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Chapter 1: Problem 61

Perform each operation. SEE EXAMPLE \(5 .\) (OBJECTIVE 2 ) $$\frac{-3(6)}{-(-2)}$$

Short Answer

Expert verified
The answer to \(\frac{-3(6)}{-(-2)}\) is -9.

Step by step solution

01

Simplify Inside Parentheses and Multiply

Apply the multiplication operation as indicated in the problem. Multiply -3 and 6 to obtain -18.
02

Address the Double Negative

Note the negative of a negative number results in a positive number. Thus, the denominator becomes positive 2.
03

Proceed with the Division

Divide -18 by 2 which will lead to -9.

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Key Concepts

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

Multiplying Integers
When we talk about multiplying integers, it simply means taking two whole numbers and multiplying them to get a product. Integers can be positive or negative and the sign plays a big role in the final result.
  • If both integers are positive or both are negative, the product is positive.
  • However, if one integer is positive and the other is negative, the product is negative.
Let's look at the example from the exercise where we multiply \(-3\) and \(6\). Despite the numbers being different in sign, the multiplication follows the simple rule of multiplying the absolute values and then applying the negative sign to the product. So, \(-3 \times 6 = -18\). The rule of thumb is to:
- Multiply the numbers.*
- Determine the sign based on the product of their signs. A negative times a positive gives you a negative result.
Division of Integers
Division of integers is similar to multiplication when it comes to dealing with positive and negative signs.
  • When both integers have the same sign, the result is positive.
  • When the signs are different, the result is negative.
In our exercise, after simplifying the inside of the parentheses, we were left with \(-18\) divided by \(2\). Since \(-18\) is negative and \(2\) is positive, we follow the rule that a negative divided by a positive results in a negative. Simply perform the division as you would with their absolute values:
\(-18 \div 2 = -9\).
This method helps to consistently determine the correct sign for your answer while performing division operations.
Simplifying Expressions
Simplifying expressions involves performing arithmetic operations in a systematic way to reduce them to their simplest form. The order of operations is key, often remembered with the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

Steps in Simplifying

  • Parentheses: Always start by simplifying expressions inside parentheses.
  • Exponents: Address any exponents that exist after simplifying parentheses.
  • M&D: Perform multiplication and division as they appear from left to right.
  • A&S: Finish with addition and subtraction, again from left to right.
In our example, we first noticed the double negative in the denominator. Understanding that \(-(-2)\) results in a positive \(2\) was crucial. This simplification allows us to proceed with dividing the numerator by the simplified denominator efficiently. The final simplification results in \(-9\), following clear steps from complex to simple.

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Most popular questions from this chapter

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