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Negative numbers are numbers that are less than zero. They are usually written with a minus sign (-) before the number. For example, -5 is a negative number. Negative numbers can be found on the left side of zero on a number line.

A key concept to understand is how negative numbers interact with each other, especially during multiplication. When you multiply two negative numbers, the result is always a positive number. This might seem a bit confusing at first, but you can think of it as a rule with no exceptions. For example, \((-3) \times (-4) = 12\).

This is why in our exercise, multiplying \(-60\) by \(-0.003\) gives a positive result.

The absolute value of a number is its distance from zero on the number line, regardless of direction. In other words, it’s the non-negative value of the number. Absolute values are always written without a sign. For instance, the absolute value of -7 is 7, written as \| -7 | = 7\.

When multiplying two numbers, you often start by considering their absolute values. This simplifies the multiplication process. For example, in our exercise, the absolute value of \(-60\) is \| -60 | = 60\, and the absolute value of \(-0.003\) is \| -0.003 | = 0.003\.

When we multiply 60 by 0.003 (their absolute values), we get 0.18. This gives us the numerical part of the answer, before we consider the sign based on the multiplication rules.

Understanding the rules of multiplication is crucial when working with both positive and negative numbers. Here are some essential rules that will help you:

• If you multiply two positive numbers, the result is positive. For example, \(2 \times 3 = 6\).
• If you multiply two negative numbers, the result is also positive. For example, \((-4) \times (-5) = 20\).
• However, if you multiply a positive number by a negative number, the result is negative. For example, \((-3) \times 4 = -12\).

In our exercise, we multiplied two negative numbers: \(-60 \times -0.003\). According to the multiplication rules for negative numbers, the product of two negatives is positive, giving us: \0.18\. Following these rules ensures you get the correct sign for your final answer.

Always remember to multiply the absolute values first, then apply the rules to determine the final sign of the result. This step-by-step approach will make it much easier to handle complex calculations.