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Multiply Negative Numbers Calculator

Reviewed by Calculator Editorial Team

Multiplying negative numbers can seem confusing at first, but there are simple rules to follow. This calculator helps you multiply negative numbers quickly and understand the result.

How to Multiply Negative Numbers

Multiplying negative numbers follows specific rules that ensure the result is mathematically correct. The key is to understand the signs of the numbers being multiplied.

Formula: a × b = product

Where a and b are negative numbers, the product will be positive if both numbers have the same sign (both negative) and negative if they have different signs.

To multiply negative numbers:

  1. Identify the signs of both numbers.
  2. Multiply the absolute values of the numbers.
  3. Apply the sign rules:
    • Negative × Negative = Positive
    • Negative × Positive = Negative
    • Positive × Negative = Negative

Rules of Multiplying Negatives

There are two fundamental rules for multiplying negative numbers:

Rule 1: Negative × Negative = Positive

When you multiply two negative numbers, the result is positive. For example, -3 × -4 = 12.

Rule 2: Negative × Positive = Negative

When you multiply a negative number by a positive number, the result is negative. For example, -5 × 6 = -30.

These rules apply regardless of the order of multiplication. For example, -2 × -3 is the same as -3 × -2.

Examples of Multiplying Negatives

Here are some examples to illustrate how to multiply negative numbers:

Example 1: Two Negative Numbers

Multiply -7 by -8:

  1. Identify signs: Both are negative.
  2. Multiply absolute values: 7 × 8 = 56.
  3. Apply rule: Negative × Negative = Positive.
  4. Result: -7 × -8 = 56.

Example 2: Negative and Positive Numbers

Multiply -9 by 10:

  1. Identify signs: One negative, one positive.
  2. Multiply absolute values: 9 × 10 = 90.
  3. Apply rule: Negative × Positive = Negative.
  4. Result: -9 × 10 = -90.

Example 3: Multiple Negative Numbers

Multiply -2 by -3 by -4:

  1. Identify signs: All three are negative.
  2. Multiply absolute values: 2 × 3 × 4 = 24.
  3. Apply rule: Negative × Negative × Negative = Negative (because there are two negative numbers).
  4. Result: -2 × -3 × -4 = -24.

Common Mistakes

When multiplying negative numbers, it's easy to make these common mistakes:

Mistake 1: Forgetting to apply the sign rules

For example, thinking -3 × -4 = -12 instead of 12.

Mistake 2: Changing the sign incorrectly

For example, thinking -5 × 6 = 30 instead of -30.

Mistake 3: Misapplying the rules to multiple negatives

For example, thinking -2 × -3 × -4 = 24 instead of -24.

To avoid these mistakes, carefully follow the sign rules and double-check your calculations.

FAQ

Why is multiplying two negative numbers positive?

Multiplying two negative numbers results in a positive because the negatives cancel each other out. This rule comes from the concept of opposite directions in mathematics.

What happens when you multiply a negative and a positive number?

The result is negative because the negative sign dominates. This is because a negative number represents the opposite direction on the number line.

Can you multiply more than two negative numbers?

Yes, you can multiply any number of negative numbers. The result will be positive if there's an even number of negatives and negative if there's an odd number of negatives.

Is there a difference between -a × -b and - (a × b)?

No, -a × -b is the same as - (a × b) because multiplying two negatives gives a positive, and then negating it gives the same result as multiplying by -1.