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Types of Fractions
Mathematical Operations

# How to Do Fraction Arithmetic

Fractions are one of the basic but very important concepts in mathematics. If you have a strong grip over fraction resolving, then you will face no difficulty in carrying out even complex computations. And if you are not good with fractions, then it is

April 14, 2023 By Arun Garg

Entrepreneur I Writer ## What Is Fraction?

Fraction represents part of a whole. This gives you a strong idea of maintaining accuracy when dealing with complicated calculations.

Types of the Fractions:

There are three types of the fraction, Proper, Improper and the Mixed fraction. When you are using the fraction calculator it is necessary to identify which types of the fraction you are dealing with and how you can find its LCM and the HCF.

• ## Proper Fraction:

In the proper fraction the numerator is less than the denominator, and you normally deal with the proper in the business and trade.

Numerator < Denominator

Examples:

⅜, ⅖,3/9, 5/9,6/18,12/13 etc

You can add and subtract two like proper fractions, but it is necessary to take the Least common multiple of the proper fractions.

• ## Improper Fraction:

In the improper fraction the numerator is larger than the denominator, and you can spot the improper fractions by learning this definition. You can use the free online Fraction Calculator to find the solution of the improper fraction.

Numerator > Denominator

Examples:

8/3, 5/2,7/3, 9/2,21/7,15/5 etc

For division, you need to reverse the fraction, then you can multiply the improper fractions.The division of the improper fraction is a little difficult for the students to learn and teach.

• ### The Mixed Fraction:

A mixed fraction is a combination of the natural number and a fraction, it is also described as the whole fraction. You need to change the mixed fraction into the proper and or the improper fraction before solving the mixed fraction.

Examples:

Like

2 ⅓, 4 ⅓, 7 3/9, 8 ⅝

You can convert the mixed fractions into simple fraction by follwin method:

Method to break the Mixed Fractions:

We are presenting the method of breaking 5[(7/9)], it is simple to break down the mixed fraction into the simpler fraction:

Let’s see:

• First multiply the 5 by the 9, and the answer would be 5(9)=45

• Now add the 7 into the 45, the answer would be 45+7 = 52

• Then the answer of the mixed fraction  5[(7/9)]= 52/9

• The new fraction is the 52/9,which is improper in nature as the numerator is larger than the denominator.

• Now you can solve the improper fraction 52/9 as the other common fraction.

The fraction calculator is used to find the answer of the mixed fraction as it is easy to break the mixed fraction into the simpler fraction.It is essential to break the mixed fraction into the simpler fraction as you can’t solve the mixed fraction directly. It is quite important to recognize the various types of the fraction to implement the arithmetic operations on the fractions.

## Operations on Fractions:

Following are four major operations that fraction calculator assists you to apply on fractions:

• First, calculate the least common denominator (LCM) of all the fractions

• Now divide the denominator of each fraction with LCM, and multiply the resulting number with the numerator of the same fraction

• Write the final number above LCM and repeat the process until all fractions are done

• Now add all the numerators and and divide the number by LCM

• This is how you get the reduced form

#### Example:

##### Solution:

13+58

The method of taking the Least common multiple or LCM of a fractions 13+58, as it is necessary to add to unlike fractions as the LCM of the denominators 8 and 3 is 24.

=8+1524

=2324

Which is the required reduced form of the fraction.

### 2. Subtraction:

Subtraction of fractions is just opposite to that of the addition.

• Repeat step 1 to step 3 as done for addition
• Now minus all the numerators and and divide the number by LCM

• This is how you get the reduced form

#### Example:

Subtract 3/7 and 6/8

=37-68

=24-4256

=-1856

=-928

### 3. Multiplication:

Multiplication of fractions can instantly be done by using the fraction calculator. Do not just think if we come to manual calculations, the process is going to be somehow complex. It is still very simple to understand!

• Multiply the numerators of al fractions
• Likewise, find the product of denominators as well

• Reduce to the most simplified form

#### Example:

Multiply 3/5, 6/3, and 2/6

Here we have:

=35*63*26

=3*6*25*3*6

=36/90

=18/45

### 4. Division:

Like addition and subtraction, multiplication and division are opposite to one another. All you need to remember is the following rule:

Keep:

• Keep the first fraction as it is

###### Change:
• Change the first division sign to product sign

###### Flip:
• Now flip the next fraction by interchanging its numerator and denominator

• Repeat the step until and unless you are done with the last fraction

Example:

Divide 5/6 and 6/9

=5669

=5696

=45/36

=5/4

## Wrapping It Up:

So now we are pretty sure that you have learned fraction arithmetic. In case of any difficulty, try reading the post once again and you will get a firm grip over the concept for sure. In case of any hurdle, you may be subject to the free online fraction calculator.

We wish you a very best of luck for your upcoming examination.