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Simplifying Complex Fractions Calculator

Simplify Complex Fractions
Enter Mixed Numbers, Fractions or Integers
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Answer:
\[ = -13 \frac{1}{3}\] Solution

Simplifying the Complex Fraction
Convert Mixed Numbers to Fractions
\[ \frac{5 \frac{1}{3}}{ \frac{-6}{15}} = \frac{ \frac{16}{3}}{ \frac{-6}{15}}\]
Reduce fractions where possible\[ \frac{ \frac{16}{3}}{ \frac{-6}{15}} = \frac{ \frac{16}{3}}{ \frac{-2}{5}}\]
Method 1 : LCD Multiplication
The LCD for 3 and 5 is 15
Multiply top and bottom by the LCD\[ \frac{15\times \frac{16}{3}}{15\times \frac{-2}{5}} = \frac{80}{-6}\]
convert to mixed numbers and
reduce fractions where possible
\[ = - \frac{80}{6} = - \frac{40}{3} = -13 \frac{1}{3}\]
Method 2 : Fraction Division
Divide the top fraction by the bottom
(multiply top by reciprocal of bottom)

\[ \frac{16}{3} \div \frac{-2}{5}\] \[ = \frac{16}{3} \times \frac{5}{-2}\] \[ = \frac{80}{-6}\]
convert to mixed numbers and
reduce fractions where possible
\[ = - \frac{80}{6} = - \frac{40}{3} = -13 \frac{1}{3}\]

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Calculator Use

This calculator will show you how to simplify complex fractions. Input any 2 mixed numbers (mixed fractions), regular fractions, improper fraction or integers and simplify the entire fraction by each of the following methods.

To add, subtract, multiply or divide complex fractions, see the Complex Fraction Calculator

How to simplify complex fractions

How to simplify complex fractions by LCD Multiplication

  1. Convert mixed numbers to improper fractions.
  2. Reduce all fractions when possible.
  3. Find the least common denominator (LCD) of all fractions appearing within the complex fraction.
  4. Multiply both the numerator and the denominator of the complex fraction by the LCD.
  5. When possible reduce, simplify and convert to mixed numbers, any final fraction results.

How to simplify complex fractions by Fraction Division

  1. Convert mixed numbers to improper fractions.
  2. Reduce all fractions when possible.
  3. The main fraction line means "divide." It is a fraction within a fraction. So, we can rewrite the fraction as a standard fraction division problem.
  4. Follow the normal rules for dividing fractions; invert the the second term and multiply the operands.
  5. When possible reduce, simplify and convert to mixed numbers, any final fraction results.

References/ Further Reading

Simplifying Complex Fractions



 

Cite this content, page or calculator as:

Furey, Edward "Simplifying Complex Fractions Calculator"; from http://www.calculatorsoup.com - Online Calculator Resource.

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