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Chapter 1: Problem 22

Evaluate each of the following expressions, if possible. $$6(-1)-10$$

Short Answer

Expert verified
-16

Step by step solution

01

Distribute the Multiplication

First, apply the multiplication in the expression. Multiply 6 by -1 to get the result: \[ 6 \times (-1) = -6 \]
02

Combine the Results

Now combine the result of the multiplication with -10: \[ -6 - 10 \]
03

Perform the Subtraction

Subtract 10 from -6 to get the final value: \[ -6 - 10 = -16 \]

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Key Concepts

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

Multiplication of Integers
Multiplying integers can sometimes be tricky, but it becomes easier once you understand the rules. When you multiply two integers:
  • If both numbers are positive or both are negative, the result is positive.
  • If one number is positive and the other is negative, the result is negative.
For example, in the expression 6(-1), we have one positive integer (6) and one negative integer (-1). According to the rules, a positive times a negative gives a negative result:
\( 6 \times (-1) = -6 \).
Once you understand and apply these rules, multiplication of integers becomes straightforward.
Subtraction of Integers
Subtraction of integers follows specific rules which help us easily determine the result. These rules help us understand what happens when we subtract one integer from another.
  • If both numbers are positive, subtract the smaller number from the larger number.
  • If both numbers are negative, subtract the larger absolute value from the smaller absolute value and keep the result negative.
  • If you have a positive number and a negative number, convert the subtraction into an addition problem by changing the sign of the number being subtracted.
For example, with the expression -6 - 10:
\( -6 - 10 = -16 \). Here, both numbers are negative, so we add the absolute values and keep the result negative. Understanding this rule makes it easier to subtract integers effectively.
Order of Operations
In mathematics, the order of operations is crucial for correctly evaluating expressions. This order determines the sequence in which operations should be performed. The correct sequence can be remembered with the acronym PEMDAS:
  • P: Parentheses first
  • E: Exponents (i.e. powers and square roots)
  • M/D: Multiplication and Division (left to right)
  • A/S: Addition and Subtraction (left to right)
For instance, in the given exercise 6(-1)-10, follow the steps:
1. First, evaluate the multiplication: \( 6 \times (-1) = -6 \).
2. Then, perform the subtraction: \( -6 - 10 = -16 \).
Adhering to the order ensures that you solve expressions correctly and consistently.

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