Basic Algebra/Introduction to Basic Algebra Ideas/Working With Negative Numbers

Vocabulary

 * Positive
 * Negative

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.
 * $$ 7 + (-4) = 7 - 4$$
 * $$ x + (-y) = x - y$$

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

Multiplying and Dividing
Multiplying a negative number by a positive number, or a positive number by a negative number makes the result negative.
 * $$ (-2) \times 3 = -6$$
 * $$ 2 \times (-3) = -6$$

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


 * $$ (-2) \times (-3) = 6$$

You do the same for dividing.
 * $$ (-6) \div 3 = -2$$
 * $$ 6 \div (-3) = -2$$
 * $$ (-6) \div (-3) = 2$$

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

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

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


 * $$ 3 + 8 \div 4 = 3 + 2 = 5$$
 * $$ -3^2 = -(3 \times 3) = -9$$
 * $$ (-3)^2 = (-3) \times (-3) = 9$$

Example Problems

 * $$4 + (-4) = 0$$
 * $$4 + (-7) = -3$$
 * $$0 + (-2) = -2$$
 * $$-5 + 7 - 2 \times (-4) = 10$$

Practice Problems
 { $$6 + (-3) =$${ 3_3 }
 * type="{}"}

{ $$3 + (-9) =$${ -6_3 }
 * type="{}"}

{ $$-4 \times 4 = $${ -16_3 }
 * type="{}"}

{ $$ 4 \times (-9) = $${ -36_3 }
 * type="{}"}

{ $$-2 \times (-4) = $${ 8_3 }
 * type="{}"}

{ $$ \frac{-25}{5^2} = $${ -1_3 }
 * type="{}"}

{ $$-4 \div 2= $${ -2_3 }
 * type="{}"}