A Negative A Positive Calculator

Multiplying a negative number by a positive number is a fundamental operation in mathematics. This calculator helps you quickly determine the product of such operations and understand the underlying rules.

How to Use This Calculator

Using the calculator is simple:

Enter the first number (can be negative or positive)
Enter the second number (can be negative or positive)
Click the "Calculate" button
View the result and explanation

The calculator will show you the product of the two numbers and explain why the result is negative or positive based on the rules of signed number multiplication.

What Is a Negative Times a Positive?

When you multiply a negative number by a positive number, the result is always negative. This is one of the fundamental rules of multiplying signed numbers:

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

This rule applies to all real numbers, including integers, decimals, and fractions.

The Formula

Multiplication Formula

For any two numbers a and b:

a × b = product

Where:

a = first number (can be negative or positive)
b = second number (can be negative or positive)
product = the result of multiplying a and b

The sign of the product depends on the signs of the original numbers:

If both numbers have the same sign (both positive or both negative), the product is positive.
If the numbers have different signs, the product is negative.

Worked Examples

Example 1: Negative × Positive

Calculate (-3) × 4

According to the rules:

Negative × Positive = Negative

So, (-3) × 4 = -12

Example 2: Positive × Negative

Calculate 5 × (-2)

According to the rules:

Positive × Negative = Negative

So, 5 × (-2) = -10

Example 3: Negative × Negative

Calculate (-6) × (-3)

According to the rules:

Negative × Negative = Positive

So, (-6) × (-3) = 18

Frequently Asked Questions

Why is a negative times a positive negative?

This is a fundamental rule of mathematics. When you multiply a negative number by a positive number, the result is negative because the negative sign indicates a direction opposite to the positive direction.

What happens when you multiply two negative numbers?

When you multiply two negative numbers, the result is positive. This is because the two negative signs cancel each other out.

Can this calculator handle decimal numbers?

Yes, the calculator can handle both integers and decimal numbers. Simply enter the numbers with decimal points as needed.

Is there a difference between multiplying a negative by a positive and vice versa?

No, there is no difference in the result. Both operations (-a × b) and (a × -b) will yield the same negative result.

Where is this concept used in real life?

This concept is used in various real-life scenarios such as calculating losses in business, understanding temperature changes, and analyzing financial deficits.