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Understanding the rules of multiplication is essential for solving problems involving both positive and negative numbers. The rules are straightforward:

• When you multiply two positive numbers, the product is always positive.


• When you multiply two negative numbers, the product is always positive.


• When you multiply a positive number and a negative number, the product is always negative.

It's important to remember these rules because they help you determine the sign of the final product. In the given exercise, multiplying 6 (positive) by -9 (negative) leads to a negative product, which follows the third rule.

The absolute value of a number is its distance from zero, regardless of its sign. In mathematical terms, it is always a positive number or zero. For example, the absolute value of 6 is 6, and the absolute value of -9 is 9.

Knowing this helps simplify the multiplication process when dealing with negative numbers. By focusing on the absolute values, you can ignore the signs until you've completed the multiplication. In the exercise, we first multiply the absolute values: \[6 \times 9 = 54\]. After performing the multiplication, you then apply the rule for the signs to determine the final product.

A negative product occurs when multiplying a positive number by a negative number. This is because the two numbers have different signs, which inherently causes the result to be negative.

To understand why this happens, consider that multiplying by a negative number means changing direction on a number line. For instance, starting at 6 and multiplying by -9 means you are taking 6 units in the positive direction and flipping it to move 9 times in the opposite (negative) direction.

Hence, after calculating the absolute value result (54), the final step is to attach a negative sign, resulting in -54. This understanding is crucial for correctly solving problems that involve both positive and negative numbers.