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TUTORIALS:

Absolute Values
Solving Two-Step Equations Algebraically
Multiplying Monomials
Factoring Trinomials
Solving Quadratic Equations
Power Functions and Transformations
Composition of Functions
Rational Inequalities
Equations of Lines
Graphing Logarithmic Functions
Elimination Using Multiplication
Multiplying Large Numbers
Multiplying by 11
Graphing Absolute Value Inequalities
Polynomials
The Discriminant
Reducing Numerical Fractions to Simplest Form
Addition of Algebraic Fractions
Graphing Inequalities in Two Variables
Adding and Subtracting Rational Expressions with Unlike Denominators
Multiplying Binomials
Graphing Linear Inequalities
Properties of Numbers and Definitions
Factoring Trinomials
Relatively Prime Numbers
Point
Inequalities
Rotating a Hyperbola
Writing Algebraic Expressions
Quadratic and Power Inequalities
Solving Quadratic Equations by Completing the Square
BEDMAS & Fractions
Solving Absolute Value Equations
Writing Linear Equations in Slope-Intercept Form
Adding and Subtracting Rational Expressions with Different Denominators
Reducing Rational Expressions
Solving Absolute Value Equations
Equations of a Line - Slope-intercept form
Adding and Subtracting Rational Expressions with Unlike Denominators
Solving Equations with a Fractional Exponent
Simple Trinomials as Products of Binomials
Equivalent Fractions
Multiplying Polynomials
Slope
Graphing Equations in Three Variables
Properties of Exponents
Graphing Linear Inequalities
Solving Cubic Equations by Factoring
Adding and Subtracting Fractions
Multiplying Whole Numbers
Straight Lines
Solving Absolute Value Equations
Solving Nonlinear Equations
Factoring Polynomials by Finding the Greatest Common Factor
Logarithms
Algebraic Expressions Containing Radicals 1
Addition Property of Equality
Three special types of lines
Quadratic Inequalities That Cannot Be Factored
Adding and Subtracting Fractions
Coordinate System
Solving Equations
Factoring Polynomials
Solving Quadratic Equations
Multiplying Radical Expressions
Solving Quadratic Equations Using the Square Root Property
The Slope of a Line
Square Roots
Adding Polynomials
Arithmetic with Positive and Negative Numbers
Solving Equations
Powers and Roots of Complex Numbers
Adding, Subtracting and Finding Least Common Denominators
What the Factored Form of a Quadratic can tell you about the graph
Plotting a Point
Solving Equations with Variables on Each Side
Finding the GCF of a Set of Monomials
Completing the Square
Solving Equations with Radicals and Exponents
Solving Systems of Equations By Substitution
Adding and Subtracting Rational Expressions
Percents
Laws of Exponents and Dividing Monomials
Factoring Special Quadratic Polynomials
Radicals
Solving Quadratic Equations by Completing the Square
Reducing Numerical Fractions to Simplest Form
Factoring Trinomials
Writing Decimals as Fractions
Using the Rules of Exponents
Evaluating the Quadratic Formula
Rationalizing the Denominator
Multiplication by 429
Writing Linear Equations in Point-Slope Form
Multiplying Radicals
Dividing Polynomials by Monomials
Factoring Trinomials
Introduction to Fractions
Square Roots
   
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Arithmetic with Positive and Negative Numbers

The absolute value of a number is its distance from zero on the number line. For example, -7 (a negative number) and 7 (a positive number) are the same distance from zero on the number line, and both have an absolute value of 7. Using absolute values simplifies the process of doing arithmetic with positive and negative numbers.

 

Part 1: Adding Positive and Negative Numbers

PROCEDURE: Determine if you are adding numbers that have the same or different signs. Then follow the appropriate set of directions below.

Adding same signs Example

-3 + (-5)

Adding opposite signs Example

-3 + 5

Step 1: Add their absolute values. 3 + 5 = 8 Step 1: Subtract the smaller absolute value from the larger. 5 - 3 = 2
Step 2: Make the sign of the answer the same as the sign of the original numbers. Because -3 and -5 are both negative, the answer will be negative.

Answer:

-3 + (-5) = –8

Step 2: Choose the sign of the number with the greater absolute value. Because 5 has a greater absolute value than 3, and 5 is positive, your answer will also be positive.

Answer:

-3 + 5 = 2

 

Part 2: Subtracting Positive and Negative Numbers

PROCEDURE: To subtract integers, find the opposite of the number you are subtracting. Then add this opposite to the number you are subtracting from. The result is your answer.

SAMPLE PROBLEM: -3 - (-5) =   ?   

Step 1: Find the opposite of the number you want to subtract.

The opposite of -5 is 5.

Step 2: Add this opposite to the number you are subtracting from. - 3 - (-5) = -3 + 5 = 2

 

Part 3: Multiplying and Dividing Positive and Negative Numbers

PROCEDURE: To multiply or divide two integers, multiply or divide their absolute values. Then apply the following rule to determine if the answer is positive or negative:

• The product or quotient of two same-sign numbers is positive.

• The product or quotient of two opposite-sign numbers is negative.

SAMPLE PROBLEM A: -7 × 11 =    ?    

Step 1: Multiply the absolute values to find the absolute value of the product.

7 × 11 = 77

Step 2: Apply the rule of signs: Because you are finding the product of oppositesign numbers, the product will be negative.

-7 × 11 = -77 

SAMPLE PROBLEM B: -12 ÷ (-4) =    ?  

Step 1: Divide the absolute values to find the absolute value of the quotient.

12 ÷ 4 = 3

Step 2: Apply the rule of signs: Because you are finding the quotient of same-sign numbers, the quotient will be positive.

-12 ÷ (-4) = 3

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