How To Perform Fraction Arithmetic: Steps And Examples

Mathematics is the basis for understanding the environment we live in. It provides us with the required methods to estimate, quantify, and analyze multiple aspects. The use of fractional calculations is necessary to solve many mathematical problems, especially when we need to calculate mixed numbers or have to perform complex calculations between different quantities. An understanding of fraction arithmetic is essential for many tasks in our everyday life.

In this article, we will discuss fraction arithmetic and provide step-by-step methods and examples to understand it. You can solve these calculations easily using tools like a mixed number calculator, especially during the exam season.

What is a Fraction?

A fraction represents a part of a whole object or collection of objects. A fraction has two parts. The number above the line is called a numerator and tells how many parts have been taken. The number below the line is called the denominator, which tells how many equal parts the object is divided into, or how many identical objects there are.

For example, ⅔ is a fraction.

Here, 2 is the numerator and 3 is the denominator.

What is a Fraction Calculator?

It is an online tool designed to calculate mixed numbers or simplify other calculations related to various fractions. It allows users to add, subtract, multiply, and divide fractions. This platform supports both common and mixed fractions and gives step-by-step explanations with accurate results. Apart from basic calculations, this tool also provides the facility to convert fractions to decimals and decimals to fractions.

Types of Fractions:

There are two most common types of fraction, which are discussed below.

Proper fraction:

The type of fraction in which the numerator is less than the denominator is known as the proper fraction.

For example: ½, ⅔, and ¾.

Improper fraction:

In this type of fraction, the numerator is greater or equal to the denominator.

For example: 5/4, 7/5, and 8/8.

Arithmetic Operations on Fraction:

Fractions can be added, subtracted, multiplied, and divided using specific rules.

1.    Addition:

• Find the same denominator for all fractions.
• Use the smallest number that all denominators can divide into (LCM or LCD).
• If the denominators are different, multiply each fraction to have the same denominator as the LCM.
• Add the top numbers (numerators).
• If the result is improper, turn it into a mixed fraction.

Example: Add 7/3 and 2/3.

7/3+2/3.

=(7+2) /3 (LCD is 3).

= 9/3.

=3.

For complex additions, you can use an adding mixed fractions calculator to simplify your calculations.

2.    Subtraction:

• Find the same denominator for all the fractions.
• Look for the smallest number that all denominators can divide into (LCM or LCD).
• If the denominators are different, multiply each fraction to have the same denominator as the LCM.
• Subtract the top numbers (numerators) and make the fraction as simple as possible.

Example: Subtract 3/7 and 9/3.

= 3(3)-7(9).

= (9-63) (LCD is 21).

= -56/21.

3.    Multiplication:

• Multiply the top numbers (numerators) of all fractions.
• Multiply the bottom numbers (denominators) the same way.
• Write the result as one fraction.
• Simplify the fraction to its smallest form.

Example: Multiply 23/10 and 45/10.

= (23*45) (10*10).

= 1035/100.

4.    Division:

• Find the opposite (reciprocal) and change division to multiplication.
• Flip the second fraction by swapping the top and bottom numbers.
• Multiply the top and bottom numbers.
• Simplify the result to its smallest form.

Example: Divide 6/3 and 4/2.

= 6/3*2/4 ( Reciprocal of divisor 4/2 is 2/4).

= 12/12.

= 1.

How to simplify fractions using the online calculator?

By using a standard fraction calculator:

• Choose if you want to simplify with 2 or 3 fractions.
• Pick the operation you want (add, subtract, multiply, or divide) from the dropdown.
• Enter the top and bottom numbers for the first fraction, and then do the same for the second one.
• Click the “Calculate” button.
• See the result, and you can also view the answer as a decimal.

Moreover, If you’re working with mixed fractions, a mixed number calculator can provide step-by-step solutions for you.

By using a mixed fraction calculator:

• Enter the whole number, top number (numerator), and bottom number (denominator) for each mixed number.
• Choose the operation you want (add, subtract, multiply, or divide).
• Click the “Calculate” button.
• The answer will appear as a mixed number, and it may also show a simplified fraction or a decimal.

FAQ’s:

1. What is the reciprocal of a fraction?

The reciprocal of a fraction is the fraction you get when you switch the numerator (top number) and the denominator (bottom number). For example, the reciprocal of 5/3 is 3/5.

2. What is the easiest way to remember the rules for fraction arithmetic?

The easiest way to remember the rules for fraction arithmetic is to “practice regularly.”

3. Can fractions simplified into decimals?

Yes, fractions can be converted to decimals by dividing the numerator by the denominator.

4. Is there a quick way to find the equality of two fractions?

Yes, the quick way is cross multiplication between two fractions. If the cross products are equal, the fractions are equivalent.

5. Is there a specific tool for fraction calculation?

Yes, numerous tools are available around the internet, such as Calculate mixed number tools, which simplify operations efficiently.