1. What is Negative Multiplication?

The multiplication of negative numbers follows specific rules in mathematics. When two negative numbers are multiplied together, the result is a positive number. This principle is fundamental in algebra and arithmetic.

2. How Negative Multiplication Works

The basic rule for multiplying negative numbers:

Where:

• \( a \) — Any real number
• \( b \) — Any real number

Examples:

• (-2) × (-3) = 6
• (-5) × (-1) = 5
• (-0.5) × (-4) = 2

3. Mathematical Explanation

Why does this work? The rule that "a negative times a negative equals a positive" comes from the need to maintain consistency in mathematics. It preserves the distributive property of multiplication over addition and ensures that the number system works coherently.

4. Using the Calculator

Instructions: Enter any two numbers (positive or negative) and the calculator will show you the product. The calculator demonstrates that multiplying two negatives gives a positive result.

5. Frequently Asked Questions (FAQ)

Q1: Why does negative × negative = positive?
A: This rule maintains mathematical consistency, particularly with the distributive property. If we didn't follow this rule, basic arithmetic would break down.

Q2: What if I multiply a negative and positive number?
A: The result is negative: (-a) × b = -(a × b)

Q3: Does this rule apply to all numbers?
A: Yes, it applies to all real numbers - integers, fractions, decimals, etc.

Q4: How is this used in real life?
A: This principle is used in finance (debt calculations), physics (vector directions), and many other fields where opposite directions or values interact.

Q5: What about multiplying more than two negative numbers?
A: The product is positive if there's an even number of negative factors, and negative if there's an odd number.