How to Solve Fractions – A Step-by-Step Guide

Mathematics is all about skills, calculations, and intelligence. Fractions are an inevitable part of basic mathematics. You will come across various types of fractions while doing calculations. Some people think that fractions are only a part of complicated calculations. While this statement could be true sometimes, it is not applicable everywhere.

Making calculations involving fractions could be a highly useful skill that often finds its applications in our everyday lives. Hence, knowing how to calculate fractions should be your priority when you aim to learn basic mathematical skills. Accurate fraction calculations require you to understand the various components and types of fractions.

Once you understand the essentials of fractions, it will be easier for you to solve them. You may need to add, subtract, multiply, or divide fractions. The process may also involve the simplification or reduction of fractions. Some people may also find solving fractions, especially complex ones, tricky. So, stick to this article, which discusses everything you should know to solve fractions easily.

This article will serve as a comprehensive guide. Let's delve further to learn more about fractions and their calculations.

Understanding the Basics

Before learning a few rules to consider while solving fractions, we must know a few basics. This section outlines these basics to help you understand the essentials of fractions. Read on to learn more.

Definition of Fraction

The term fraction refers to a mathematical value that is less than one. It denotes the portion of a whole. You can understand the concept of fractions by assuming a cake was cut into 12 equal pieces during a birthday celebration, and all those pieces were distributed among people attending the party. So, considering it mathematically, we can say that everyone received the 12th part or one-twelfth of the cake. We will mathematically denote this part as 1/12, which is considered a fraction in mathematics.

Various Parts of a Fraction

The example given with the definition gives a value that denotes the fraction. We can see 3 basic elements in this value. All these elements have a name. Here is what you need to know about these elements.

• A numerator is the digit coming before '/' or above the fraction line.
• The symbol '/' is called the fraction bar. It separates both numbers that make a fraction.
• A denominator is the digit coming after '/' or below the fraction line.

How to Solve Fraction Problems?

After understanding the basics of fractions, it is time to learn how to solve fractions. This section will help you learn how to add, subtract, multiply, divide, and simplify fractions. Further details are given below.

Rules to Consider

Before we start learning the addition, subtraction, multiplication, division, and simplification of fractions, you should learn a few basic rules to solve fractions and keep them in mind to perform accurate solutions.

• Ensure the dominators of two or more fractions have equal values before you perform addition or subtraction using the given values. Doing so will help you use a common denominator, making the process easier.
• During multiplication, you must multiply the two fractions' numerators and denominators. After multiplying numerators and denominators, you must simplify the resultant fraction to get an accurate result.
• Determine the reciprocal of the one fraction while dividing fractions.

Addition and Subtraction of Fractions

Here are a few steps you should perform to add or subtract fractions.

1. Finding a Common Denominator

In most cases, you may not get a common denominator when adding or subtracting fractions. So, you must make the denominator of both fractions similar to solve them. You can do it by multiplying each part of a fraction with the denominator of the other and vice versa. Doing so will help you get a common denominator to make adding or subtracting fractions easier. 

For instance, here are two fractions, 7/6 and 4/9. When you multiply both fractions with the denominator of the other, you will get a common dominator. In this case, it will be 54. Both the fractions will become 63/54 and 24/54.

2. Adding or Subtracting the Numerators

Once you get the common denominator, it is time to perform the calculation. Simply add or subtract the numerators of both fractions and get the resultant value. For example, when we add both fractions:

63/54 + 24/54 = 87/54

Similarly, after subtraction:

63/54 – 24/54 = 39/54

Remember that only numerators are added or subtracted when adding or subtracting fractions, and denominators are not involved in the calculation.

3. Simplifying the Sum

Once you have calculated the resultant values after adding or subtracting fractions, it is time to simplify the answer, which could be a larger fraction. For instance, 39/54 can be reduced to 13/18, and 87/54 can be reduced to 29/18.

Multiplication of Fractions

Here is a step-by-step guide to help you perform the multiplication of fractions. So, let's dive into the details.

