How to Add Fractions: Steps and Examples
Adding fractions is a common math operation that kids learn in school. It can seem scary initially, but it becomes simple with a shred of practice.
This blog article will guide the process of adding two or more fractions and adding mixed fractions. We will then provide examples to demonstrate what must be done. Adding fractions is necessary for a lot of subjects as you move ahead in science and math, so be sure to master these skills early!
The Process of Adding Fractions
Adding fractions is an ability that many kids have a problem with. Despite that, it is a somewhat hassle-free process once you understand the basic principles. There are three major 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 look into some examples.
Step 1: Finding a Common Denominator
With these valuable tips, you’ll be adding fractions like a professional in an instant! The first 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 uniformly.
If the fractions you wish to sum share the equal denominator, you can avoid this step. If not, to find 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 say 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 uniformly into that number.
Here’s a good tip: if you are unsure regarding 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
Now that you acquired the common denominator, the next step is to change each fraction so that it has that denominator.
To change these into an equivalent fraction with the exact denominator, you will multiply both the denominator and numerator by the exact number necessary to attain the common denominator.
Following the prior example, 6 will become the common denominator. To change the numerators, we will multiply 1/3 by 2 to achieve 2/6, while 1/6 will stay the same.
Considering that both the fractions share common denominators, we can add the numerators simultaneously to achieve 3/6, a proper fraction that we will continue to simplify.
Step Three: Simplifying the Results
The last step is to simplify the fraction. As a result, it means we need to lower the fraction to its lowest 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 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 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 applying the steps above, you will observe that they share equivalent denominators. You are lucky, this means you can avoid the first step. At the moment, all you have to do is sum of the numerators and allow it to be the same denominator as it was.
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 can 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 ultimate result of 2 by dividing the numerator and denominator by two.
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 need an extra 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 prior to this, to add unlike fractions, you must obey all three procedures stated above to convert these unlike denominators into equivalent fractions
Examples of How to Add Fractions with Unlike Denominators
At this point, we will focus on another example by summing up the following fractions:
1/6+2/3+6/4
As demonstrated, the denominators are distinct, and the lowest common multiple is 12. Thus, we multiply each 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
Since 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 ultimate result of 7/3.
Adding Mixed Numbers
We have talked about like and unlike fractions, but presently we will go through mixed fractions. These are fractions accompanied by whole numbers.
The Steps to Adding Mixed Numbers
To figure out addition exercises with mixed numbers, you must initiate by changing 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
Note down your result 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.
First, 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
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 end up with this result:
7/4 + 5/4
By adding the numerators with the exact denominator, we will have a conclusive 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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