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Chapter 2: Problem 6

Find each product. $$-6 \cdot-6$$

Short Answer

Expert verified
The product of \(-6 \cdot -6\) is \(36\).

Step by step solution

01

Identify the Numbers

In this multiplication problem, we need to find the product of two numbers, \(-6\) and \(-6\).
02

Apply the Rule for Multiplying Negative Numbers

The rule for multiplying two negative numbers is that the product is positive. So, the product of \(-6\) and \(-6\) will be positive.
03

Multiply the Absolute Values

Determine the absolute value of each number. The absolute value of \(-6\) is 6. Multiply the absolute values together: 6 times 6 equals 36.
04

Combine the Results

Since both numbers were negative, using the rule from Step 2, the product is positive. Thus, the product of \(-6\) and \(-6\) is \(36\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Negative Numbers
Negative numbers might appear a bit tricky at first, but they're quite straightforward once you get the hang of them. Every negative number is less than zero, and it is represented with a minus sign (-) before the number. For example, -1, -6, and -100 are all negative numbers. Negative numbers are often used to represent losses, debts, or decreases in various contexts.
When multiplying negative numbers, remember this simple rule: the product of two numbers is negative if only one of the numbers is negative. However, if both numbers are negative, their product is positive. This leads us to our next crucial concept.
Exploring Absolute Value
Absolute value is a must-know concept, especially when dealing with negative numbers. It refers to the distance of a number from zero on the number line, without considering which direction from zero the number lies. Essentially, it's the 'size' or 'magnitude' of the number.
For instance, the absolute value of both 6 and -6 is 6. We notate the absolute value with vertical bars like this:
  • \(|6| = 6\)
  • \(|-6| = 6\)
This concept helps simplify calculations, such as when you're multiplying negative numbers by focusing first on their absolute values.
The Product Rule for Multiplication of Negative Numbers
The product rule for multiplication, also known as the sign rule, is a crucial tool in understanding how to multiply negative numbers. It states:
  • If both numbers are positive, the product is positive.
  • If one number is positive and the other is negative, the product is negative.
  • If both numbers are negative, the product is positive.
This is why, in the problem of \(-6 \times -6\), the answer is positive. After calculating the absolute values (6 times 6), we apply the product rule: two negatives make a positive, giving us a positive 36. This rule is vital as it helps ensure you determine the correct sign of the product in multiplication problems.

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Most popular questions from this chapter

The melting point of metal mercury is \(-39^{\circ} \mathrm{C}\). The freezing point of alcohol is \(-114^{\circ} \mathrm{C} .\) How much warmer is the melting point of mercury than the freezing point of alcohol? \(\mathbf{A}-153^{\circ} \mathrm{C}\) c \(75^{\circ} \mathrm{C}\) \(B-75^{\circ} \mathrm{C}\) D \(153^{\circ} \mathrm{C}\)

Positive integers \(A\) and \(C\) satisfy \(A(A-C)=23 .\) What is the value of \(C\) ?

Graph each set of integers on a number line. $$\\{-2,-4,-5,-8\\}$$

Find each sum. $$-4+(-3)+(-7)$$

Evaluate each expression. $$|-15|$$
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