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Chapter 1: Problem 94

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

Short Answer

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Step by step solution

01

- Simplify inside the Innermost Parentheses

Evaluate the expression inside the innermost parentheses first. Inside the expression: Evaluate Evaluate 5 - 3 = 2 the expression becomes: Evaluate the brackets: Solving inside the brackets: Evaluate inside the square brackets: 9 - 3(2)= 9 - 6 = 3 the entire expression becomes: 8 - 2[3] Finally: 3 the remaining term and gives: 8 - 6 = 2 the full solution content: the :TOP finish short_answer content: solution end process dummy.

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Key Concepts

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

Evaluating Expressions
Evaluating an expression means simplifying it to find its value. This often involves working through multiple layers of arithmetic, following specific rules to ensure accuracy.

One key rule is the order of operations. It's a guideline for the order in which mathematical operations should be performed. The typical order is:
  • Parentheses or Brackets
  • Exponents (Powers and Roots, etc.)
  • Multiplication and Division (left to right)
  • Addition and Subtraction (left to right)
In short, remember the acronym PEMDAS: Parentheses, Exponents, Multiplication/Division, and Addition/Subtraction.
Understanding this order is crucial to correctly evaluating expressions and achieving the right answer.
Innermost Parentheses
When evaluating expressions, always start with the innermost set of parentheses. Parentheses are used to group numbers and operations that need to be solved first.

Look at our example expression: \(8-2[9-3(5-3)]\). The innermost parentheses here is \(5-3\). We solve this first:
  • Evaluate \(5-3\), which is 2.
  • The expression now looks like this: \(8-2[9-3(2)]\).
By tackling the innermost parentheses first, we simplify the expression step by step, making it easier to reach the final solution.
Square Brackets
Square brackets work similarly to parentheses and are often used when expressions have multiple layers of grouping.

In our example, once we have simplified the inner parentheses, we need to handle the square brackets next.
  • After solving \(5-3\) to get 2, the expression becomes \(8-2[9-3(2)]\).
  • Next, evaluate inside the square brackets: \(9-3(2)\).
  • Simplify further: \(9-6\) which gives us 3.
  • The expression now is \(8-2[3]\).
  • Finally, solve the bracketed term: \(8-2 \times 3\), which equals \(8-6=2\).
By carefully working through nested groups step-by-step, we prevent mistakes and simplify complex expressions accurately.

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Most popular questions from this chapter

Compute the given expression. Round off your answer to two decimal places where necessary. $$-2(-5.3)$$

If possible, list three numbers that are members and three numbers that are not members of the given set. If it is not possible, explain why. \(\\{x | x \text { is a real number but not an integer }\\}\)

Graph the given set on a number line. \(\\{a | a \text { is a natural number less than } 12 \text { and not divisible by } 3\\}\)

Evaluate the given expression. Remember to follow the order of operations. $$6+4(3+2)$$

Sketch the given set on a number line. $$\\{x | x>4\\}$$
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