Fraction Calculator

With our online fraction calculator, simplify addition, subtraction, multiplication, and division of fractional terms and also carry out other operations with ease. This reduce fractions calculator can also handle any type of fraction including mixed, improper, and complex fractions. 

Arithmetic Operations of Fraction:

The Fraction Calculator will reduce fractional terms to its simplest form. You can also add, subtract, multiply, and divide fractions, as well as, convert to a decimal and work with mixed numbers and reciprocals. We also offer step by step solutions.

How to Add or Subtract The Fractions?

Here is a more general rule to understand how to add and subtract fractions:

• Find the least common multiple of the denominators.
• Rewrite each fraction with the least common multiple as the denominator.
• In addition, you should add the fraction denominators 
• For subtraction equations, subtract the fraction numerators

Fraction Addition Formula:

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

Fraction Subtraction Formula:

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

Fraction Addition Example:

$$ = \dfrac{3}{2}+\dfrac{1}{3} = \dfrac{11}{6} $$

$$ = \dfrac{3}{4}+\dfrac{2}{5} = \dfrac{23}{20} $$

$$ = \dfrac{5}{6}+\dfrac{7}{8} = \dfrac{82}{48} $$

Fraction Subtraction Example:

$$ = \dfrac{3}{2}-\dfrac{1}{3} = \dfrac{4}{6} $$

$$ = \dfrac{3}{4}-\dfrac{2}{5} = \dfrac{7}{20} $$

$$ = \dfrac{5}{6}-\dfrac{7}{8} = \dfrac{-2}{48} $$

To add fractions it is necessary to have the same denominators and if there is a difference in denominators then find out common denominators. This is the LCM of two denominators. 

Once you have a common denominator, simply add the numerators and keep the denominator the same. 

How to Multiply Fractions?

To understand the basic rules of fractional multiplication, easily solve a variety of math problems. The basic factors are as follows:

• For multiplying fractions, multiply the numerators together and the denominators together.
• After that simplify the results by canceling out the common factors

Use a fraction calculator to get the multiplication and division of fractional values because it has the ability to turn a number of fractions into their lowest decimal and mixed number fractions. 

Fraction Multiplication Formula:

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

Multiplication Example:

$$ = \dfrac{2}{3} \times \dfrac{2}{5} = \dfrac {4}{15} $$

$$ = \dfrac{1}{6} \times \dfrac{5}{4} = \dfrac {5}{24} $$

$$ = \dfrac{4}{6} \times \dfrac{5}{7} = \dfrac {10}{21} $$

How to Divide Fractions:

Our fraction calculator can perform arithmetic operations on fractions. Their division rules are as follows:

• Invert the divisor same to divide by a/b, and it becomes b/a
• Instead of dividing fractions, change the division operation to multiplication.
• Multiply the numerators of the fractions to get the new numerator
• Multiply the denominators to get the new denominator

Dividing fractions is the same as multiplying the first fractions by the reciprocal of the second fraction. The fractional division is made easy by taking into service the below formula:

Fraction Division Formula:

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

Division Example: 

$$ = \dfrac{2}{3} \div \dfrac{3}{4} = \dfrac {8}{9} $$

$$ = \dfrac{4}{7} \div \dfrac{5}{4} = \dfrac {16}{35} $$

$$ = \dfrac{6}{7} \div \dfrac{5}{3} = \dfrac {18}{35} $$

Important Fraction Symbols:

Fraction Table:

Honors:

Wikipedia: Fraction, Forms of fractions, Arithmetic with fractions, Fractions in abstract mathematics. 

Wikihow: How to Do Fractions.