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Chapter 2: Problem 12

Multiply. See Examples 5 through 7. $$ -8(-3)(-3) $$

Short Answer

Expert verified
The product is \(-72\).

Step by step solution

01

Understanding the Task

Our task is to multiply the numbers given in the expression: \(-8 \times (-3) \times (-3)\). Each of these numbers will affect the result. We need to consider both the numeric values and their signs.
02

Multiply the First Two Numbers

Start with the first two numbers in the expression: \(-8\) and \(-3\). Multiplying these gives \(-8 \times (-3) = 24\). The result is positive because multiplying two negative numbers results in a positive number.
03

Multiply the Result by the Third Number

Take the result from Step 2, which is \(24\), and multiply it by the third number \(-3\). \(24 \times (-3) = -72\). Since you are multiplying a positive number by a negative number, the result is negative.

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Key Concepts

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

Negative Numbers
Negative numbers are numbers that are less than zero. They are often used to represent values below a baseline, like temperature below freezing or decreases in finance. On the number line, negative numbers are to the left of zero.
  • They are usually denoted with a minus sign (鈭�) in front of the number, such as \(-8\).
  • Being unfamiliar with negative numbers can sometimes lead to confusion, especially when it comes to arithmetic operations.
That is why it's crucial to understand how they interact with each other when performing operations like multiplication.
Multiplication Rules
In mathematics, there are specific rules to follow when multiplying numbers, especially with negative ones. These rules clarify whether a product will be positive or negative.
  • **Multiplying two positive numbers** results in a positive product.
  • **Multiplying two negative numbers** also gives a positive product. For example, \(-8 \times (-3) = 24\).
  • **Multiplying a positive number by a negative number** results in a negative product. For example, \(24 \times (-3) = -72\).
Understanding these rules is essential when tackling problems that involve integer multiplication, ensuring accurate results in expressions and equations.
Order of Operations
The order of operations is a set of rules that helps us solve expressions consistently and accurately. For expressions involving multiple operations like \(-8 \times (-3) \times (-3)\), it's important to follow this order to avoid mistakes.
  • First, perform any operations within **parentheses**. Although our example doesn't include explicit parentheses, consider the sequence as such when multiple operations are present.
  • Next, complete **multiplication** and **division** from left to right.
  • Finally, perform **addition** and **subtraction** from left to right.
By following these steps, we ensure consistency: start with the initial multiplication \(-8 \times (-3)\), then take the result and continue multiplying with any subsequent numbers, in this case, \(24 \times (-3)\), resulting in the final answer, \(-72\). Following the order of operations guarantees correct calculations and is a fundamental skill in mathematics.

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Most popular questions from this chapter

Graph each integer in the list on the same number line. $$ 3,-3,5,-5,6 $$

Explain how to determine which of two signed numbers is larger.

Evaluate: \((-|-(-7)|)\)

Insert \(<\) or \(>\) between each pair of integers to make a true statement. $$ -8 \quad 0 $$

Add. $$ 362+37+90 $$
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