Created by: Shivam midha
Did you learn fractional calculations before but are now failing to remember some basics? Or are you new to the concept of fractions and want to learn how to calculate them? If so, this article is worth reading for you. In this post, we will walk you through a strategic procedure to help you know how to add, subtract, multiply, and divide fractions. However, before that, let’s recall what a fraction is and what it has. Let’s get started.
In mathematics, a fraction usually refers to a part of a whole. Here, one thing that needs to be clarified is that the term “whole” entails an object or a group of objects. So, in simple words, a fraction is a small or large part of a quantity. It has two universal components: numerator and denominator.
For example, in 3/4, 3 is the numerator and 4 is the denominator. In some cases, a whole number may be combined with a fraction, which creates a mixed fraction. For instance, in 5 3/4, the number 5 makes the fraction mixed.
Now that you have understood what a fraction is and what its components are. Let's learn how to calculate them with the implementation of different mathematical operators.
Adding and subtracting fractions is no doubt an easy task. However, one thing that you have to take care of is to remember whether you are performing addition or subtraction of proper, improper, or mixed fractions. Another important thing that matters in this regard is whether the denominators are identical or different. So, let’s learn the calculation of fractions in both cases.
Fractions With Identical Denominators
The simple rule to add or subtract two fractions with the same denominators is to simply add the numerators. Now, you may be wondering what to do with the denominator; well, just keep it unchanged.
Examples
Addition: 5/9 + 6/9 = 5+6/9 = 11/9
Subtraction: 11/7 − 4/7 = 11−4/7 = 7/7 = 1
Fractions With Different Denominators
In the cases of different denominators, the method of adding and subtracting fractions changes a little bit. When you have two fractions with dissimilar denominators, first, you have to find their LCM. Next, you are required to convert the fractions so that they have the same denominator. Once the denominators become equal, the rest of the process is the same as stated above.
Examples
Addition:
5/7 + 9/5
LCM of 7 and 5 is 35.
Now, multiple numerators and denominators with such numbers that we get identical denominators.
5×5/7×5 + 9×7/5×7
25/35 + 63/35
25+63/35
88/35
Subtraction:
7/3 − 4/5
LCM of 3 and 5 is 15.
So now, convert fractions to have the same denominators.
7×5/3×5 − 4×3/5×3
35/15 − 12/15
35−12/15
23/15
Multiplication is the easiest operation to apply to fractions. In this calculation, you don’t have to have the same numerators or denominators. Instead, the process is simple, requiring you to multiply numerators and denominators of fractions with each other in a normal manner.
For instance, if you are going to multiply 3 fractions, just multiply the numerator of the first one by the second fraction and the resultant number by the third one. You need to do the same with the denominators of all the 3 fractions. However, if it’s a mixed fraction, you will have to first convert it to a proper or improper fraction to apply multiplication. Let’s learn these calculations by examples.
Examples
Proper Fraction: 4/6 × 3/9 = 4 × 3 / 6 × 9 = 12 / 63 = 4 / 21
Improper Fraction: 11/3 × 9/2 = 11 × 9 / 3 × 2 = 99 / 6 = 33 / 2
Mixed Fraction: 3 7/3 × 2 5/4 = 16/3 × 13/4 = 13 × 16/3 × 4 = 208/12 = 52/3 = 17 1/3
Dividing a fraction is nearly the same as multiplying them. Now, you may be wondering that multiplication and division are two completely different operations, so how could they be applied in the same way to fractions? Well, the twist is that you have to flip the numerator with the denominator of the second fraction to perform division.
This is how fractional division is partially identical to fractional multiplication but completely different from normal division. An important thing to remember in this regard is that the sign of division gets converted to multiplication when you take the reciprocal of the second fraction.
Then, the rest of the calculation procedure becomes the same as multiplication. Here are some examples that will help you better understand this concept.
Examples
Proper Fraction: 6/9 ÷ 3/12 = 6/9 × 12/3 = 6 × 12 / 9 × 3 = 72/27 = 24/9 = 8/3
Improper Fraction: 14/6 ÷ 18/4 = 14/6 × 4/18 = 14×4/6×18 = 56/108 = 14/27
Mixed Fraction: 3 7/3 ÷ 2 5/4 = 16/3 ÷ 13/4 = 16/3 × 4/13 = 16 × 4/3 × 13 = 64/39
By going through the above examples, you might have learned to calculate fractions. However, if you want to remember the concepts involved in these computations for longer, you must practice daily. You may be wondering if practicing fractional calculations requires sufficient time, as an easy division or multiplication involves multiple steps.
However, worry not; the technology has provided you with a robust solution, such as a fraction calculator to help you learn effortlessly. Whether it’s adding, subtracting, or applying any other operation on a fraction, you can do it quickly using a calculator for fractions.
What makes this learning approach worth considering is that the calculators offer step-by-step solutions, allowing you to know the science behind each calculation. So, a fraction calculator could be a great learning partner if you use it consistently to improve your concepts.
Now that you have learned the methods to calculate fractions, solving all kinds of fractions should be easy for you. Remember, regular practice can make you a master in applying different operations on fractions. Along with manual practice, using an automated calculator can cut your practice time and effort. So, combine both techniques for faster and better learning.