Free Algebra
Tutorials!
 
Home
Point
Arithmetic Operations with Numerical Fractions
Multiplying a Polynomial by a Monomial
Solving Linear Equation
Solving Linear Equations
Solving Inequalities
Solving Compound Inequalities
Solving Systems of Equations Using Substitution
Simplifying Fractions 3
Factoring quadratics
Special Products
Writing Fractions as Percents
Using Patterns to Multiply Two Binomials
Adding and Subtracting Fractions
Solving Linear Inequalities
Adding Fractions
Solving Systems of Equations -
Exponential Functions
Integer Exponents
Example 6
Dividing Monomials
Multiplication can Increase or Decrease a Number
Graphing Horizontal Lines
Simplification of Expressions Containing only Monomials
Decimal Numbers
Negative Numbers
Factoring
Subtracting Polynomials
Adding and Subtracting Fractions
Powers of i
Multiplying and Dividing Fractions
Simplifying Complex Fractions
Finding the Coordinates of a Point
Fractions and Decimals
Rational Expressions
Solving Equations by Factoring
Slope of a Line
Percent Introduced
Reducing Rational Expressions to Lowest Terms
The Hyperbola
Standard Form for the Equation of a Line
Multiplication by 75
Solving Quadratic Equations Using the Quadratic Formula
Raising a Product to a Power
Solving Equations with Log Terms on Each Side
Monomial Factors
Solving Inequalities with Fractions and Parentheses
Division Property of Square and Cube Roots
Multiplying Two Numbers Close to but less than 100
Solving Absolute Value Inequalities
Equations of Circles
Percents and Decimals
Integral Exponents
Linear Equations - Positive and Negative Slopes
Multiplying Radicals
Factoring Special Quadratic Polynomials
Simplifying Rational Expressions
Adding and Subtracting Unlike Fractions
Graphuing Linear Inequalities
Linear Functions
Solving Quadratic Equations by Using the Quadratic Formula
Adding and Subtracting Polynomials
Adding and Subtracting Functions
Basic Algebraic Operations and Simplification
Simplifying Complex Fractions
Axis of Symmetry and Vertices
Factoring Polynomials with Four Terms
Evaluation of Simple Formulas
Graphing Systems of Equations
Scientific Notation
Lines and Equations
Horizontal and Vertical Lines
Solving Equations by Factoring
Solving Systems of Linear Inequalities
Adding and Subtracting Rational Expressions with Different Denominators
Adding and Subtracting Fractions
Solving Linear Equations
Simple Trinomials as Products of Binomials
Solving Nonlinear Equations by Factoring
Solving System of Equations
Exponential Functions
Computing the Area of Circles
The Standard Form of a Quadratic Equation
The Discriminant
Dividing Monomials Using the Quotient Rule
Squaring a Difference
Changing the Sign of an Exponent
Adding Fractions
Powers of Radical Expressions
Steps for Solving Linear Equations
Quadratic Expressions Complete Squares
Fractions 1
Properties of Negative Exponents
Factoring Perfect Square Trinomials
Algebra
Solving Quadratic Equations Using the Square Root Property
Dividing Rational Expressions
Quadratic Equations with Imaginary Solutions
Factoring Trinomials Using Patterns
Try the Free Math Solver or Scroll down to Tutorials!

 

 

 

 

 

 

 

 
 
 
 
 
 
 
 
 

 

 

 
 
 
 
 
 
 
 
 

Please use this form if you would like
to have this math solver on your website,
free of charge.


Negative Numbers

Why Use Negative Numbers?

Have you seen negative numbers somewhere in your life? Think about some instance for a minute – I would bet it has something to do with direction, along with the value.

Negative numbers generally occur when a change is measured from some reference.

What Are Negative Numbers

Negative numbers are numbers less than (to the left of) zero. The number line below demonstrates this idea. Notice that both positive and negative numbers go on forever.

Numbers get larger as you go to the right and smaller as you go to the left. Notice for example that –3 is smaller than –2.

Two numbers are opposites if they are the same distance from zero on a number line, but on opposite sides of zero. The number -5 is read “negative five” or “the opposite of five”.

Is +0 the same as –0? These are two different names for the same point on the number line. They mean the same thing. Adding zero is identical to subtracting zero.

Addition and subtraction with negative numbers is particularly convenient, since there is nothing special about the number zero. There is no extra “special case” to handle when you combine numbers on either side of zero. You simply add and subtract them as usual.

Negatives on Your Calculator

Every calculator seems to have a different way to enter negative numbers. The +/- key on your calculator gives the opposite of the number (changes the sign) on the display.

A Few Words About Parentheses

A parenthesis is a symbol like “(“ or the matching symbol “)”. The plural of parenthesis is parentheses.

Parentheses in mathematics are used to group things together. They tell you that items inside them belong together; they are slightly separated from things outside them. Operations inside parentheses must be done before other operations.

We use parentheses with negative numbers to avoid confusion with other operations such as addition or subtraction. For example, “3 + (-5)” means, “three plus negative five” and tells you the minus sign is working on the five. Otherwise, you would see the “+ -” together and it would be confusing.

Adding: a + (-b)

This is just another way to write regular subtraction! a + (-b) = a - b

Start with the first number you are given and move:

· to the left if you are adding a negative number;

· to the right if you are adding a positive number.

 

 

Why would you ever write subtraction that way? First, because there is no longer any subtraction. That is, all your subtraction problems are merely addition, and you just happen to have some negative numbers thrown into the mix. Second, because addition problems let you easily swap the order of the numbers. Sometimes it is handy to write a + (-b) in another form such as (-b) + a.

Subtracting: a - (-b)

This is just another way to write regular addition The two negative signs cancel each other out!

Start with the first number you are given and move:

· to the left if you are subtracting a positive number;

· to the right if you are subtracting a negative number.

Multiplying and Dividing: (-a) ×·(-b) or (-a)/(-b)

To multiply or divide positive or negative numbers

· Ignore the sign (positive or negative) and multiply or divide as usual.

· The answer is positive if both numbers have the same sign.

· The answer is negative if the numbers have opposite signs.

Examples:

6 × 3 = 18 6 × (-3) = -18 -6 × 3 = -18 -6 × (-3) = 18
10 / 2 = 5 10 / (-2) = -5 -10 / 2 = -5 -10 / (-2) = 5

Do parentheses first, then exponents, then multiplication and division, and addition and subtraction last.

Just as two negatives in a sentence mean positive, so a negative times a negative equals a positive: -3 × -4 = 12

All Right Reserved. Copyright 2005-2017