Fractions Calculator

What is a fraction and examples?

A fraction is a number that represents a part of the whole. The word fraction comes from a latin word ‘fractio’ which means to break.

A fraction consists of a numerator and a denominator. The numerator represents the number of equal parts out of whole and the denominator represents the total number of parts in which the whole has been divided.

For example,

• in the fraction 4/9, 4 is the numerator and 9 is the denominator.
• Fraction 4/9 represents 4 equal parts out of the total 9 parts.

Denominator of the fraction cannot be 0 as that would mean that the total number of parts are 0 making the fraction value undefined.

A fraction can be classified into different types, namely proper fraction, improper fraction, and mixed fraction.

1. Proper fraction – The numerator is less than the denominator
2. improper fraction – The numerator is greater than the denominator
3. mixed fraction – The number is the combination of the whole number and a proper fraction

You can also use below free fractions calculators

Fractions

• Fraction calculator – To perform mathematical Operations (addition, subtraction, multiplication, division)
• Fraction Simplifier calculator – To simplify fractions
• Fraction Converter
  • Fraction to Decimal calculator
  • Decimal to Fraction calculator
  • Fraction to Percent calculator
  • Percent to Fraction calculator

Mixed Fractions

• Mixed Fraction calculator – To perform mathematical Operations (addition, subtraction, multiplication, division)
• Mixed Fraction Simplifier calculator – To simplify Mixed fractions
• Mixed Fraction Converter
  • Mixed Fraction to Decimal calculator
  • Mixed Fraction to Percent calculator
  • Mixed Fraction to improper fraction calculator

Mathematical Operations on Fractions

There are a lot of different arithmetic operations that can be performed on fractions. Learn How to Add, Subtract, Multiply, and Divide Fractions

Addition of Fractions – How to Add fractions?

In order to perform addition on fractions, a common denominator is required. How to Find Common Denominator?

Method 1: Calculation using fraction addition formula

One of the ways to find a common denominator is to multiply the numerator and denominator of each fraction involved in the operation with the denominator of all the fractions involved. But the resultant fraction using this method may not be in simplified form.

a/b + c/d = a*d/b*d + c*b/d*b = (ad + cb)/ bd

Let’s look at it through an example

For Example, 2/5 + 4/9

= (2 * 9)/(5 * 9) + (4 * 5)/(9 * 5)

= (2 * 9 + 4 * 5)/(9 * 5)

= (18 + 20)/45

= 38/45

Method 2: Calculation using LCD

Another way to find a common denominator is to find the Least Common Multiple (LCM) of all the denominators of the fractions to be added. This method is better than the above because the result would be in simplified form in this case.

Let’s look at it through an example

2/9 + 4/3 + 7/12

Multiples of 9 = 9, 18, 27, 36, 45

Multiples of 3 = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36

Multiples of 12 – 12, 24, 36, 48

The first multiple that all the denominators share is 36, so this is the Least Common Multiple (LCM). Multiply the numerator and denominator of all the fractions with a value that makes the denominator as 36 and then perform addition of the numerators like integers.

Continuing with our example, 2/9 + 4/3 + 7/12

= 2*4/9*4 + 4*12/3*12 + 7*3/12*3

= 8/36 + 48/36 + 21/36

= (8+48+21)/36

= 77/36

Subtraction of Fractions – How to subtract fraction?

Subtraction of fractions is very similar to Addition. A common denominator is required to perform the operation.

Refer to the addition section to know how to find the common denominator in detail.

a/b – c/d = a*d/b*d – c*b/d*b = (ad – cb)/db

For Example, 4/9 – 2/5

= 4*5/9*5 – 2*9/5*9

= (20-18)/45

= 2/45

Multiplication of Fractions – How to multiply fraction?

Multiplication of fractions is pretty straightforward. A common denominator is not required for multiplication. Simply, multiply the numerators and the denominators to obtain a new fraction with new numerator and denominator. Simplify the result, if required.

a/b * c/d = (a*c)/(b*d) = ac/bd

For Example, 4/9 * 2/5

= 4*2/9*5

= 8/45

Division of Fractions – How to divide fraction?

Division of fractions is similar to multiplication. In order to calculate the result of division of fractions, the numerator fraction is multiplied by the reciprocal of the denominator fraction.

In case of fractions, the position of numerator and denominator are interchanged in reciprocal i.e. reciprocal of a/b would become b/a.

(a/b) / (c/d) = (a/b) * (d/c) = ad/bc

For Example, (4/9) / (2/5)

= 4/9 * 5/2

= 20/18

How to Use the Fractions Calculator?

Use the fractions calculator to perform all mathematical operations

• Step 1: Enter the fractions (Numerator and denominator) in the respective input field
• Step 2: Click the “Calculate” button to get the results
• Step 3: Finally, the resultant fraction will be displayed below with detailed steps on the right.