What is the result of multiplying two numbers with different signs?

When two numbers with different signs are multiplied, the product is always negative. This is a fundamental rule in arithmetic that arises from the definition of multiplication with positive and negative numbers.

For instance, consider multiplying a positive number by a negative number. If we take 3 (a positive number) and -2 (a negative number), the calculation yields -6. This indicates that the product adopts the sign of the negative number, resulting in a negative outcome. This principle holds true universally for any two numbers where one is positive and the other is negative.

The reasoning behind this can also be reflected on a number line. If you move to the right (positive direction) for positive numbers and to the left (negative direction) for negative numbers, multiplying by a negative number effectively reverses the direction of movement, resulting in a position on the left side of zero, hence a negative value.

Therefore, when multiplying a positive number by a negative number or a negative number by a positive number, the outcome is invariably negative.