Algebra Tutorials!
Wednesday 23rd of September
 Home Rotating a Parabola Multiplying Fractions Finding Factors Miscellaneous Equations Mixed Numbers and Improper Fractions Systems of Equations in Two Variables Literal Numbers Adding and Subtracting Polynomials Subtracting Integers Simplifying Complex Fractions Decimals and Fractions Multiplying Integers Logarithmic Functions Multiplying Monomials Mixed The Square of a Binomial Factoring Trinomials The Pythagorean Theorem Solving Radical Equations in One Variable Multiplying Binomials Using the FOIL Method Imaginary Numbers Solving Quadratic Equations Using the Quadratic Formula Solving Quadratic Equations Algebra Order of Operations Dividing Complex Numbers Polynomials The Appearance of a Polynomial Equation Standard Form of a Line Positive Integral Divisors Dividing Fractions Solving Linear Systems of Equations by Elimination Factoring Multiplying and Dividing Square Roots Functions and Graphs Dividing Polynomials Solving Rational Equations Numbers Use of Parentheses or Brackets (The Distributive Law) Multiplying and Dividing by Monomials Solving Quadratic Equations by Graphing Multiplying Decimals Use of Parentheses or Brackets (The Distributive Law) Simplifying Complex Fractions 1 Adding Fractions Simplifying Complex Fractions Solutions to Linear Equations in Two Variables Quadratic Expressions Completing Squares Dividing Radical Expressions Rise and Run Graphing Exponential Functions Multiplying by a Monomial The Cartesian Coordinate System Writing the Terms of a Polynomial in Descending Order Fractions Polynomials Quadratic Expressions Solving Inequalities Solving Rational Inequalities with a Sign Graph Solving Linear Equations Solving an Equation with Two Radical Terms Simplifying Rational Expressions Exponents Intercepts of a Line Completing the Square Order of Operations Factoring Trinomials Solving Linear Equations Solving Multi-Step Inequalities Solving Quadratic Equations Graphically and Algebraically Collecting Like Terms Solving Equations with Radicals and Exponents Percent of Change Powers of ten (Scientific Notation) Comparing Integers on a Number Line Solving Systems of Equations Using Substitution Factoring Out the Greatest Common Factor Families of Functions Monomial Factors Multiplying and Dividing Complex Numbers Properties of Exponents Multiplying Square Roots Radicals Adding or Subtracting Rational Expressions with Different Denominators Expressions with Variables as Exponents The Quadratic Formula Writing a Quadratic with Given Solutions Simplifying Square Roots Adding and Subtracting Square Roots Adding and Subtracting Rational Expressions Combining Like Radical Terms Solving Systems of Equations Using Substitution Dividing Polynomials Graphing Functions Product of a Sum and a Difference Solving First Degree Inequalities Solving Equations with Radicals and Exponents Roots and Powers Multiplying Numbers
Try the Free Math Solver or Scroll down to Tutorials!

 Depdendent Variable

 Number of equations to solve: 23456789
 Equ. #1:
 Equ. #2:

 Equ. #3:

 Equ. #4:

 Equ. #5:

 Equ. #6:

 Equ. #7:

 Equ. #8:

 Equ. #9:

 Solve for:

 Dependent Variable

 Number of inequalities to solve: 23456789
 Ineq. #1:
 Ineq. #2:

 Ineq. #3:

 Ineq. #4:

 Ineq. #5:

 Ineq. #6:

 Ineq. #7:

 Ineq. #8:

 Ineq. #9:

 Solve for:

 Please use this form if you would like to have this math solver on your website, free of charge. Name: Email: Your Website: Msg:

# Simplifying Complex Fractions

Complex fractions are fractions whose numerator and denominator themselves contain fractions. The goal of simplifying a complex fraction is to rewrite it as an equivalent fraction in which the numerator and denominator do not contain any other fractions. When we’re considering numerical fractions, this means that the numerator and the denominator of the final form are each just single numbers.

The most effective procedure consists of several steps involving the operations we have already

1. simplify the expression in the numerator of the complex fraction to a single fraction in simplest form

2. simplify the expression in the denominator of the complex fraction to a single fraction in simplest form

3. the original complex fraction now looks like one fraction divided by another fraction. Carry out the division and simplify the result.

Example: Simplify .

solution: This is a complex fraction because the numerator is a sum of two fractions and the denominator is a difference of two fractions. You might be tempted to immediately do some cancellations (since, for example, the numerator and denominator both contain , etc.), but none of the common “things” in any of the fractions present are factors of either the numerator or the denominator, and so cancellations to attempt to simplify things here would be an error. Instead, we follow the systematic approach described above.

(1) simplify the expression in the numerator of the complex fraction to a single fraction in simplest form

(2) simplify the expression in the denominator of the complex fraction to a single fraction in

(3) now:

This last sequence includes whatever simplification appears possible. Thus, the final answer is

Example: Simplify

solution: In steps

So

as the final answer.

The method described here also covers the case where either a whole number is divided by a fraction, or a fraction is divided by a whole number.

Examples:

You can see that the general rule for this kind of problem is:

When a fraction is divided by a whole number, you just multiply that whole number into the denominator of the fraction.

 Copyrights © 2005-2020