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.

• $7+(-4)=7-4$
• $x+(-y)=x-y$

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

1

$6+(-3)=$

2

$3+(-9)=$

3

$-4\times 4=$

4

$4\times (-9)=$

5

$-2\times (-4)=$

6

${\frac {-25}{5^{2}}}=$

7

$-4\div 2=$