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Absolute values are always non-negative. They represent the distance of a number from zero on the number line. For any number, whether positive or negative, the absolute value is always positive. For example, the absolute value of -5 is 5, and the absolute value of 7 is 7. This property is crucial when multiplying negative numbers because it allows us to focus on the magnitude (size) of the numbers without worrying about their signs initially. In the exercise, we first find the absolute values of -0.5 and -0.6, which are 0.5 and 0.6 respectively. We then multiply these absolute values: \(0.5 \times 0.6 = 0.3\). Once this step is correct, we can apply the appropriate sign to the final answer.

Understanding the sign rules in multiplication is key to solving problems involving negative numbers. Here are the basic rules:

• Positive × Positive = Positive


• Positive × Negative = Negative


• Negative × Positive = Negative


• Negative × Negative = Positive

These rules determine the sign of the result in a multiplication problem. For example, in the exercise given, we multiply two negative numbers: \(-0.5 \times -0.6\). According to the sign rules, multiplying two negative numbers results in a positive product. Hence, \(-0.5 \times -0.6 = 0.3\). Reviewing and practicing these rules can make solving such problems easier and faster.

Negative and positive numbers refer to numbers with a sign: negative numbers are less than zero and positive numbers are greater than zero. For example, -3 is a negative number, while 5 is a positive number. When multiplying these numbers, you must pay attention to both their signs and their absolute values.

In the step-by-step solution of the exercise, we deal with two negative numbers, -0.5 and -0.6. To solve it, we:

• Ignore the signs initially and find the absolute values: 0.5 and 0.6.


• Multiply the absolute values: \(0.5 \times 0.6 = 0.3\).


• Then, apply the sign rule: the product of two negative numbers is positive.

Therefore, the final product is 0.3, which is positive. Understanding how to handle negative and positive numbers in multiplication is essential for accurate results.