How to Add Fractions: Examples and Steps
Adding fractions is a regular math operation that students learn in school. It can appear daunting initially, but it can be easy with a bit of practice.
This blog article will guide the steps of adding two or more fractions and adding mixed fractions. We will also provide examples to demonstrate what must be done. Adding fractions is essential for several subjects as you advance in mathematics and science, so be sure to adopt these skills initially!
The Process of Adding Fractions
Adding fractions is an ability that many students have difficulty with. Nevertheless, it is a somewhat hassle-free process once you understand the basic principles. There are three primary steps to adding fractions: looking for a common denominator, adding the numerators, and simplifying the answer. Let’s closely study each of these steps, and then we’ll do some examples.
Step 1: Look for a Common Denominator
With these helpful tips, 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 share uniformly.
If the fractions you wish to add share the identical denominator, you can avoid this step. If not, to look for the common denominator, you can determine the number of the factors of each number until you find a common one.
For example, let’s say we want 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 good tip: if you are not sure about 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
Once you have the common denominator, the following step is to turn each fraction so that it has that denominator.
To change these into an equivalent fraction with an identical denominator, you will multiply both the denominator and numerator by the same number necessary to get the common denominator.
Following the last 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 would remain the same.
Now that both the fractions share common denominators, we can add the numerators together to achieve 3/6, a proper fraction that we will continue to simplify.
Step Three: Streamlining the Answers
The final step is to simplify the fraction. Consequently, it means we are required to diminish the fraction to its minimum terms. To obtain this, we search 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 ultimate answer 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 using the process shown above, you will see that they share the same denominators. You are lucky, this means you can avoid the first step. Now, all you have to do is sum of the numerators and let it be the same denominator as it was.
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 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 conclusive answer of 2 by dividing the numerator and denominator by 2.
Provided that 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
This process will need an additional step when you add or subtract fractions with dissimilar 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 stated before this, to add unlike fractions, you must obey all three steps mentioned prior to transform these unlike denominators into equivalent fractions
Examples of How to Add Fractions with Unlike Denominators
Here, we will put more emphasis on another example by adding the following fractions:
1/6+2/3+6/4
As shown, the denominators are different, and the lowest common multiple is 12. Thus, we multiply each fraction by a value to achieve the denominator of 12.
1/6 * 2 = 2/12
2/3 * 4 = 8/12
6/4 * 3 = 18/12
Now 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 final result of 7/3.
Adding Mixed Numbers
We have mentioned like and unlike fractions, but now we will revise 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 start by turning 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
Take down your result as a numerator and retain the denominator.
Now, you move forward by adding these unlike fractions as you usually 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 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 result of 12/4. We simplify the fraction by dividing both the numerator and denominator by 4, resulting in 3 as a final answer.
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