Elimination Using Multiplication
Prime Factors
Equations Involving Rational Exponents
Working with Percentages and Proportions
Rational Expressions
Interval Notation and Graphs
Simplifying Complex Fractions
Dividing Whole Numbers with Long Division
Solving Compound Linear Inequalities
Raising a Quotient to a Power
Solving Rational Equations
Solving Inequalities
Adding with Negative Numbers
Quadratic Inequalities
Dividing Monomials
Using the Discriminant in Factoring
Solving Equations by Factoring
Subtracting Polynomials
Cube Root
The Quadratic Formula
Multiply by the Reciprocal
Relating Equations and Graphs for Quadratic Functions
Multiplying a Polynomial by a Monomial
Calculating Percentages
Solving Systems of Equations using Substitution
Comparing Fractions
Solving Equations Containing Rational Expressions
Factoring Polynomials
Negative Rational Exponents
Roots and Radicals
Intercepts Given Ordered Pairs and Lines
Factoring Polynomials
Solving Linear Inequalities
Mixed Expressions and Complex Fractions
Solving Equations by Multiplying or Dividing
The Addition Method
Finding the Equation of an Inverse Function
Solving Compound Linear Inequalities
Multiplying and Dividing With Square Roots
Exponents and Their Properties
Equations as Functions
Factoring Trinomials
Solving Quadratic Equations by Completing the Square
Dividing by Decimals
Lines and Equations
Simplifying Complex Fractions
Graphing Solution Sets for Inequalities
Standard Form for the Equation of a Line
Checking Division with Multiplication
Elimination Using Addition and Subtraction
Complex Fractions
Multiplication Property of Equality
Solving Proportions Using Cross Multiplication
Product and Quotient of Functions
Quadratic Functions
Solving Compound Inequalities
Operating with Complex Numbers
Equivalent Fractions
Changing Improper Fractions to Mixed Numbers
Multiplying by a Monomial
Solving Linear Equations and Inequalities Graphically
Dividing Polynomials by Monomials
Multiplying Cube Roots
Operations with Monomials
Properties of Exponents
Mixed Numbers and Improper Fractions
Equations Quadratic in Form
Simplifying Square Roots That Contain Whole Numbers
Dividing a Polynomial by a Monomial
Writing Numbers in Scientific Notation
Solutions to Linear Equations in Two Variables
Solving Linear Inequalities
Multiplying Two Mixed Numbers with the Same Fraction
Special Fractions
Solving a Quadratic Inequality
Parent and Family Graphs
Solving Equations with a Fractional Exponent
Evaluating Trigonometric Functions
Solving Equations Involving Rational Expressions
Laws of Exponents
Multiplying Polynomials
Vertical Line Test
Solving Inequalities with Fractions and Parentheses
Multiplying Polynomials
Solving Quadratic and Polynomial Equations
Extraneous Solutions
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Powers/Exponents and Operations


Integers = {..., -3, -2, -1, 0, 1, 2, 3, ...}

Addition Rules

Same signs: Add the absolute values and use the common sign.

Different signs: Subtract the lesser absolute value from the greater absolute value. Use the sign of the number with the greater absolute value.

Subtraction Rule

To subtract an integer, add its opposite.

Multiplication and Division Rules

Same signs: The product/quotient is positive. Different signs: The product/quotient is negative.


matches -3

“The gray squares represent negative integers and the white squares represent positive integers. has a greater absolute value, so the answer is negative. And so the answer is ”


2 - (-3 ) matches 5.

“When you add the opposite, you have 2 + 3 = 5.”


3(-4) matches -12

“The signs are different, so the answer will be negative. Because 3 × 4= 12, the answer is -12.”



An exponent represents the number of times a base is used as a factor. An exponent of 2 is the second power; an exponent of 3 is the third power.

In the expression -32, only the 3 is raised to a power, so -32 = -9.

The expression (-3)2 = (-3)(-3) = 9.


-52 matches -25.

“Only the 5 is being squared, so the answer is -25.”


Order of Operations


You use order of operations to evaluate an expression that has more than one operation:

1. Evaluate expressions inside grouping symbols.

2. Evaluate powers.

3. Multiply and divide from left to right.

4. Add and subtract from left to right.


-8 - (-6) + 4 matches 2.

“Subtraction is done first, so -8 - (-6) is -8 + 6, which equals -2. Then add -2 + 4, which is 2.”


Distributive Property

Background Warm-Up

5(6 + 8) matches 5(6) + 5(8).

“Distribute the 5, and the answer is 5 times 6 plus 5 times 8.”

Distributive Property

a(b + c) = ab + ac

a(b - c) = ab - ac


6(8 + 5) = 6(8) + 6(5)

7(9 - 4) = 7(9) - 7(4)


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