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Chapter 1: Problem 34

Evaluate each of the following expressions, if possible. $$9(-3)(2)(-4)$$

Short Answer

Expert verified
216

Step by step solution

01

Multiply the first two numbers

Start by multiplying the first two numbers: 9 and -3. i.e., 9(-3) = -27
02

Multiply the result by the third number

Now, take the result from Step 1 and multiply it by 2. i.e., -27(2) = -54
03

Multiply the result by the fourth number

Finally, multiply the result from Step 2 by -4. i.e., -54(-4) = 216

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Key Concepts

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

Order of Operations
When solving math problems, especially complex ones, the order of operations is vital. The order of operations is a rule that ensures the correct sequence of steps to get the correct answer. The basic sequence is often remembered using the acronym PEMDAS, which stands for:
  • Parentheses
  • Exponents
  • Multiplication and Division (from left to right)
  • Addition and Subtraction (from left to right)
Ensuring you follow this order will help you avoid mistakes. In the provided exercise, multiplication is carried out in succession, and it's crucial to perform each step correctly. Starting with the first multiplication, proceeding step by step, and following the correct sequence ensures we get the right result.
Multiplication of Integers
Understanding how to multiply integers is essential for evaluating expressions. Integers include positive numbers, negative numbers, and zero. Here are some fundamental rules to keep in mind:
  • Multiplying two positive numbers results in a positive product.
  • Multiplying two negative numbers also results in a positive product, because the negatives cancel each other out.
  • Multiplying a positive number by a negative number results in a negative product.
Applying these rules to our exercise:
  • First, multiply 9 (positive) by -3 (negative), resulting in -27.
  • Next, multiply -27 (negative) by 2 (positive), resulting in -54.
  • Finally, multiply -54 (negative) by -4 (negative), resulting in 216, since two negatives make a positive.
Understanding these rules simplifies the multiplication process and helps avoid errors.
Algebraic Steps
Breaking down algebraic problems into smaller steps can make them easier to handle. Here's how to follow systematic algebraic steps:
  • Identify the problem and understand all numbers and operations involved.
  • Follow the order of operations to solve the problem step-by-step.
  • Check each step as you go along to ensure accuracy.
In the given exercise, we apply algebraic steps as follows:
  • Step 1: Multiply 9 by -3 to get -27.
  • Step 2: Take the result from Step 1 (-27) and multiply it by 2 to get -54.
  • Step 3: Multiply the result from Step 2 (-54) by -4 to obtain the final result, 216.
Each step builds on the last, showing the importance of accuracy and methodical work. Completing problems one step at a time helps ensure you don't miss any details and produces the right answer.

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Most popular questions from this chapter

Evaluate the given expression. Remember to follow the order of operations. $$30-(5 \cdot 4)-2$$

If possible, list three numbers that are members and three numbers that are not members of the given set. If it is not possible, explain why. \(\\{t | t \text { is a real number but not a rational number }\\}\)

Compute the given expression. Round off your answer to two decimal places where necessary. $$0.02(28.6-13.5)$$

What is the difference between the set \(N\) (the set of natural numbers) and the set \(W\) (the set of whole numbers)?

Evaluate the given expression. Remember to follow the order of operations. $$18+2 \cdot 9+5$$
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