Negative Times Positive Calculator

When you multiply a negative number by a positive number, the result is always negative. This calculator helps you understand and compute this operation quickly.

What is negative times positive?

Multiplying a negative number by a positive number results in a negative product. This is a fundamental rule of arithmetic that applies to all real numbers. The sign of the product depends on the signs of the factors:

Positive × Positive = Positive
Negative × Negative = Positive
Positive × Negative = Negative
Negative × Positive = Negative

This rule is consistent across all real numbers, including integers, fractions, and decimals.

How to calculate negative times positive

To calculate the product of a negative and positive number:

Identify the absolute values of both numbers (ignore their signs)
Multiply the absolute values together
Apply the sign rule: if one number is negative and the other is positive, the product is negative

Formula

If a = negative number and b = positive number, then:

a × b = - (|a| × |b|)

Important Note

The sign of the product depends only on the signs of the factors, not their magnitudes. A large negative number multiplied by a small positive number will still result in a negative product.

Examples

Let's look at some examples to illustrate how negative times positive multiplication works:

Example 1: -5 × 3

Step 1: Absolute values are 5 and 3

Step 2: 5 × 3 = 15

Step 3: Apply sign rule (- × + = -)

Result: -15

Example 2: -2.5 × 4

Step 1: Absolute values are 2.5 and 4

Step 2: 2.5 × 4 = 10

Step 3: Apply sign rule (- × + = -)

Result: -10

Example 3: -100 × 0.1

Step 1: Absolute values are 100 and 0.1

Step 2: 100 × 0.1 = 10

Step 3: Apply sign rule (- × + = -)

Result: -10

FAQ

Why is the product negative when multiplying a negative and positive number?

The product's sign follows the sign rule of multiplication. When you multiply a negative number by a positive number, the negative sign dominates, resulting in a negative product.

Does the magnitude of the numbers affect the sign of the product?

No, the magnitude (size) of the numbers does not affect the sign. Only the signs of the factors determine the sign of the product.

Can negative times positive multiplication be used in real-world applications?

Yes, this operation is fundamental in many real-world applications, including accounting (debits and credits), physics (forces and directions), and engineering (negative and positive values in calculations).

What happens when you multiply a negative number by zero?

Any number multiplied by zero equals zero. The sign of the original number doesn't matter because zero is neither positive nor negative.