Basic Operations with Negatives Calculator

This guide explains how to perform basic arithmetic operations with negative numbers, including addition, subtraction, multiplication, and division. We'll cover the rules, provide examples, and show you how to use our calculator to verify your results.

How to Use This Calculator

Our calculator performs all four basic operations with negative numbers. Simply enter your numbers, select the operation, and click "Calculate" to see the result. The calculator follows standard arithmetic rules for negative numbers.

Remember that a negative number is less than zero. When performing operations with negatives, the rules are:

Negative + Negative = Negative
Negative - Negative = Negative
Positive × Negative = Negative
Negative × Negative = Positive
Negative ÷ Negative = Positive

Addition with Negatives

When adding two negative numbers, you combine their absolute values and keep the negative sign. For example:

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

This means you're moving 3 units to the left on the number line and then 2 more units to the left, totaling 5 units to the left.

Subtraction with Negatives

Subtracting a negative number is the same as adding its positive counterpart. For example:

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

This is because subtracting a negative is like removing a debt - it increases your total.

Multiplication with Negatives

When multiplying two negative numbers, the result is positive. For example:

-4 × -3 = 12

This follows the rule that a negative times a negative equals a positive.

Division with Negatives

When dividing two negative numbers, the result is positive. For example:

-12 ÷ -3 = 4

This is because the negatives cancel each other out in division.

Worked Examples

Example 1: Addition

Calculate -7 + (-4):

-7 + (-4) = -(7 + 4) = -11

Example 2: Subtraction

Calculate 10 - (-6):

10 - (-6) = 10 + 6 = 16

Example 3: Multiplication

Calculate -5 × -2:

-5 × -2 = 10

Example 4: Division

Calculate -20 ÷ -5:

-20 ÷ -5 = 4

Frequently Asked Questions

Why does a negative times a negative equal a positive?

This rule comes from the concept of opposite directions. Two negatives represent opposite directions, and their product represents moving in the same direction, hence positive.

What happens when you divide a negative by a positive?

The result will be negative. For example, -8 ÷ 2 = -4. This is because you're moving in the opposite direction of the positive number.

Can you add a positive and a negative number?

Yes, you subtract the smaller absolute value from the larger one and keep the sign of the number with the larger absolute value. For example, 5 + (-3) = 2.

What's the difference between -3 and 3?

-3 represents 3 units to the left of zero on the number line, while 3 represents 3 units to the right. They are opposites and have equal magnitudes but different directions.