How to Add Fractions: Examples and Steps
Adding fractions is a common math application that students study in school. It can appear scary at first, but it turns easy with a bit of practice.
This blog post will walk you through the process of adding two or more fractions and adding mixed fractions. We will also provide examples to demonstrate what must be done. Adding fractions is necessary for several subjects as you progress in science and math, so be sure to adopt these skills early!
The Steps of Adding Fractions
Adding fractions is an ability that numerous kids have a problem with. However, it is a somewhat simple process once you master the fundamental 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 look into some examples.
Step 1: Finding a Common Denominator
With these helpful points, you’ll be adding fractions like a professional in an instant! The first step is to determine a common denominator for the two fractions you are adding. The smallest common denominator is the minimum number that both fractions will divide equally.
If the fractions you desire to sum share the equal denominator, you can skip this step. If not, to look for the common denominator, you can determine the amount of 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 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 unsure 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 possess the common denominator, the following step is to turn each fraction so that it has that denominator.
To convert these into an equivalent fraction with the same denominator, you will multiply both the denominator and numerator by the exact number necessary to achieve 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 will stay the same.
Considering that both the fractions share common denominators, we can add the numerators together to get 3/6, a proper fraction that we will be moving forward to simplify.
Step Three: Simplifying the Answers
The last process 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 largest 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 exact 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 applying the steps above, you will notice that they share identical denominators. Lucky you, this means you can avoid the first stage. Now, 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 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 necessarily the case 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 conclusive 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 expert at adding fractions in matter of days.
Adding Fractions with Unlike Denominators
This process will require an supplementary 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 stated before this, to add unlike fractions, you must obey all three steps stated prior to convert these unlike denominators into equivalent fractions
Examples of How to Add Fractions with Unlike Denominators
At this point, we will concentrate on another example by adding the following fractions:
1/6+2/3+6/4
As you can see, the denominators are dissimilar, and the least common multiple is 12. Therefore, we multiply each 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
Once 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, concluding with a final answer 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 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
Write down your result as a numerator and keep 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 solve 1 3/4 + 5/4.
First, let’s transform the mixed number into a fraction. You will need to multiply the whole number by the denominator, which is 4. 1 = 4/4
Next, 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 final result of 12/4. We simplify the fraction by dividing both the numerator and denominator by 4, ensuing in 3 as a conclusive answer.
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