How to Add Fractions: Steps and Examples
Adding fractions is a common math problem that students learn in school. It can appear scary at first, but it turns simple with a shred of practice.
This blog post will walk you through the steps of adding two or more fractions and adding mixed fractions. We will also give examples to show what must be done. Adding fractions is crucial for a lot of subjects as you advance in math and science, so ensure to master these skills initially!
The Steps of Adding Fractions
Adding fractions is a skill that a lot of children have difficulty with. Despite that, it is a somewhat hassle-free process once you master the essential principles. There are three primary steps to adding fractions: determining 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: Look for a Common Denominator
With these helpful points, you’ll be adding fractions like a expert in no time! The initial step is to look for a common denominator for the two fractions you are adding. The least common denominator is the minimum number that both fractions will split equally.
If the fractions you desire to add 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 respective number until you determine a common one.
For example, let’s assume we desire to add the fractions 1/3 and 1/6. The lowest common denominator for these two fractions is six because both denominators will split evenly into that number.
Here’s a good 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
Once you have the common denominator, the following step is to change each fraction so that it has that denominator.
To turn these into an equivalent fraction with the exact denominator, you will multiply both the denominator and numerator by the identical number needed to achieve the common denominator.
Subsequently the prior example, six will become the common denominator. To change the numerators, we will multiply 1/3 by 2 to get 2/6, while 1/6 would stay the same.
Now that 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 Answers
The last process is to simplify the fraction. Doing so means we need to diminish the fraction to its lowest terms. To accomplish this, we look 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 same process to add and subtract fractions.
Examples of How to Add Fractions
Now, let’s move forward to add these two fractions:
2/4 + 6/4
By using the procedures mentioned above, you will notice that they share equivalent denominators. Lucky you, this means you can skip the first stage. At the moment, 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 see 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 instance, the numerator and denominator can be divided by 4, its most common denominator. You will get a ultimate answer of 2 by dividing the numerator and denominator by 2.
As long as you follow 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 extra step when you add or subtract fractions with distinct denominators. To do these operations with two or more fractions, they must have the same denominator.
The Steps to Adding Fractions with Unlike Denominators
As we mentioned prior to this, to add unlike fractions, you must obey all three steps mentioned prior to convert these unlike denominators into equivalent fractions
Examples of How to Add Fractions with Unlike Denominators
Here, we will focus 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 smallest common multiple is 12. Hence, 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 move ahead to add the numerators:
2/12 + 8/12 + 18/12 = 28/12
We simplify the fraction by dividing the numerator and denominator by 4, finding a ultimate result of 7/3.
Adding Mixed Numbers
We have discussed like and unlike fractions, but presently we will go through mixed fractions. These are fractions followed by whole numbers.
The Steps to Adding Mixed Numbers
To solve addition problems with mixed numbers, you must initiate by changing 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 answer as a numerator and keep the denominator.
Now, you proceed by adding these unlike fractions as you normally would.
Examples of How to Add Mixed Numbers
As an example, we will solve 1 3/4 + 5/4.
First, let’s convert 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 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, resulting in 3 as a final result.
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