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Finding the Greatest Common Factor
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Absolute Value Function
A Summary of Factoring Polynomials
Solving Equations with One Radical Term
Adding Fractions
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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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Solving Equations

Using Multiplication and Division

After studying this lesson, you will be able to:

  • Solve equations using multiplication and division.

Review of Steps for Solving Equations:

1. Remove parentheses by multiplying (this step is not always necessary)

2. Collect like terms on each side of the equal sign

3. Isolate the variable by undoing the operation

4. Check by substituting the solution into the original equation

 

Example 1

This equation can be solved by cross multiplying.
12r = 120 Use cross multiplication to create a new equation. (5 times r and 12 times 24)
To isolate the variable we have to undo the 12 times r. The opposite of multiplication is division, so we divide each side by 12.we use the fraction bar symbol for division.
r = 10 12r divided by 12 is r and 120 divided by 12 is 10

Check:

substitute 10 for r in the equation we created by cross multiplying

12 (10) = 120

120 = 120 (always be sure the 2 sides are equal)

 

Example 2

First, lets convert the mixed numbers to improper fractions
Since we have multiplied by m, we need to undo by dividing Remember, dividing by a fraction is done by multiplying by the reciprocal
Multiply each side by
cancel out; cross cancel 28 and 7 and 9 and 3 to get

Check:

Substitute for m in the equation where we converted to improper fractions

 

Example 3

-6x = 11 Since is multiplied by x, we need to undo the operation by dividing by - 6
Both sides are divided by -6
In Algebra, we usually leave answers as improper fractions (reduced)

Check by substituting in the original equation

(the s cancel)

11 = 11

 

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