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Chapter 3: Problem 459

In the following exercises, simplify each expression. $$ -2(-18) \div 9 $$

Short Answer

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Step by step solution

01

- Simplify Inside the Parentheses

First, simplify inside the parentheses. Here, we have \( -2(-18) \). Since \( -2 \) and \( -18 \) are being multiplied, we find the product: \( -2 \times -18 = 36 \).
02

- Perform the Division

Next, take the result of \( -2 \times -18 \), which is 36, and divide it by 9: \( 36 \div 9 = 4 \).

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Key Concepts

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

multiplication of integers
Understanding the multiplication of integers is key to simplifying expressions. Remember, when multiplying two integers, the result's sign depends on both integers' signs. Here are important rules:
  • If both integers are positive, the product is positive. For example, \( 5 \times 3 = 15 \).
  • If both integers are negative, the product is positive. As shown in the exercise, \( -2 \times -18 = 36 \).
  • If one integer is positive and the other is negative, the product is negative. For example, \( 6 \times -4 = -24 \).
In our exercise, \( -2 \times -18 = 36 \), we multiply two negative integers. The result is positive 36.
division
Once you have completed any necessary multiplication steps, it's time for division. Remember, for division, you're essentially splitting a number into equal parts. Here's a refresher on the rules:
  • Dividing a positive number by a positive number results in a positive quotient, like \( 20 \div 5 = 4 \).
  • Dividing two negative numbers also results in a positive quotient, such as \( -12 \div -3 = 4 \).
  • Dividing a positive number by a negative number yields a negative quotient, for example, \( 15 \div -3 = -5 \).
  • Dividing a negative number by a positive number also gives a negative quotient, like \( -24 \div 6 = -4 \).
In our case, we take the positive result from the multiplication step, 36, and divide it by 9. This results in 4 since \( 36 \div 9 = 4 \).
order of operations
The order of operations is crucial when simplifying or evaluating expressions. The commonly used acronym PEMDAS helps us remember the order: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
Here鈥檚 a quick summary for our expression, \( -2(-18) \div 9 \):
  • First, solve any operations inside Parentheses: Here, we simplify \( -2(-18) \) to get 36.
  • Next, handle any Multiplication and Division from left to right: After parentheses, we only have division left, \( 36 \div 9 = 4 \).
Following PEMDAS allows us to solve expressions in the correct order. Missing a step might give you the wrong answer. Hence, always be clear with every operation!

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