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Polynomials
Finding the Greatest Common Factor
Factoring Trinomials
Absolute Value Function
A Summary of Factoring Polynomials
Solving Equations with One Radical Term
Adding Fractions
Subtracting Fractions
The FOIL Method
Graphing Compound Inequalities
Solving Absolute Value Inequalities
Adding and Subtracting Polynomials
Using Slope
Solving Quadratic Equations
Factoring
Multiplication Properties of Exponents
Completing the Square
Solving Systems of Equations by using the Substitution Method
Combining Like Radical Terms
Elimination Using Multiplication
Solving Equations
Pythagoras' Theorem 1
Finding the Least Common Multiples
Multiplying and Dividing in Scientific Notation
Adding and Subtracting Fractions
Solving Quadratic Equations
Adding and Subtracting Fractions
Multiplication by 111
Adding Fractions
Multiplying and Dividing Rational Numbers
Multiplication by 50
Solving Linear Inequalities in One Variable
Simplifying Cube Roots That Contain Integers
Graphing Compound Inequalities
Simple Trinomials as Products of Binomials
Writing Linear Equations in Slope-Intercept Form
Solving Linear Equations
Lines and Equations
The Intercepts of a Parabola
Absolute Value Function
Solving Equations
Solving Compound Linear Inequalities
Complex Numbers
Factoring the Difference of Two Squares
Multiplying and Dividing Rational Expressions
Adding and Subtracting Radicals
Multiplying and Dividing Signed Numbers
Solving Systems of Equations
Factoring Out the Opposite of the GCF
Multiplying Special Polynomials
Properties of Exponents
Scientific Notation
Multiplying Rational Expressions
Adding and Subtracting Rational Expressions With Unlike Denominators
Multiplication by 25
Decimals to Fractions
Solving Quadratic Equations by Completing the Square
Quotient Rule for Exponents
Simplifying Square Roots
Multiplying and Dividing Rational Expressions
Independent, Inconsistent, and Dependent Systems of Equations
Slopes
Graphing Lines in the Coordinate Plane
Graphing Functions
Powers of Ten
Zero Power Property of Exponents
The Vertex of a Parabola
Rationalizing the Denominator
Test for Factorability for Quadratic Trinomials
Trinomial Squares
Solving Two-Step Equations
Solving Linear Equations Containing Fractions
Multiplying by 125
Exponent Properties
Multiplying Fractions
Adding and Subtracting Rational Expressions With the Same Denominator
Quadratic Expressions - Completing Squares
Adding and Subtracting Mixed Numbers with Different Denominators
Solving a Formula for a Given Variable
Factoring Trinomials
Multiplying and Dividing Fractions
Multiplying and Dividing Complex Numbers in Polar Form
Power Equations and their Graphs
Solving Linear Systems of Equations by Substitution
Solving Polynomial Equations by Factoring
Laws of Exponents
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Systems of Linear Equations
Properties of Rational Exponents
Power of a Product and Power of a Quotient
Factoring Differences of Perfect Squares
Dividing Fractions
Factoring a Polynomial by Finding the GCF
Graphing Linear Equations
Steps in Factoring
Multiplication Property of Exponents
Solving Systems of Linear Equations in Three Variables
Solving Exponential Equations
Finding the GCF of a Set of Monomials
 
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Dividing Fractions

The objective of this lesson is that you learn how to divide fractions correctly.

Numerator and Denominator

The number or algebraic expression that appears on the top line of a fraction is called the numerator of the fraction.

The number of algebraic expression that appears on the bottom line of a fraction is called the denominator of the fraction.

Dividing Fractions

Expressed in symbols, the rule for dividing one fraction by another is as follows:

The rule for dividing one fraction by another is usually called inverting and multiplying. To divide one fraction by another, you “flip” (or “invert”) the fraction on the bottom and then multiply.

Example

Work out each of the following divisions of fractions.

Solution

(a)

(b) 

When you get to the multiplication step of these calculations, you have to remember to multiply entire quantities by entire quantities (which will usually involve FOILing). For example, after the fraction has been inverted, the multiplication involves multiplying (x + 2) by (3·x +1). Multiplying these two quantities together will require you to FOIL the two brackets.

(c) 

Again, note the necessity for FOILing once the inversion has been carried out and the multiplication is begun.

 

Dividing Numbers by Fractions

It is sometimes confusing to work out the result when a number is divided by a fraction. The key thing to bear in mind here is that a number is the same as a fraction – you just use a denominator of “1.”

Example

Simplify: 

Solution

You can covert this to a fraction division problem by writing the fraction  instead of the “number” x. 

This is certainly simpler than it was, but is not the simplest format that is possible. Each of the terms in the numerator has a common factor of x, which can be factored out and canceled with the x in the numerator (provided x " 0). 

provided x ≠ 0.

 

Dividing Fractions by Numbers

You can also deal with potentially confusing problems in which fractions are divided by numbers by converting the numbers to fractions. This will convert the confusing problem into a fraction division problem.

Example

Simplify:

Solution

Again, the key is to write the “number” as the fraction  instead of just the “number” x + 9. This converts the problem into a fraction division problem that you can solve by “inverting and multiplying.” 

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