How to Add Fractions: Steps and Examples
Adding fractions is a usual math problem that children learn in school. It can seem intimidating initially, but it turns easy with a shred of practice.
This blog post will guide the steps of adding two or more fractions and adding mixed fractions. We will ,on top of that, provide examples to show how this is done. Adding fractions is crucial for several subjects as you move ahead in mathematics and science, so ensure to adopt these skills early!
The Steps of Adding Fractions
Adding fractions is a skill that a lot of kids have difficulty with. Despite that, it is a somewhat easy process once you grasp the basic principles. There are three main steps to adding fractions: looking for a common denominator, adding the numerators, and streamlining the answer. Let’s carefully analyze each of these steps, and then we’ll look into some examples.
Step 1: Determining a Common Denominator
With these useful points, you’ll be adding fractions like a expert in no time! The first step is to look for a common denominator for the two fractions you are adding. The smallest common denominator is the lowest number that both fractions will divide uniformly.
If the fractions you want to sum share the same denominator, you can avoid this step. If not, to determine the common denominator, you can list out the factors of respective number as far as you determine 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 uniformly into that number.
Here’s a quick tip: if you are uncertain regarding 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
Once you possess the common denominator, the immediate step is to convert 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 identical number necessary to achieve the common denominator.
Subsequently the last 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 collectively to get 3/6, a proper fraction that we will proceed to simplify.
Step Three: Simplifying the Results
The final step is to simplify the fraction. As a result, it means we need to lower the fraction to its minimum 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 greatest common factor of 3 and 6 is 3. When we divide both numbers by 3, we get the concluding result of 1/2.
You follow the exact steps to add and subtract fractions.
Examples of How to Add Fractions
Now, let’s proceed to add these two fractions:
2/4 + 6/4
By using the steps above, you will see that they share the same denominators. Lucky you, this means you can avoid the initial step. 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 might indicate that you can simplify the fraction, but this is not possible when we deal 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 answer of 2 by dividing the numerator and denominator by 2.
Provided that you follow these steps when dividing two or more fractions, you’ll be a professional at adding fractions in no time.
Adding Fractions with Unlike Denominators
The procedure will require an extra step when you add or subtract fractions with dissimilar denominators. To do these operations with two or more fractions, they must have the exact denominator.
The Steps to Adding Fractions with Unlike Denominators
As we stated above, to add unlike fractions, you must obey all three steps stated above to change these unlike denominators into equivalent fractions
Examples of How to Add Fractions with Unlike Denominators
Here, we will concentrate on another example by adding the following fractions:
1/6+2/3+6/4
As shown, the denominators are different, and the lowest common multiple is 12. Thus, we multiply each fraction by a number to achieve the denominator of 12.
1/6 * 2 = 2/12
2/3 * 4 = 8/12
6/4 * 3 = 18/12
Now that 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 splitting the numerator and denominator by 4, coming to the ultimate answer 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 work out addition exercises with mixed numbers, you must start by converting 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
Take down your answer as a numerator and keep 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 out 1 3/4 + 5/4.
Foremost, 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
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 be left with this operation:
7/4 + 5/4
By adding the numerators with the same denominator, we will have a ultimate answer 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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