View source for Basic Algebra/Introduction to Basic Algebra Ideas/Working With Negative Numbers

== Vocabulary ==

;Positive
;Negative

== Lesson ==

===Negative Numbers===

A '''positive''' number is a number greater than zero. 

A '''negative''' number is a number less than zero.  You make a negative number by doing the negative operation on a positive number.  You use the '''" – "''' sign for the negative operation.  This sign is the same you use for subtracting.

===Adding and Subtracting===

Adding a negative number is the same as subtracting a positive number.
* <math> 7 + (-4) = 7 - 4</math>
* <math>  x + (-y) = x - y</math>

Subtracting a negative number is the same as adding a positive number.
* <math> 7 - (-4) = 7 + 4</math>
* <math> x - (-y) = x + y</math>

===Multiplying and Dividing===

Multiplying a negative number by a positive number, or a positive number by a negative number makes the result negative.
* <math> (-2) \times 3 = -6</math>
* <math> 2 \times (-3) = -6</math>

Multiplying a negative number by a negative number makes the result positive.

* <math> (-2) \times (-3) = 6</math>

You do the same for dividing.
* <math>  (-6) \div 3 = -2</math>
* <math>  6 \div (-3) = -2</math>
* <math> (-6) \div (-3) = 2</math>

===Exponentiating===

Exponentiating a negative number to an even (a number you can divide by two) power makes the result positive.
* <math> (-3)^2 = 9</math>
* <math> (-x)^2 = (-x) \times (-x) = x^2</math>

Exponentiating a negative number to an odd(a number you can not divide by two) power makes the result negative.
* <math> (-2)^3 = -8</math>
* <math> (-x)^3 = (-x) \times (-x) \times (-x) = x^2 \times (-x) = -x^3</math>

===Order of Operations===

The negative operation has the same precedence as multiplying and dividing.

* <math> 3 + 8 \div 4 = 3 + 2 = 5</math>
* <math> -3^2 = -(3 \times 3) = -9</math>
* <math> (-3)^2 = (-3) \times (-3) = 9</math>

== Example Problems ==

* <math>4 + (-4) = 0</math>
* <math>4 + (-7) = -3</math>
* <math>0 + (-2) = -2</math>
* <math>-5 + 7 - 2 \times (-4) = 10</math>

== Practice Games ==

== Practice Problems ==
<quiz display=simple points="1/1">
{
|type="{}"}
 <math>6 + (-3) =</math>{ 3_3 }

{
|type="{}"}
 <math>3 + (-9) =</math>{ -6_3 }

{
|type="{}"}
 <math>-4 \times 4 = </math>{ -16_3 }

{
|type="{}"}
 <math> 4 \times (-9) = </math>{ -36_3 }

{
|type="{}"}
 <math>-2 \times (-4) = </math>{ 8_3 }

{
|type="{}"}
 <math> \frac{-25}{5^2} = </math>{ -1_3 }

{
|type="{}"}
 <math>-4 \div 2= </math>{ -2_3 }
</quiz>
{{BookCat}}
<noinclude>{{Simple Page Navigation|BookName=[[Basic Algebra]]|CurrentPage=Working With Negative Numbers|PrevPage=[[Basic Algebra/Introduction to Basic Algebra Ideas/Variables and Expressions|Variables and Expressions]]|NextPage=[[Basic Algebra/Introduction to Basic Algebra Ideas/Solving Equations Using Properties of Mathematics|Solving Equations Using Properties of Mathematics]]}}</noinclude>