1. Converting Mixed Fractions or Whole Numbers to Improper Fractions

Ambiguity may arise during the calculation that involves mixed fractions or whole numbers. Hence, to avoid ambiguity, it is essential to turn mixed and whole numbers into improper fractions before performing multiplication. 

If you get a whole number or mixed fraction for calculation, simply convert it to an improper fraction. 

For instance, you may need to turn 5 into an improper fraction if you want it to multiply with 2/4. You must turn 5 into a fraction, which could be its reciprocal '5/1'. Similarly, while dealing with a mixed fraction, you must multiply the denominator with the whole number and then add the numerator. For example, the improper fraction of 21/7 will be 15/7.

2. Multiplying the Numerators and Denominators

You don't need to add or subtract while multiplying two fractions. The process is quite simple. All you need to do is multiply the numerators of both fractions with each other and do the same with the denominators. 

For instance, if you are multiple 2/4 and 15/7, the answer will be 30/28. Here is how it will happen.

2/4 x 15/7 = 2 x 15 / 4 x 7 = 30 / 28

3. Simplifying the Answer

Once you get the answer, try to determine whether it can be reduced and look for the greatest common divisor (GCD) of the numerator and the denominator. For instance, the simplified version of the answer we have calculated in the above example will be 15/14. We will determine it by dividing both values by their GCD, which in this case is 2.

Division of Fractions

Fractions can be divided as well. However, you may find it a bit tricky and laborious. You can also use an efficient fraction calculator to perform such calculations in a matter of seconds without any possible chances of mistakes. Nevertheless, here is a step-by-step guide to dividing fractions.

1. Inverting the Second Fraction

To perform division using fractions, you must invert the second fraction and find its reciprocal. You don't need to have similar denominators to perform division using fractions. 

Here is an example:

9/6 ÷ 5/8 would require you to flip the second fraction and make it 8/5.

2. Multiplying the Numerators and Denominators

Once you flip the second fraction, it is time to multiply the fractions directly by multiplying the numerator of the first fraction with that of the reciprocal of the second fraction. Also, do the same with the denominators. Now mention the resultant fraction. Here is how you will do it.

9/6 ÷ 8/5 = 9 x 8 / 6 x 5 = 72/30

3. Simplifying the Resultant Fraction

Once you get the resultant fraction by multiplying numerators and denominators, it is time to reduce or simplify it to get an accurate result. Here is how you can do it.

72/30 = 12/5

First, you will divide both numbers with the GCD, which is 6, and write the reduced fraction as a result. Since the resultant fraction is improper, you can convert it into a mixed fraction to derive the proper answer. 

So, the reduced fraction we have found as an answer can be converted into a whole number. The process is simple and reverses what we do to convert mixed fractions into improper ones. You can divide the numerator by the denominator, write down the quotient as the whole number part of the mixed fraction, and put the remainder above the fraction line as the numerator. 

So, if we convert 12/5 to a mixed fraction, the answer will be 22/5.

Easy Way to Solve Fractions

Considering the steps and process to add, subtract, multiply, divide, and simplify fractions, you can understand why many people find it tricky and fail to solve fractions accurately. If you also shy away from manually solving fractions, then there is no need to worry. Like many other everyday tasks, you can also solve fractions with the help of an easily usable web-based fraction-calculators.org tool. Here are a few steps to solve fractions using a free fraction calculator.

1. Choose the fraction you want to solve, i.e., simple or mixed.
2. Input values accurately.
3. Choose the action you want to perform, such as addition, subtraction, multiplication, or division.
4. The calculator will show step-by-step calculations and the answer.
5. It will also convert the answer into decimals to ensure ease.

Conclusion

Solving fractions is nothing less than a skill. You must follow a few rules to perform accurate calculations. However, it can be tricky for some people who don't want to put much effort and time into the process. An online fraction calculator is a simple way for such people to solve fractions. Nevertheless, this article discusses everything you must know to solve fractions easily. It will be a perfect guide to help you perform calculations involving various fractions. Hopefully, you will find it helpful!