Cal11 calculator
Search calculator...

Multiplying Positive and Negative Numbers Calculator

Reviewed by Calculator Editorial Team

Multiplying positive and negative numbers is a fundamental math operation that follows specific rules about signs. This calculator helps you quickly find the product of two numbers while understanding the underlying rules.

How to Multiply Positive and Negative Numbers

Multiplying numbers with signs follows these basic rules:

  1. Positive × Positive = Positive
  2. Positive × Negative = Negative
  3. Negative × Positive = Negative
  4. Negative × Negative = Positive

These rules can be remembered with the phrase "like signs give positive, unlike signs give negative."

Formula

For any two numbers a and b:

a × b = product with the correct sign based on the rules above

The absolute value of the product is always the product of the absolute values of the numbers. The sign is determined by the rules above.

Rules of Signs in Multiplication

The sign rules for multiplication can be visualized with a sign chart:

× Positive Negative
Positive Positive Negative
Negative Negative Positive

This table shows that the product's sign depends only on the combination of signs of the numbers being multiplied.

Worked Examples

Example 1: Positive × Positive

Calculate 5 × 3:

  1. Both numbers are positive
  2. Product is positive: 5 × 3 = 15

Example 2: Positive × Negative

Calculate 4 × -2:

  1. One positive, one negative number
  2. Product is negative: 4 × -2 = -8

Example 3: Negative × Positive

Calculate -6 × 7:

  1. One negative, one positive number
  2. Product is negative: -6 × 7 = -42

Example 4: Negative × Negative

Calculate -5 × -3:

  1. Both numbers are negative
  2. Product is positive: -5 × -3 = 15

Common Mistakes

When multiplying numbers with signs, common mistakes include:

  • Forgetting to consider the sign of the product
  • Incorrectly applying the rules (e.g., thinking positive × negative equals positive)
  • Miscounting the number of negative signs in a multiplication chain

Tip

To avoid mistakes, always count the number of negative numbers in the multiplication. An even count results in a positive product, while an odd count results in a negative product.

FAQ

What is the rule for multiplying positive and negative numbers?
The rule is: positive × positive = positive, positive × negative = negative, negative × positive = negative, and negative × negative = positive.
Why do two negative numbers multiply to a positive number?
Two negative numbers cancel each other out, resulting in a positive product. This is because the negatives "annihilate" each other.
Can I multiply more than two numbers with signs?
Yes, the same rules apply. Count the total number of negative numbers in the multiplication. If the count is even, the product is positive; if odd, it's negative.
What happens when you multiply by zero?
Any number multiplied by zero equals zero, regardless of the other number's sign.