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Chapter 1: Problem 47

In Exercises \(1-72\), compute the value of each expression. $$4-8-(6+3)$$

Short Answer

Expert verified
-13

Step by step solution

01

- Simplify the innermost parentheses

First, simplify the expression inside the parentheses. Calculate the sum inside the parentheses: \(6 + 3 = 9\)
02

- Substitute the simplified value back

Replace the parentheses with the simplified value: \(4 - 8 - 9\)
03

- Perform subtraction operations

Now perform the subtractions from left to right. \(4 - 8 = -4\), then \(-4 - 9 = -13\)

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Key Concepts

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

Order of Operations
In elementary algebra, the order of operations is a set of rules that indicate the sequence in which operations should be carried out to accurately solve mathematical expressions.
These rules are crucial as they ensure consistency and prevent misinterpretation.
The standard order is often remembered by the acronym PEMDAS, which stands for:
  • Parentheses
  • Exponents
  • Multiplication and Division (from left to right)
  • Addition and Subtraction (from left to right)
For the expression given in the original problem, we adhere to this order, starting with computations inside the parentheses. Without following PEMDAS, results can be inconsistent and incorrect.
For instance, not simplifying within parentheses first or misplacing the subtraction steps would yield a wrong solution.
Parentheses
Parentheses are used in algebra to indicate that the operations contained within them should be performed first.
This is crucial when multiple operations are involved.
In the given problem, the parentheses are around the expression 6+3, indicating that this addition should be resolved before any other operations.
Consider the expression: $$4-8-(6+3)$$ The step-by-step solution starts with calculating the sum inside the parentheses: $$6+3=9$$ This is a necessary step before engaging in other operations.
Once simplified, our expression is transformed to: $$4-8-9$$ This simplification helps to clarify the next steps and align them with the order of operations.
Subtraction
Subtraction is a fundamental arithmetic operation that represents removing quantities or finding the difference between numbers.
In the given problem, subtraction occurs twice:
  • First, between 4 and 8
  • Second, subtracting 9 from the result of the first subtraction
Starting with the expression after simplifying parentheses: $$4-8-9$$ Perform the first subtraction: $$4-8 = -4$$
This means removing 8 from 4, which results in -4.
Then, perform the second subtraction: $$-4 - 9 = -13$$ This translates to removing 9 from -4.
Negative numbers can initially be tricky, but practicing these steps makes solving more intuitive.
Always subtract sequentially from left to right for accuracy when multiple subtractions are involved.

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Most popular questions from this chapter

Compute the given expression. Round off your answer to two decimal places where necessary. $$15.7-35(0.6)-4.6$$

Evaluate the given expression. Remember to follow the order of operations. $$9-4[6-2(3-1)]$$

In Exercises \(73-84\), evaluate the given expression. $$9-(5 \cdot 4-2)$$

Compute the given expression. Round off your answer to two decimal places where necessary. $$\frac{-6}{1.5}+\frac{21.6}{-1.2}$$

Evaluate the given expression. Remember to follow the order of operations. $$8-2[9-3(5-3)]$$
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