers, you must initiate 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
Write down your result as a numerator and keep the denominator.
Now, you proceed 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.
Foremost, let’s transform 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 adding the numerators with the exact denominator, we will have a conclusive result of 12/4. We simplify the fraction by dividing both the numerator and denominator by 4, resulting in 3 as a final answer.
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