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Chapter 1: Problem 48

Use the order of operations to simplify. $$-23-6^{2} \div 4$$

Short Answer

Expert verified
The simplified expression using the order of operations (PEMDAS) for \(-23-6^2\div4\) is \(-32\).

Step by step solution

01

Exponentiation

Evaluate the exponent term in the expression: $$-23 - 6^2 \div 4$$ $$-23 - 36 \div 4$$
02

Division

Evaluate the division term in the expression: $$-23-36\div 4 = -23 - 9$$
03

Subtraction

Evaluate the subtraction term in the expression: $$-23-9 = -32$$ So, the simplified expression is \(-32\).

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Key Concepts

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

Simplification
Simplification involves reducing an expression to its simplest form. This can make a math problem easier to work with and understand. When simplifying, it's important to follow the order of operations, known commonly as PEMDAS:
  • P: Parentheses
  • E: Exponents
  • M/D: Multiplication and Division (left to right)
  • A/S: Addition and Subtraction (left to right)
Following this order ensures that the expression is evaluated correctly and consistently. In this exercise, simplification helps us break down \(-23 - 6^2 \div 4\) into smaller, more approachable parts that follow the mathematical rules of evaluation, ultimately leading us to \(-32\).
Exponentiation
Exponentiation is the process of raising a number to the power of another. This means multiplying the base number by itself a specified number of times. For example, in the expression \(6^2\), 6 is the base and 2 is the exponent. Here, 6 is multiplied by itself, resulting in 36 (\(6 \times 6 = 36\)).Exponentiation is often one of the first operations performed in an expression, after any operations within parentheses, according to the order of operations rules. In our example, evaluating \(6^2\) first turns the original expression into \(-23 - 36 \div 4\), paving the way for the subsequent steps.
Division
Division is the process of splitting a number into equal parts. It's represented by the \(\div\) symbol in equations. When dividing, you take the dividend and divide it by the divisor to get a quotient. In the given expression \(-23 - 36 \div 4\), once exponentiation is resolved, division becomes the next primary operation to tackle.Dividing 36 by 4 yields 9, because \(36 \div 4 = 9\). This conversion simplifies the expression further to \(-23 - 9\). It is crucial to solve any multiplication or division from left to right after resolving exponents, as per the order of operations.
Subtraction
Subtraction involves taking one quantity away from another. It is often symbolized by a minus (\(-\)) sign. In our ongoing example, after resolving division, we are left with \(-23 - 9\). This expression needs subtraction to fully simplify it.Performing the operation involves removing 9 from -23. This results in a value of -32, as the numbers move further into the negative direction. Understanding subtraction as finding the difference between values or reducing a number helps simplify mathematical expressions accurately and aligns with the final step of the order of operations.

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Most popular questions from this chapter

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