How to Add Fractions: Examples and Steps
Adding fractions is a regular math problem that children study in school. It can look intimidating at first, but it becomes simple with a bit of practice.
This blog post will take you through the process of adding two or more fractions and adding mixed fractions. We will then give examples to see how it is done. Adding fractions is essential for a lot of subjects as you move ahead in science and math, so ensure to adopt these skills initially!
The Process of Adding Fractions
Adding fractions is an ability that a lot of kids have difficulty with. Despite that, it is a moderately easy process once you understand the basic principles. There are three primary steps to adding fractions: finding a common denominator, adding the numerators, and simplifying the results. Let’s take a closer look at each 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 expert in a flash! The first step is to determine a common denominator for the two fractions you are adding. The smallest common denominator is the lowest number that both fractions will divide uniformly.
If the fractions you wish to sum share the same denominator, you can skip this step. If not, to determine the common denominator, you can list out the factors of respective number as far as you find a common one.
For example, let’s say we wish to add the fractions 1/3 and 1/6. The smallest common denominator for these two fractions is six in view of the fact that both denominators will divide equally into that number.
Here’s a great tip: if you are not sure regarding 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 next step is to convert each fraction so that it has that denominator.
To convert these into an equivalent fraction with the exact denominator, you will multiply both the denominator and numerator by the identical number necessary to get the common denominator.
Following the previous 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 remain the same.
Considering that both the fractions share common denominators, we can add the numerators together to achieve 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 need to reduce the fraction to its minimum terms. To achieve this, we find the most common factor of the numerator and denominator and divide them by it. In our example, the biggest common factor of 3 and 6 is 3. When we divide both numbers by 3, we get the ultimate answer of 1/2.
You follow the exact procedure 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 utilizing the process shown above, you will observe that they share identical denominators. Lucky for you, this means you can skip the initial step. At the moment, all you have to do is sum of the numerators and leave 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 larger than the denominator. This might indicate that you could simplify the fraction, but this is not feasible when we work 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 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 stated prior to this, to add unlike fractions, you must follow all three procedures mentioned prior 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 summing up the following fractions:
1/6+2/3+6/4
As you can see, the denominators are dissimilar, and the lowest common multiple is 12. Therefore, we multiply each 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 total the numerators:
2/12 + 8/12 + 18/12 = 28/12
We simplify the fraction by splitting the numerator and denominator by 4, finding a ultimate result of 7/3.
Adding Mixed Numbers
We have mentioned like and unlike fractions, but now we will touch upon 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 turning the mixed number into a fraction. Here are the procedures 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 result as a numerator and retain the denominator.
Now, you proceed 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.
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
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 end up with this result:
7/4 + 5/4
By adding the numerators with the similar denominator, we will have a final answer of 12/4. We simplify the fraction by dividing both the numerator and denominator by 4, ensuing in 3 as a final answer.
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