How to Calculate Negative Integers

Negative integers are whole numbers that are less than zero. They are essential in mathematics, science, and everyday life. This guide explains how to work with negative integers, including addition, subtraction, multiplication, and division.

What Are Negative Integers?

Negative integers are numbers that represent values below zero on the number line. They are written with a minus sign (-) before the number, such as -1, -2, -3, etc. Negative integers are distinct from positive integers (1, 2, 3, ...) and zero.

Key properties of negative integers:

They are less than zero
They are whole numbers (no fractions or decimals)
They can be added, subtracted, multiplied, and divided

Basic Operations with Negative Integers

Addition

When adding two negative integers, you add their absolute values and keep the negative sign.

-a + (-b) = -(a + b)

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

Subtraction

Subtracting a negative integer is the same as adding its absolute value.

-a - (-b) = -a + b

Example: -7 - (-4) = -7 + 4 = -3

Multiplication

When multiplying two negative integers, the result is positive.

(-a) × (-b) = a × b

Example: -2 × -6 = 2 × 6 = 12

Division

When dividing two negative integers, the result is positive.

(-a) ÷ (-b) = a ÷ b

Example: -15 ÷ -3 = 15 ÷ 3 = 5

Real-World Examples

Negative integers are used in various real-world scenarios:

Temperature: -5°C represents 5 degrees below freezing
Finance: A -$100 balance means you owe $100
Elevation: -100 meters means 100 meters below sea level

Scenario	Negative Integer Example	Meaning
Temperature	-4°C	4 degrees below freezing
Bank Balance	-$50	You owe $50
Elevation	-200m	200 meters below sea level

Common Mistakes to Avoid

When working with negative integers, these common errors occur:

Adding negative numbers by subtracting: -3 + (-2) = -5, not -1
Confusing subtraction with addition: -5 - (-3) = -2, not -8
Forgetting that negative × negative = positive

Remember: Two negatives make a positive!

FAQ

What is the difference between negative integers and negative numbers?

Negative integers are whole numbers less than zero (-1, -2, -3). Negative numbers include all numbers less than zero, including fractions and decimals (-0.5, -1.25).

Can you multiply a negative integer by zero?

Yes, any number multiplied by zero equals zero. So -5 × 0 = 0.

What happens when you divide a negative integer by a positive integer?

The result is negative. For example, -10 ÷ 2 = -5.