How to Add Fractions: Examples and Steps
Adding fractions is a usual math operation that children learn in school. It can look intimidating at first, but it turns easy with a shred of practice.
This blog post will walk you through the procedure of adding two or more fractions and adding mixed fractions. We will then give examples to see how it is done. Adding fractions is crucial for several subjects as you advance in math and science, so make sure to adopt these skills initially!
The Steps of Adding Fractions
Adding fractions is an ability that many kids struggle with. Nevertheless, it is a relatively simple process once you master the essential principles. There are three major steps to adding fractions: determining a common denominator, adding the numerators, and simplifying the results. Let’s carefully analyze every one of these steps, and then we’ll do some examples.
Step 1: Determining a Common Denominator
With these helpful tips, you’ll be adding fractions like a professional in a flash! The initial step is to look for 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 want to add share the identical denominator, you can skip this step. If not, to find 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 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 great tip: if you are unsure 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 acquired the common denominator, the immediate 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 needed to achieve the common denominator.
Following the previous example, six will become the common denominator. To change the numerators, we will multiply 1/3 by 2 to get 2/6, while 1/6 would stay the same.
Now that both the fractions share common denominators, we can add the numerators collectively to achieve 3/6, a proper fraction that we will be moving forward to simplify.
Step Three: Simplifying the Results
The last step is to simplify the fraction. Consequently, it means we are required to reduce the fraction to its lowest terms. To accomplish this, we search for 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 concluding result of 1/2.
You go by the same steps to add and subtract fractions.
Examples of How to Add Fractions
Now, let’s move forward to add these two fractions:
2/4 + 6/4
By applying the procedures mentioned above, you will notice that they share the same denominators. Lucky you, this means you can skip the initial stage. At the moment, 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 higher 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 instance, the numerator and denominator can be divided by 4, its most common denominator. You will get a final answer of 2 by dividing the numerator and denominator by two.
Provided that you go by these procedures when dividing two or more fractions, you’ll be a expert 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 identical denominator.
The Steps to Adding Fractions with Unlike Denominators
As we mentioned above, to add unlike fractions, you must follow all three procedures mentioned above 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 different, and the lowest common multiple is 12. Hence, we multiply every fraction by a number to get 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 go forward to add the numerators:
2/12 + 8/12 + 18/12 = 28/12
We simplify the fraction by dividing the numerator and denominator by 4, coming to the ultimate result of 7/3.
Adding Mixed Numbers
We have mentioned 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 initiate by converting 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 retain the denominator.
Now, you proceed by summing 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.
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
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 be left with this operation:
7/4 + 5/4
By summing 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, resulting in 3 as a final result.
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