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Suimplify Complex Fraction Without Variables Calculator

Reviewed by Calculator Editorial Team

A complex fraction is a fraction where either the numerator or the denominator is also a fraction. Simplifying a complex fraction without variables means reducing it to its simplest form where both the numerator and denominator are integers.

What is a complex fraction?

A complex fraction is a fraction that contains other fractions in its numerator, denominator, or both. For example:

Example of a complex fraction:

(3/4) ÷ (5/6)

This can also be written as:

(3/4) / (5/6)

Complex fractions can be simplified to a single, simpler fraction.

How to simplify a complex fraction

To simplify a complex fraction, follow these steps:

  1. Find a common denominator for all fractions in the numerator and denominator.
  2. Rewrite each fraction with the common denominator.
  3. Combine the fractions in the numerator and denominator.
  4. Simplify the resulting fraction by dividing both the numerator and denominator by their greatest common divisor (GCD).

Remember: The goal is to eliminate all fractions from the numerator and denominator, resulting in a single simplified fraction.

Step-by-step example

Let's simplify the complex fraction (3/4) ÷ (5/6):

  1. First, rewrite the division as a fraction:

    (3/4) / (5/6)

  2. Multiply the numerator by the reciprocal of the denominator:

    (3/4) × (6/5)

  3. Multiply the numerators and denominators:

    (3 × 6) / (4 × 5) = 18/20

  4. Simplify the fraction by dividing numerator and denominator by 2:

    9/10

The simplified form of (3/4) ÷ (5/6) is 9/10.

Common mistakes to avoid

When simplifying complex fractions, avoid these common errors:

  • Forgetting to find a common denominator before combining fractions
  • Incorrectly multiplying numerators and denominators
  • Not simplifying the final fraction to its lowest terms
  • Miscounting the number of terms in the numerator or denominator

Double-check your work at each step to ensure accuracy.

FAQ

What is the difference between a complex fraction and a mixed number?
A complex fraction contains other fractions in its numerator or denominator, while a mixed number combines a whole number and a proper fraction.
Can I simplify a complex fraction with variables?
Yes, but the process is similar to simplifying without variables. You'll need to factor and cancel like terms.
What if the numerator and denominator don't simplify to integers?
If the simplified form still contains fractions, you may need to convert it to a mixed number or decimal.