How to Add Fractions: Steps and Examples
Adding fractions is a regular math problem that kids study in school. It can seem daunting at first, but it can be easy with a bit of practice.
This blog post will take you through the steps of adding two or more fractions and adding mixed fractions. We will then provide examples to see how this is done. Adding fractions is necessary for various subjects as you advance in math and science, so make sure to learn these skills early!
The Procedures for Adding Fractions
Adding fractions is an ability that many students have a problem with. However, it is a relatively hassle-free process once you grasp the basic principles. There are three main 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 work on some examples.
Step 1: Finding a Common Denominator
With these useful tips, you’ll be adding fractions like a professional in no time! The initial step is to find a common denominator for the two fractions you are adding. The smallest common denominator is the minimum number that both fractions will share equally.
If the fractions you wish to sum share the same denominator, you can avoid this step. If not, to determine the common denominator, you can list out the factors of each number as far as you determine a common one.
For example, let’s assume we wish to add the fractions 1/3 and 1/6. The lowest common denominator for these two fractions is six because both denominators will divide evenly into that number.
Here’s a quick tip: if you are uncertain regarding 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 change each fraction so that it has that denominator.
To convert these into an equivalent fraction with an identical denominator, you will multiply both the denominator and numerator by the identical number necessary 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 collectively to achieve 3/6, a proper fraction that we will be moving forward to simplify.
Step Three: Streamlining the Results
The final step is to simplify the fraction. Consequently, it means we are required to lower the fraction to its minimum 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 concluding answer of 1/2.
You go by 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 utilizing the process shown above, you will notice that they share equivalent denominators. You are lucky, this means you can avoid the initial stage. Now, all you have to do is add the numerators and allow it to 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 might indicate that you could 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 final answer of 2 by dividing the numerator and denominator by two.
Considering you go by these procedures when dividing two or more fractions, you’ll be a pro at adding fractions in no time.
Adding Fractions with Unlike Denominators
The procedure will need an supplementary 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 before 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 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 different, and the least common multiple is 12. Thus, we multiply every fraction by a value 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 move ahead 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 talked about 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 figure out addition sums 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
Note down your answer as a numerator and keep the denominator.
Now, you go ahead by adding these unlike fractions as you generally would.
Examples of How to Add Mixed Numbers
As an example, we will solve 1 3/4 + 5/4.
Foremost, let’s change the mixed number into a fraction. You will need 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 operation:
7/4 + 5/4
By summing the numerators with the exact denominator, we will have a ultimate answer of 12/4. We simplify the fraction by dividing both the numerator and denominator by 4, ensuing in 3 as a conclusive result.
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