How to Add Fractions: Steps and Examples
Adding fractions is a usual math problem that kids study in school. It can look daunting at first, but it can be easy with a shred of practice.
This blog article will guide the steps of adding two or more fractions and adding mixed fractions. We will then provide examples to show what must be done. Adding fractions is essential for several subjects as you progress in science and mathematics, so be sure to learn these skills initially!
The Process of Adding Fractions
Adding fractions is a skill that a lot of students have a problem with. However, it is a somewhat easy process once you understand the basic principles. There are three primary steps to adding fractions: looking for a common denominator, adding the numerators, and streamlining the answer. Let’s closely study every one of these steps, and then we’ll look into some examples.
Step 1: Look for a Common Denominator
With these useful points, you’ll be adding fractions like a professional in a flash! The first step is to determine a common denominator for the two fractions you are adding. The smallest common denominator is the lowest number that both fractions will divide equally.
If the fractions you wish to add share the equal denominator, you can skip this step. If not, to find the common denominator, you can list out the factors of respective number until you look for a common one.
For example, let’s say we wish to add the fractions 1/3 and 1/6. The lowest common denominator for these two fractions is six for the reason that both denominators will divide equally into that number.
Here’s a good tip: if you are uncertain about this process, you can multiply both denominators, and you will [[also|subsequently80] get a common denominator, which would be 18.
Step Two: Adding the Numerators
Now that you acquired the common denominator, the immediate step is to change 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 exact number necessary to achieve the common denominator.
Subsequently the prior example, 6 will become the common denominator. To change the numerators, we will multiply 1/3 by 2 to attain 2/6, while 1/6 will remain the same.
Since both the fractions share common denominators, we can add the numerators simultaneously to get 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 minimum 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 final result 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 applying the procedures mentioned above, you will observe that they share identical denominators. You are lucky, this means you can avoid the first stage. Now, all you have to do is add the numerators and leave 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 larger than the denominator. This might suggest that you can 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 ultimate answer of 2 by dividing the numerator and denominator by two.
Considering you follow these procedures when dividing two or more fractions, you’ll be a professional at adding fractions in a matter of time.
Adding Fractions with Unlike Denominators
This process will require an additional step when you add or subtract fractions with distinct denominators. To do this function with two or more fractions, they must have the exact denominator.
The Steps to Adding Fractions with Unlike Denominators
As we stated prior to this, to add unlike fractions, you must obey all three steps stated prior to change 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 demonstrated, the denominators are distinct, and the least common multiple is 12. Hence, we multiply every 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
Since 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 dividing the numerator and denominator by 4, concluding with 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 figure out addition exercises with mixed numbers, you must start by turning 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
Note down your result as a numerator and retain the denominator.
Now, you proceed by summing these unlike fractions as you generally 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 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 end up with this result:
7/4 + 5/4
By adding the numerators with the similar 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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