How to Add Fractions: Examples and Steps
Adding fractions is a common math problem that children study in school. It can look daunting at first, but it can be simple with a shred 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 demonstrate how it is done. Adding fractions is crucial for a lot of subjects as you move ahead in mathematics and science, so be sure to master these skills early!
The Process of Adding Fractions
Adding fractions is a skill that many kids struggle with. However, it is a relatively hassle-free process once you understand the basic principles. There are three primary steps to adding fractions: finding a common denominator, adding the numerators, and streamlining the results. 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 pro in an instant! The initial 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 split equally.
If the fractions you desire to sum share the equal denominator, you can avoid this step. If not, to find the common denominator, you can determine the amount of the factors of each number until 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 for the reason that both denominators will divide evenly into that number.
Here’s a good tip: if you are not sure regarding 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 have the common denominator, the immediate step is to change each fraction so that it has that denominator.
To turn these into an equivalent fraction with the same denominator, you will multiply both the denominator and numerator by the exact number necessary to attain the common denominator.
Following the last example, 6 will become the common denominator. To convert the numerators, we will multiply 1/3 by 2 to get 2/6, while 1/6 would stay the same.
Since both the fractions share common denominators, we can add the numerators together to attain 3/6, a proper fraction that we will be moving forward to simplify.
Step Three: Simplifying the Results
The final step is to simplify the fraction. Doing so means we need 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 biggest common factor of 3 and 6 is 3. When we divide both numbers by 3, we get the final result of 1/2.
You follow the same process 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 process shown above, you will see that they share identical denominators. You are lucky, this means you can avoid the initial step. At the moment, 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 notice that this is an improper fraction, as the numerator is greater than the denominator. This may suggest that you can simplify the fraction, but this is not necessarily the case 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 ultimate result of 2 by dividing the numerator and denominator by 2.
Provided that you follow these steps when dividing two or more fractions, you’ll be a professional at adding fractions in a matter of time.
Adding Fractions with Unlike Denominators
This process will need an additional step when you add or subtract fractions with distinct denominators. To do these operations with two or more fractions, they must have the identical denominator.
The Steps to Adding Fractions with Unlike Denominators
As we mentioned prior to this, to add unlike fractions, you must follow all three procedures mentioned above to change 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 adding the following fractions:
1/6+2/3+6/4
As shown, the denominators are distinct, 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
Once 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 ultimate result of 7/3.
Adding Mixed Numbers
We have discussed 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 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
Write down your result as a numerator and retain the denominator.
Now, you move forward 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 change 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 ultimate result of 12/4. We simplify the fraction by dividing both the numerator and denominator by 4, ensuing in 3 as a final answer.
Use Grade Potential to Improve Your Math Skills Now
If you're struggling to understand adding fractions, think about signing up for a tutoring class with Grade Potential. One of our professional tutors can help you grasp the material and ace your next test.
