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Chapter 1: Problem 91

Simplify each expression. $$-3(-1)-(-3)(2)$$

Short Answer

Expert verified
The simplified form of the given expression is 9.

Step by step solution

01

Apply the multiplication operation

According to the order of operations, perform multiplication before moving on to addition operations. We have two multiplication operations:1) \( -3 \times -1 = 3 \)2) \( -3 \times 2 = -6 \). Thus, the expression becomes \(3-(-6)\).
02

Simplify the double negatives

Converting the double negative to a positive, the expression becomes \(3+6\) .
03

Perform the final addition

Add together 3 and 6 to obtain the final simplified result.\(3 + 6 = 9 \)

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Key Concepts

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

Order of Operations
When simplifying an expression, it's vital to follow the order of operations, often remembered by the acronym PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). Skipping or misordering these steps can lead to incorrect solutions.
Let's break this down with our expression example. In \(-3(-1)-(-3)(2)\), the first operation to address is the multiplication, following the PEMDAS rule. It's important to perform all multiplication operations before adding or subtracting.
  • First, multiply \(-3\) and \(-1\).
  • Next, multiply \(-3\) and \(2\).
Now, with multiplication done first, we can tackle any addition or subtraction, leading us to a correct and simplified expression.
Simplification
Simplification is the process of making an expression easier to work with or understand, while keeping the mathematical value the same. It often involves combining like terms or reducing fractions. In the expression \(-3(-1)-(-3)(2)\), simplification helps in managing complex components.
Our first step of simplification came from solving the multiplication portions. After that, noticing double negatives is a key part of simplifying.
  • When you see double negatives, such as \(-(-6)\), they can be simplified to a positive, turning the expression from \(3 - (-6)\) to \(3 + 6\).
Simplifying expressions by recognizing these parts turns them into a more straightforward format that's easier to solve.
Multiplication of Integers
Understanding the multiplication of integers is crucial in algebra and arithmetic. When multiplying integers, always keep in mind the rule:
  • A positive number times a positive number equals a positive number.
  • A positive number times a negative number equals a negative number.
  • A negative number times a negative number equals a positive number.
In our initial expression \(-3(-1)-(-3)(2)\), consider these rules:
  • The first operation \(-3 \times -1\) turns into \(3\), because two negative numbers make a positive.
  • The second operation \(-3 \times 2\) results in \(-6\), since a negative number multiplied by a positive number leads to a negative outcome.
Grasping these multiplication rules aids in confidently tackling and simplifying more complex algebraic expressions.

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