What happens when multiplying a positive number by a negative number?

When multiplying a positive number by a negative number, the result is negative. This concept is rooted in the rules of arithmetic concerning multiplication and the properties of numbers. A positive number represents a quantity that is greater than zero, while a negative number represents a quantity that is less than zero.

Thus, when you multiply two numbers with differing signs (one positive and one negative), the product will always take on the sign of the negative factor. For instance, if you take 5 (positive) and multiply it by -3 (negative), the operation can be viewed as taking 5 groups of -3, which results in -15. This clear relationship between the signs and the result of multiplication is fundamental in mathematics and helps to convey the notion of direction or loss in various real-world applications.

Understanding this rule can aid in various contexts, whether in simple arithmetic or more complex mathematical problem-solving, affirming the consistency of the properties of numbers.