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Chapter 1: Problem 42

Evaluate each of the following expressions, if possible. $$11-(6 \cdot 2-7)$$

Short Answer

Expert verified
6

Step by step solution

01

Evaluate the expression inside the parentheses

The expression inside the parentheses is \(6 \cdot \ 2 \- 7\). Calculate this first.\[6 \cdot 2 = 12\] and then we have \[12 \- 7 = 5\]
02

Substitute the simplified value back into the expression

Replace the expression inside the parentheses with its simplified value:\(11 \- (5)\)
03

Evaluate the simplified expression

Perform the subtraction:\[ 11 - 5 = 6\]

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Key Concepts

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

Order of Operations
When evaluating mathematical expressions, it's crucial to follow the order of operations. This ensures that everyone solves the expression the same way. The most common acronym to remember this order is PEMDAS:
  • Parentheses: Do all operations inside parentheses first.
  • Exponents: Next, handle exponents (or radicals).
  • Multiplication and Division: From left to right.
  • Addition and Dubtraction: From left to right.
In the given exercise, we first focused on the operations within the parentheses, which is consistent with the 'P' in PEMDAS. Following the order of operations ensures that the solution is computed correctly and consistently.
Arithmetic Operations
The exercise also illustrates basic arithmetic operations such as multiplication and subtraction. Let's break down these operations:
  • Multiplication: This means combining equal groups. In our example, we calculated \(6 \cdot 2\) to get 12. Multiplication simplifies repeated addition.
  • Subtraction: This operation tells us how much remains when quantities are taken away. From the previous step, we subtracted 7 from 12 to get 5.
By understanding each arithmetic operation, you can simplify expressions systematically and accurately.
Parentheses in Math
Parentheses are used in math to group parts of an expression that should be treated as a single unit. They tell us which operations to perform first before dealing with the rest of the expression.
In the provided problem, parentheses group the expression \(6 \cdot 2 - 7\). This indicates that everything inside the parentheses should be calculated first. After simplifying what's inside the parentheses to 5, we then substituted this result back into the overall expression to get \(11 - 5\). The parentheses ensure clarity and correctness in complex calculations.
In summary, always handle the innermost parentheses first and work your way out, aligning with the order of operations.

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