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Negative Numbers Calculator Multiplying and Dividing

Reviewed by Calculator Editorial Team

This guide explains how to multiply and divide negative numbers, including the rules for negative signs and practical examples. Use the calculator to quickly perform these operations and understand the results.

How to Multiply Negative Numbers

Multiplying negative numbers follows specific rules that determine whether the result is positive or negative. Here's how it works:

Multiplication Rule: The product of two negative numbers is positive.

a × b = c

If a and b are both negative, then c is positive.

For example:

  • -2 × -3 = 6 (positive result)
  • -4 × -5 = 20 (positive result)

When multiplying a negative number by a positive number, the result is negative:

  • -3 × 4 = -12 (negative result)
  • 5 × -2 = -10 (negative result)

How to Divide Negative Numbers

Dividing negative numbers follows similar rules to multiplication. The key is to count the number of negative signs:

Division Rule: The quotient of two negative numbers is positive.

a ÷ b = c

If a and b are both negative, then c is positive.

For example:

  • -10 ÷ -2 = 5 (positive result)
  • -15 ÷ -3 = 5 (positive result)

When dividing a negative number by a positive number, the result is negative:

  • -8 ÷ 4 = -2 (negative result)
  • 12 ÷ -3 = -4 (negative result)

Negative Number Rules

Here are the key rules for working with negative numbers:

  1. Negative × Negative = Positive: Two negative numbers multiplied together give a positive result.
  2. Negative × Positive = Negative: A negative number multiplied by a positive number gives a negative result.
  3. Negative ÷ Negative = Positive: Two negative numbers divided give a positive result.
  4. Negative ÷ Positive = Negative: A negative number divided by a positive number gives a negative result.
  5. Negative Sign Count: Count the number of negative signs. If the count is even, the result is positive. If the count is odd, the result is negative.

Remember: A negative number is less than zero. The negative sign indicates direction on the number line, not quantity.

Examples

Let's look at some practical examples of multiplying and dividing negative numbers:

Multiplication Examples

  • -4 × -6 = 24 (positive result)
  • -7 × 3 = -21 (negative result)
  • -2 × -2 × -2 = -8 (three negatives = negative result)

Division Examples

  • -20 ÷ -5 = 4 (positive result)
  • -16 ÷ 4 = -4 (negative result)
  • -27 ÷ -3 ÷ -3 = -3 (three negatives = negative result)

FAQ

Why is multiplying two negative numbers positive?
This is a fundamental rule in mathematics. When you multiply two negative numbers, the negatives cancel each other out, resulting in a positive product.
What happens when you divide a negative number by a positive number?
The result will be negative. This is because you're essentially subtracting the positive number from the negative number repeatedly.
How do you know if the result of negative operations will be positive or negative?
Count the number of negative signs. If there's an even number of negatives, the result is positive. If there's an odd number, the result is negative.
Can negative numbers be used in real-world applications?
Yes, negative numbers are used in many real-world applications, including temperature measurements, financial transactions, and scientific calculations.