Negative Numbers Cheat Sheet

Definition

A negative number is a real number that is less than zero.

Example: -5, -2.7, -1/2 are negative numbers.

Number Line

Negative numbers are located to the left of zero on a number line. The further left, the smaller the number.

Example: On a number line, -5 is to the left of -2, so -5 < -2.

Opposites

Every positive number has a negative counterpart, called its opposite. The opposite of a negative number is positive.

Example: The opposite of 3 is -3. The opposite of -7 is 7.

Real-World Examples

Negative numbers can represent debt, temperature below zero, or locations below sea level.

Example: A bank balance of -$20 means you owe $20. A temperature of -5°C is 5 degrees below zero.

Adding a Negative

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

Example: 5 + (-3) = 5 - 3 = 2

Subtracting a Negative

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

Example: 7 - (-2) = 7 + 2 = 9

Adding Two Negatives

Adding two negative numbers results in a negative number. Add their absolute values and keep the negative sign.

Example: -4 + (-6) = -10

Subtracting a Larger Number

Subtracting a larger number from a smaller number results in a negative number.

Example: 3 - 5 = -2

Positive x Negative

A positive number multiplied by a negative number results in a negative number.

Example: 4 x (-2) = -8

Negative x Positive

A negative number multiplied by a positive number results in a negative number.

Example: (-3) x 5 = -15

Negative x Negative

A negative number multiplied by a negative number results in a positive number.

Example: (-2) x (-6) = 12

Positive / Negative

A positive number divided by a negative number results in a negative number.

Example: 10 / (-2) = -5

Negative / Positive

A negative number divided by a positive number results in a negative number.

Example: (-15) / 3 = -5

Negative / Negative

A negative number divided by a negative number results in a positive number.

Example: (-8) / (-4) = 2