Fraction Calculations Made Easy – Learn How to Calculate Fractions

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Date: October 4, 2023

Are you facing problems in mathematical calculations? If yes, then you are not alone. Millions of individuals, especially students, face severe challenges in managing math problems. Fraction calculation is one of the most challenging tasks for most students.

If you want to learn the ways of calculating fractions, read this blog till the end.

This article will discuss fractions and some of the best ways to calculate them efficiently. So, let’s begin without any further ado! 

What are Fractions?

In mathematics, fractions are the numerical quantities that denote values less than one. A fraction can be a portion of any larger quantity out of a whole, where the whole can be any number or a thing. The following example will help you understand this concept easily.

Imagine you have a pizza that is divided into 8 equal parts. Now, if you need to denote any one selected part of the pizza, you can define it as 1/8, which shows that out of 8 equal parts, we are referring to 1 portion of pizza.

So, fractional numbers are mainly used to measure parts of a whole. For example,

• One-third (1/2)
• One-fourth (1/4)
• Two-thirds (2/3)

Basic Elements of Fractions

A fraction has a simple-to-learn structure. There is a numerator and a denominator in a fraction divided by a line known as the fractional bar. 

The integer above the bar which gets divided is the numerator. Similarly, the integer below the fractional bar which divides is called the denominator.

● Numerator 

The numerator defines how many fractional parts are selected. The numerator is positioned just above the fractional bar in the upper section of the fraction. 

For example: In the fraction x/y, the numerator is x.

● Denominator 

The denominator denotes the number of equal components into which a hole will be divided. The denominator is placed below the fractional bar in the lower section of the fraction. The denominator specifies how many pieces the whole will be divided into.

For example: In the fraction x/y, the denominator is y. 

● Fraction Bar 

The fraction bar is the line that separates the numerator from the denominator.

Types of Fractions

Fractions have different types based on the numerator and denominator. Some of them are discussed below. 

1. Unit Fraction

This is the type of fraction in which the numerator is 1. 

For example: 1/2, 1/4, 1/8, and more.

2. Proper Fraction

These are the fractions in which the numerator is smaller than its denominator. 

For example: 3/7, 5/8, 4/5, etc.

3. Improper Fraction

An improper fraction is a fraction in which the numerator value is larger than the denominator value. 

For Example: 8/5, 18/10, etc.

4. Mixed fractions

A mixed fraction is a fraction that is the mixture of a whole number and a proper fraction. 

For example, 5 ¾, where 5 is the whole number, and 3/4 is the proper fraction.

5. Like fractions

 These are the fractions that have the same denominators. 

For example: 3/10, 2/10, 7/10, and 1/10, etc. 

6. Unlike fractions

If fractions have different denominators, then they will be called unlike fractions. 

For example: 5/7, 9/11, 2/15, and 23/36, etc.

7. Equivalent fractions

A fraction with different numerators and denominators but equal when reduced to its simplest form.

To find equivalent fractions of any shared fraction:

• Multiply the numerator and the denominator of the fraction by the same number.
• Divide the numerator and the denominator of the fraction by the same number.

Example: 

Let’s find the two fractions that are equivalent to 3/5.

Solution:

Equivalent Fraction 1: Multiply the numerator and the denominator with the same number 2. 

3/5= (3 × 2) / (5 × 2) = 6/10

Equivalent Fraction 2: Multiply the numerator and the denominator with the same number 3. 

This means, 3/5 = (3 × 3) / (5 × 3) = 9/15

Therefore, 6/10, 9/15, and 3/5 are equivalent fractions.

Rules for Fraction Calculation 

Following are some rules you must learn before solving problems based on fractions.

Rule #1: It is essential to ensure that denominators are equal before adding or subtracting fractions. Thus, you can use a common denominator to add or subtract fractions.

Rule #2: The numerators and denominators are multiplied whenever we multiply two fractions. You need to simplify the fraction after that.

Rule #3: We need to find the reciprocal of another fraction and then multiply with the first one to get the answer to divide the fraction from another fraction. 

How to Calculate Fractions?

Calculating fractions is difficult, especially if you don’t know the calculation methods. However, there are different ways to calculate fractions, including the following. 

1- Adding or Subtracting Fractions

● Identify Fractions with Like Denominators

To add or subtract any fraction, make sure they have common denominators before you make your calculations. So, look at the denominators of the fractions to ensure they’re the same.

For example: 1/5 + 4/5

● Find A Common Denominator If the Denominators Are Unlike

If the denominators in the fractions are not the same, then it is essential for you to change the fractions to have the same denominators. To look for a common denominator, multiply each part of the fraction by the denominator of the other fraction.  

For instance, to check the common denominator for 1/4 + 4/5, multiply 1 and 4 by 5, and multiply 4 and 5 by 4. You will get 5/20 + 16/20. Now, you can calculate the fractions.

● Add or Subtract the Numerators to Calculate the Fractions

After finding the common denominator and multiplying the numerators if required, it’s time to add or subtract. Add or subtract the numerators, mention the output over a dividing line, and place the common denominator below the line.

For example:

5/20 + 16/20 = 21/20.

It is important to understand that denominators won’t be added or subtracted.

● Simply The Sum 

If the fractions don’t have a common denominator, and you have had to find it, then you may have a large fraction that can be simplified.

For example, if you have a resultant value of 32/40, then you can simplify it to 4/5.

2- Multiplying and Simplifying Fractions

● Turn Mixed Fractions or Whole Numbers into Improper Fractions

To multiply without ambiguity, you must work with proper or improper fractions. If you have a whole number or mixed fraction that you want to multiply, simply convert it into its fraction.

For example, to multiply 3/6 by 9, turn 9 into a fraction. Then, you can multiply 3/6 by 9/1.

If you have a mixed fraction like 2. 1/5, convert it into an improper fraction, 11/5, before you multiply.

● Multiply The Numerators and Denominators

Rather than adding the numerators, multiply both of the numerators and write the result over your dividing line. You are also required to multiply the denominators and mention the result under the line.

For example, multiply 2/5 by 5/6 and multiply 2 by 5 to get the numerator. Multiply 5 by 6 to get the denominator. Your answer will be 10/30.

● Simplify Your Result 

In different situations, you’ll be required to reduce the result to a simplified fraction, mainly if you start with improper fractions. Find the greatest common factor and use it to simplify the numerator and denominator.

For example, if your answer is 10/30, then 10 is the greatest common factor. Reduce the fraction by 10 to get 1/3.

3- Dividing Fractions 

● Invert The Second Fraction

Flipping the second fraction is the simplest way to divide fractions, even if they have unlike denominators.

For example, with 10/8 ÷ 2/4, you should flip the 2/4 fraction to appear 4/2.

● Multiply The Numerators and Denominators

After inverting the second fraction, multiply the fractions directly in front of the numerators to multiply them. Mention the result over a dividing line and multiply the denominators. Mention the result under the dividing line.

To continue the example, multiply 10/8 by 4/2 to get 40/16.

● Simplify The Results

If the resultant answer is an improper fraction or can be reduced, simplify the fraction.

Use the greatest common factor to decrease the fraction.

For example, the greatest common factor for 10/8 is 2, so your simplified answer is 5/4.

Since this is an improper fraction, convert it into a whole number with a fraction. 5/4 becomes 1. 1/4.

Conclusion:

Solving fractions is a laborious task for many students. However, calculating fractions is something every student needs to learn to complete the given assignments. The information shared in this blog post helps you learn about fractions, their different types and methods to calculate fractions accurately.