How to Add Fractions: Examples and Steps
Adding fractions is a usual math operation that children learn in school. It can look daunting at first, but it becomes easy with a tiny bit of practice.
This blog article will take you through the steps of adding two or more fractions and adding mixed fractions. We will also provide examples to show how this is done. Adding fractions is necessary for a lot of subjects as you advance in math and science, so be sure to master these skills initially!
The Process of Adding Fractions
Adding fractions is an ability that numerous kids struggle with. However, it is a somewhat simple process once you master the essential principles. There are three main steps to adding fractions: determining a common denominator, adding the numerators, and simplifying the answer. Let’s closely study each of these steps, and then we’ll do some examples.
Step 1: Determining a Common Denominator
With these valuable tips, you’ll be adding fractions like a pro in a flash! The initial step is to look for a common denominator for the two fractions you are adding. The least common denominator is the lowest number that both fractions will split uniformly.
If the fractions you want to sum share the equal denominator, you can skip this step. If not, to look for the common denominator, you can list out the factors of respective number as far as you find 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 because both denominators will split equally into that number.
Here’s a quick tip: if you are unsure 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
Once you acquired the common denominator, the following step is to change 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 same number needed to get the common denominator.
Following the previous 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 will remain the same.
Since both the fractions share common denominators, we can add the numerators collectively to attain 3/6, a proper fraction that we will continue to simplify.
Step Three: Streamlining the Results
The last step is to simplify the fraction. As a result, it means we are required to reduce the fraction to its lowest terms. To achieve this, we search 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 final result of 1/2.
You go by the exact 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 steps above, you will see that they share the same denominators. You are lucky, this means you can avoid the first step. Now, all you have to do is add the numerators and let it be the same denominator as before.
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 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 professional at adding fractions in matter of days.
Adding Fractions with Unlike Denominators
This process will need 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 same denominator.
The Steps to Adding Fractions with Unlike Denominators
As we stated prior to this, to add unlike fractions, you must follow all three procedures mentioned prior to convert 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 adding 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 value to get the denominator of 12.
1/6 * 2 = 2/12
2/3 * 4 = 8/12
6/4 * 3 = 18/12
Now that all the fractions have a common denominator, we will go forward to total 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 result of 7/3.
Adding Mixed Numbers
We have talked about 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 solve addition problems with mixed numbers, you must initiate by converting 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 solve 1 3/4 + 5/4.
Foremost, 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
Next, add the whole number described as a fraction to the other fraction in the mixed number.
4/4 + 3/4 = 7/4
You will be left with this result:
7/4 + 5/4
By adding the numerators with the same denominator, we will have a conclusive answer of 12/4. We simplify the fraction by dividing both the numerator and denominator by 4, ensuing in 3 as a final result.
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