Simplifying Complex Fractions Calculator

Basic Calculator

Calculators

Math

Fractions

Simplifying Complex Fractions Calculator

Simplify Complex Fractions

Enter Mixed Numbers, Fractions or Integers

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
\[ = - \frac{80}{6} = - \frac{40}{3} = -13 \frac{1}{3}\]

Share this Answer Link: help
Paste this link in email, text or social media.

Get a Widget for this Calculator

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

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

How to simplify complex fractions by Fraction Division

Convert mixed numbers to improper fractions.
Reduce all fractions when possible.
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.
Follow the normal rules for dividing fractions; invert the the second term and multiply the operands.
When possible reduce, simplify and convert to mixed numbers, any final fraction results.

Related Fractions Calculators

For math with fractions see our Fractions Calculator. Perform fraction addition, subtraction, multiplication and division.

To do math with complex fractions see our Complex Fractions Calculator. Complete complex fraction addition, subtraction, multiplication and division.