Fraction Calculator

This Fraction calculator simplify fractions of addition, subtraction, multiplication, and division. Perform simplifying fractions effortlessly by entering the numerator and denominator.

Whether you have fractions or mixed numbers, The fraction calculator will reduce them to the most simplified form within seconds. 

Formula Used By Fraction Calculator:

The mixed number calculator displays a fraction addition, subtraction, multiplication, and division. This utilizes the below formulas by taking the hassle out of fractions and gives you accurate results.

How to Add Fractions?

• Identify the common denominators
• Find the least common multiple (LCM) or least common denominator (LCD) 
• If the denominators are not the same, multiply each fraction by a factor that makes its common denominator equal to the LCM
• Add the numerators and convert the given improper fractions to the mixed.

Formula for Adding Fractions:

$$\dfrac{a}{b} + \dfrac{c}{d} = \dfrac{ad + bc}{bd}$$

Example:

How to add fractions 4/3 & 2/3?

Solution:

4/3 + 2/3
= (4+2)/3 (LCD is 3)
= 6/3
= 2

How to Subtract Fractions?

• Identify the common denominators
• Find the least common multiple or the least common denominator
• If the denominators are not the same, multiply each fraction by a factor that makes its denominator equal to the LCM
• Subtract the numerators and simplify fractions to the lowest terms

Formula for Fractions Subtraction:

$$ \dfrac{a}{b} – \dfrac{c}{d} = \dfrac{ad – bc}{bd} $$

Example:

How to subtract fractions 2/7 & 8/3?

Solution:

2/7 - 8/3
= 2(3) - 7(8) / 21 (LCD is 21)
= (6-56) / 21
= -50 / 21

How to Multiply Fractions?

• Multiply numerators of all fractions
• Likewise, go by multiplying denominators as well
• Write the results as a single fraction
• Simplify to reduce the fraction to lowest terms

Formula for Fractions Multiplication:

$$ \dfrac{a}{b} \times \dfrac{c}{d} = \dfrac{ac}{bd} $$

Example:

How to multiply the numbers 1/7 & 8/9?

Solution:

1/7 & 8/9
= (1*8)/(7*9)
= 8/63

How to Divide Fractions?

• Find the reciprocal and rewrite the Division as Multiplication
• Flip the second fractions by switching the top and bottom numbers
• Multiply Numerators and Denominators
• Simplify the results to the lowest form

Formula for Fractions Division:

$$ \dfrac{a}{b} \div \dfrac{c}{d} = \dfrac{ad}{bc} $$

Example:

How to divide fractions 7/3 ÷ 7/2?

Solution:

Here we have:

7/3 ÷ 7/2

The reciprocal of the divisor (7/2) is 2/7. So we have;

7/3 x 2/7
= (7*2)/(3*7)
= 14/21
= 2/3

Common Fractions to Decimals:

Our fraction calculator helps you to simplify and reduce fractions to the lowest form. It performs fraction operations, and expressions with integers, decimals, and mixed numbers.

The following table is packed with fractions values that you may encounter on a daily basis and may help you simplify fractions value in seconds:

References:

Wikipedia: Fractions, Reciprocals and the "invisible denominator", Ratios, Decimal fractions and percentages, Historical notions, Arithmetic with fractions.