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How To Add, Subtract, Multiply, And Divide Fractions?
Learn How To Add, Subtract, Multiply, And Divide Fractions?
Submitted by IncludeHelp, on January 25, 2025
Is it hard for you to apply basic mathematical operations to fractions? If yes, you are not alone. Instead, it’s a problem for many students. While it’s just a fundamental thing, many still don’t know how to add, subtract, multiply, or divide fractions. There might be many reasons behind it. For instance, one may have not understood the concept properly or forgotten the calculation process.
Well, whatever the reason is, you don’t need to worry about anything. Because we are going to teach you the basics of fractions once again. In this article, we will guide you on addition, subtraction, multiplication, and division of fractional numbers. Additionally, we will reveal a secret method of solving fractions. So, if you want to refresh your concepts or wish to learn them from scratch, make sure you read this post till the end.
Adding And Subtracting Fractions
When it comes to adding or subtracting two or more fractions, the same method is used. That’s why we will learn both these operations collectively. Since fractions have a numerator and denominator, their addition and subtraction are not like the normal numbers. You have to adopt a special approach to apply these operators on fractions.
However, it’s not difficult; rather, it’s just a few steps away. One important thing to remember in this regard is that there could be two cases in addition and subtraction. In the first one you may have the common denominators, and in the second one, the denominators may have different values. Let’s discuss both cases in detail.
Addition Of Fractions With Common Denominator
When you are given multiple fractions with an identical denominator, addition and subtraction become super easy. All you need to do is:
- Add the numerators.
- Keep the denominator unchanged.
Example (Addition)
3/7 + 4/7 + 2/7 = 3+4+2/7 = 9/7
Example (Subtraction)
9/11 − 7/11 = 9−7/11 = 2/11
Addition Of Fractions With Different Denominator
In case when the denominators are not the same, the process of addition and subtraction changes a little bit. In such problems, you have to:
- Find the LCM of denominators.
- Convert fractions to have the same denominator.
- When denominators become identical, simply add or subtract them.
Example (Addition & Subtraction)
Let’s say we want to add 2/4 and 5/6.
The LCM of the denominators 4 and 6 is 12.
Now, if you convert 2/4, it becomes 6/12.
Similarly, the fraction 5/6 becomes 10/12.
Since the denominators have become identical, the addition will be as follows:
6/12 + 10/12 = 6+10/12 = 16/12 = 4/3
Note: If we have to solve the same fractions with a minus sign between them, the process will be the same. All you need to do is subtract the fractions after converting them to have a common denominator. For instance, the subtraction of 2/4 and 5/6 after the conversion will be as follows:
6/12 − 10/12 = 6−10/12 = −4/12 = −1/3
Multiplication Of Fractions
If we say that multiplication of the fractions is the easiest operation, it would not be wrong. This is because whether you have two or more fractions, there is no conversion (such as in addition and subtraction) or any other complicated process involved. Instead, you are only required to multiply numerators and denominators of all fractions just like you perform normal multiplication.
After multiplying, you get a new fraction, which can be further simplified in some cases. So, if you find the possibility of simplification, just do it to reduce the new fraction to its lowest possible value. Let’s practically multiply some fractions.
Multiplying Proper & Improper Fractions
The process of the multiplication of both proper and improper fractions is the same as mentioned above. Here are their examples:
Proper Fraction
3/5 x 5/9 = 3x5 / 5x9 = 15/45 = ⅓
Improper Fractions
7/4 x 6/3 = 7x6 / 4x3 = 42/12 = 7/2
Division Of Fractions
The division of fractions involves a twist that is reciprocal. It basically involves flipping the numerator with the denominator. However, this doesn’t mean that you flip the two involved in the division. Instead, make sure you follow the below-mentioned process:
- Write the fractions as they are.
- Apply reciprocal to the second one.
Once you do so, all you need to do is multiply the first and the flipped fraction to perform division on both of them. Remember, there is no difference in the division of both proper and improper fractions. In the case of mixed numbers, you have to first convert them to one of the previously mentioned fractions to apply division.
Examples Of Division
3/9 ÷ 7/11 = 3/9 x 11/7 = 3x11 / 9x7 = 33/63 = 11/21
5/4 ÷ 2/6 = 5/4 x 6/2 = 5x6 / 4x2 = 30/8 = 15/4
Using Fraction Calculator For Basic Fractional Operations
Till now, all you have learned is to apply fractional operations manually. So now, let’s reveal the secret method. Here, we are talking about using an online calculator for fractions. Yes, you heard that right. While adding, subtracting, multiplying, and dividing fractions is not a big deal, it still requires sufficient manual effort and time. Moreover, you may sometimes fall victim to calculational errors while doing all these operations.
This is where a fraction calculator comes in handy. It not only reduces the efforts and time consumption on fractional operations, it also eliminates the risk of mistakes. All you have to do is provide the calculator with the given fractions. The tool automatically applies the respective operation and generates accurate and simplified results, leaving no need for manual hassles. So, you must try it to save time and get rid of calculational errors.
To Sum Up
After reading this article, we hope that you have learned all the basic fractional operations. We have tried to make everything clear with the help of practical examples. So, we are sure that you will barely need any further clarification for any operation. Apart from that, we also revealed an efficient yet less-known method to solve fractions. So, from now on, adding, subtracting, dividing, and multiplying fractions doesn’t have to be difficult for you.