How to Add Fractions: Steps and Examples
Adding fractions is a regular math problem that children learn in school. It can look intimidating at first, but it can be easy with a bit of practice.
This blog post will guide the procedure of adding two or more fractions and adding mixed fractions. We will then provide examples to demonstrate how it is done. Adding fractions is crucial for various subjects as you progress in science and mathematics, so make sure to adopt these skills initially!
The Steps of Adding Fractions
Adding fractions is an ability that a lot of children struggle with. Despite that, it is a moderately easy process once you understand the fundamental principles. There are three main steps to adding fractions: determining a common denominator, adding the numerators, and streamlining the results. Let’s take a closer look at every one of these steps, and then we’ll look into some examples.
Step 1: Look for a Common Denominator
With these useful tips, you’ll be adding fractions like a pro 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 split evenly.
If the fractions you want to sum share the identical denominator, you can skip this step. If not, to determine the common denominator, you can determine the number of the factors of respective number as far as you look for a common one.
For example, let’s assume we want to add the fractions 1/3 and 1/6. The lowest common denominator for these two fractions is six in view of the fact that both denominators will split evenly into that number.
Here’s a great tip: if you are not sure about 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 immediate step is to turn 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 exact number necessary to get 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 achieve 2/6, while 1/6 would remain the same.
Now that both the fractions share common denominators, we can add the numerators simultaneously to attain 3/6, a proper fraction that we will be moving forward to simplify.
Step Three: Simplifying the Answers
The final step is to simplify the fraction. Doing so means we need to lower the fraction to its lowest terms. To accomplish 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 result of 1/2.
You follow the same procedure 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 procedures mentioned above, you will observe that they share the same denominators. Lucky you, this means you can avoid the initial stage. At the moment, all you have to do is add the numerators and allow it to be the same denominator as it was.
2/4 + 6/4 = 8/4
Now, let’s attempt to simplify the fraction. We can perceive that this is an improper fraction, as the numerator is greater than the denominator. This could indicate that you could simplify the fraction, but this is not feasible when we work 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 final result 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 additional step when you add or subtract fractions with dissimilar 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 have said before this, to add unlike fractions, you must obey all three procedures mentioned above to convert 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 summing up the following fractions:
1/6+2/3+6/4
As demonstrated, the denominators are dissimilar, and the least common multiple is 12. Therefore, we multiply every fraction by a number 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 proceed to add the numerators:
2/12 + 8/12 + 18/12 = 28/12
We simplify the fraction by splitting the numerator and denominator by 4, coming to the final answer 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 figure out 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 move forward by adding these unlike fractions as you normally would.
Examples of How to Add Mixed Numbers
As an example, we will work with 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
Then, add the whole number represented as a fraction to the other fraction in the mixed number.
4/4 + 3/4 = 7/4
You will conclude with this result:
7/4 + 5/4
By adding the numerators with the exact denominator, we will have a conclusive 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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