How to Add Fractions: Examples and Steps
Adding fractions is a usual math operation that children study in school. It can seem daunting initially, but it can be easy with a bit of practice.
This blog post will walk you through the process of adding two or more fractions and adding mixed fractions. We will then provide examples to show what must be done. Adding fractions is crucial for a lot of subjects as you progress in science and mathematics, so be sure to learn these skills initially!
The Process of Adding Fractions
Adding fractions is a skill that a lot of kids struggle with. However, it is a somewhat hassle-free process once you understand the fundamental principles. There are three major steps to adding fractions: looking for a common denominator, adding the numerators, and simplifying the answer. Let’s closely study each of these steps, and then we’ll work on some examples.
Step 1: Look for a Common Denominator
With these helpful tips, you’ll be adding fractions like a expert in no time! The initial step is to determine 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 desire to add share the same denominator, you can skip this step. If not, to find the common denominator, you can list out the factors of respective number until you look for a common one.
For example, let’s assume we wish 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 split evenly into that number.
Here’s a quick tip: if you are unsure about this process, 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 possess the common denominator, the next step is to change each fraction so that it has that denominator.
To turn these into an equivalent fraction with an identical denominator, you will multiply both the denominator and numerator by the identical number needed to get the common denominator.
Subsequently the prior example, 6 will become the common denominator. To change the numerators, we will multiply 1/3 by 2 to attain 2/6, while 1/6 would remain the same.
Now that both the fractions share common denominators, we can add the numerators simultaneously to attain 3/6, a proper fraction that we will continue to simplify.
Step Three: Streamlining the Answers
The last step is to simplify the fraction. Consequently, it means we need to diminish the fraction to its lowest terms. To obtain this, we find 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 concluding answer 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 applying the process shown above, you will see that they share identical denominators. Lucky you, this means you can avoid the initial stage. At the moment, 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 higher than the denominator. This may indicate that you could simplify the fraction, but this is not necessarily the case 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 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 pro at adding fractions in matter of days.
Adding Fractions with Unlike Denominators
The procedure will require an supplementary 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 have said prior to this, to add unlike fractions, you must obey all three steps 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 you can see, the denominators are dissimilar, and the smallest common multiple is 12. Therefore, we multiply every fraction by a number to attain the denominator of 12.
1/6 * 2 = 2/12
2/3 * 4 = 8/12
6/4 * 3 = 18/12
Considering that all the fractions have a common denominator, we will proceed 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 answer of 7/3.
Adding Mixed Numbers
We have discussed like and unlike fractions, but now we will revise through mixed fractions. These are fractions followed by whole numbers.
The Steps to Adding Mixed Numbers
To solve addition sums 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
Note down your answer as a numerator and retain the denominator.
Now, you go ahead by summing these unlike fractions as you generally would.
Examples of How to Add Mixed Numbers
As an example, we will work out 1 3/4 + 5/4.
First, let’s convert the mixed number into a fraction. You are required 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 conclusive answer 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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