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

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Vocabulary

Positive

Negative

Lesson

Negative Numbers

A positive number is a number more 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 answer negative.

• -2 * 3 = -6
• 2 * -3 = -6

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

• -2 * -3 = 6

You do the same for dividing.

• -6 / 3 = -2
• 6 / -3 = -2
• -6 / -3 = 2

Exponentiating

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

• (-3)^2 = 9
• (-x)^2 = -x * -x = x^2

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

• (-2)^3 = -8
• (-x)^3 = -x * -x * -x = x^2 * -x = -x^3

Order of Operations

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

• 3 - -8 / 4 = 3 + 2 = 5
• -3 ^ 2 = -(3 * 3) = -9
• (-3) ^ 2 = (-3 * -3) = 9

Practice Problems

-2*-3=

-7*11=

-4+7(-2)=