	Algebra Tutorials!

Thursday 21st of November



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	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

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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

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.