Calculate Negative

Negative numbers are essential in mathematics, representing values below zero. This guide explains how to work with negative numbers in addition, subtraction, multiplication, and division, with practical examples and a built-in calculator.

What is a Negative Number?

Negative numbers are numbers less than zero, represented with a minus sign (-). They are used to indicate values opposite to positive numbers, such as debt, temperature below freezing, or positions below a reference point.

Key properties of negative numbers:

Any number multiplied by -1 becomes negative
Adding a negative number is the same as subtracting its absolute value
Subtracting a negative number is the same as adding its absolute value
Multiplying two negatives gives a positive result

Negative numbers are fundamental in algebra, calculus, and many real-world applications like finance, physics, and engineering.

Negative Number Operations

Addition and Subtraction

When adding or subtracting negative numbers, follow these rules:

Positive + Negative = Subtract the smaller absolute value from the larger
Negative + Negative = Add absolute values and keep the negative sign
Positive - Negative = Add absolute values
Negative - Positive = Subtract and keep the negative sign

Example: (-5) + (-3) = -8

Example: 7 - (-4) = 11

Multiplication

Multiplying negative numbers follows these rules:

Positive × Positive = Positive
Positive × Negative = Negative
Negative × Positive = Negative
Negative × Negative = Positive

Example: (-3) × (-4) = 12

Example: 5 × (-2) = -10

Division

Division with negative numbers follows the same sign rules as multiplication:

Positive ÷ Positive = Positive
Positive ÷ Negative = Negative
Negative ÷ Positive = Negative
Negative ÷ Negative = Positive

Example: (-12) ÷ (-3) = 4

Example: 15 ÷ (-5) = -3

Worked Examples

Addition Example

Calculate (-7) + (-4):

Add the absolute values: 7 + 4 = 11
Keep the negative sign: -11
Final answer: -11

Subtraction Example

Calculate 8 - (-3):

Subtracting a negative is the same as adding: 8 + 3 = 11
Final answer: 11

Multiplication Example

Calculate (-2) × (-6):

Multiply the absolute values: 2 × 6 = 12
Two negatives make a positive: +12
Final answer: 12

Division Example

Calculate (-18) ÷ (-3):

Divide the absolute values: 18 ÷ 3 = 6
Two negatives make a positive: +6
Final answer: 6

FAQ

What does a negative number mean?: A negative number represents a value below zero, indicating direction opposite to positive numbers.
How do you add negative numbers?: Add the absolute values of the numbers and keep the negative sign if both numbers are negative.
What happens when you multiply two negative numbers?: The result is positive because the negatives cancel each other out.
How do you divide negative numbers?: Divide the absolute values and apply the same sign rules as multiplication.
When are negative numbers used in real life?: Negative numbers are used in finance (debt), temperature (below freezing), and measurements (below sea level).