How to Add Fractions: Steps and Examples
Adding fractions is a usual math operation that children study in school. It can appear daunting initially, but it becomes simple with a shred of practice.
This blog post will take you through the steps 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 necessary for various subjects as you move ahead in mathematics and science, so ensure to master these skills early!
The Procedures for Adding Fractions
Adding fractions is an ability that many students have a problem with. However, it is a moderately simple process once you understand the essential principles. There are three main steps to adding fractions: finding a common denominator, adding the numerators, and streamlining the results. Let’s closely study every one of these steps, and then we’ll work on some examples.
Step 1: Finding a Common Denominator
With these valuable points, you’ll be adding fractions like a pro 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 minimum number that both fractions will divide evenly.
If the fractions you want to add share the identical denominator, you can avoid this step. If not, to look for the common denominator, you can determine the amount of the factors of each number until you look for a common one.
For example, let’s assume we desire to add the fractions 1/3 and 1/6. The smallest common denominator for these two fractions is six because both denominators will split uniformly into that number.
Here’s a good 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
Now that you acquired the common denominator, the immediate step is to convert 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 required to get the common denominator.
Subsequently the prior example, six will become the common denominator. To convert the numerators, we will multiply 1/3 by 2 to attain 2/6, while 1/6 will stay the same.
Considering that both the fractions share common denominators, we can add the numerators simultaneously to get 3/6, a proper fraction that we will continue to simplify.
Step Three: Streamlining the Answers
The final process is to simplify the fraction. As a result, it means we need to lower the fraction to its lowest 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 concluding result of 1/2.
You go by the exact process 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 observe that they share identical 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 before.
2/4 + 6/4 = 8/4
Now, let’s attempt to simplify the fraction. We can see 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 result of 2 by dividing the numerator and denominator by two.
Considering you go by 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 this function with two or more fractions, they must have the identical denominator.
The Steps to Adding Fractions with Unlike Denominators
As we stated before this, to add unlike fractions, you must follow 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 put more emphasis on another example by adding the following fractions:
1/6+2/3+6/4
As you can see, the denominators are distinct, and the least common multiple is 12. Thus, we multiply every fraction by a number to get 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 add the numerators:
2/12 + 8/12 + 18/12 = 28/12
We simplify the fraction by splitting 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 followed by whole numbers.
The Steps to Adding Mixed Numbers
To work out addition problems with mixed numbers, you must start 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 keep the denominator.
Now, you proceed by adding these unlike fractions as you generally would.
Examples of How to Add Mixed Numbers
As an example, we will work with 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 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, ensuing in 3 as a final result.
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