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

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 a negative number is the same as subtracting a positive number.

• ${\displaystyle 7+(-4)=7-4}$
• ${\displaystyle x+(-y)=x-y}$

Subtracting a negative number is the same as adding a positive number.

• ${\displaystyle 7-(-4)=7+4}$
• ${\displaystyle x-(-y)=x+y}$

Multiplying and Dividing

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

• ${\displaystyle (-2)\times 3=-6}$
• ${\displaystyle 2\times (-3)=-6}$

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

• ${\displaystyle (-2)\times (-3)=6}$

You do the same for dividing.

• ${\displaystyle (-6)\div 3=-2}$
• ${\displaystyle 6\div (-3)=-2}$
• ${\displaystyle (-6)\div (-3)=2}$

Exponentiating

Exponentiating a negative number to an even (a number you can divide by two) power makes the result positive.

• ${\displaystyle (-3)^{2}=9}$
• ${\displaystyle (-x)^{2}=(-x)\times (-x)=x^{2}}$

Exponentiating a negative number to an odd (a number you can not divide by two) power makes the result negative.

• ${\displaystyle (-2)^{3}=-8}$
• ${\displaystyle (-x)^{3}=(-x)\times (-x)\times (-x)=x^{2}\times (-x)=-x^{3}}$

Order of Operations

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

• ${\displaystyle 3+8\div 4=3+2=5}$
• ${\displaystyle -3^{2}=-(3\times 3)=-9}$
• ${\displaystyle (-3)^{2}=(-3)\times (-3)=9}$

Example Problems

• ${\displaystyle 4+(-4)=0}$
• ${\displaystyle 4+(-7)=-3}$
• ${\displaystyle 0+(-2)=-2}$
• ${\displaystyle -5+7-2\times (-4)=10}$

Practice Problems

1

 ${\displaystyle 6+(-3)=}$

2

 ${\displaystyle 3+(-9)=}$

3

 ${\displaystyle -4\times 4=}$

4

 ${\displaystyle 4\times (-9)=}$

5

 ${\displaystyle -2\times (-4)=}$

6

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

7

 ${\displaystyle -4\div 2=}$

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