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Chapter 1: Problem 67

\(6-4^{2} \div 2\)

Short Answer

Expert verified
-2

Step by step solution

01

- Identify the Order of Operations

Use the order of operations (PEMDAS/BODMAS) to decide the sequence of operations. PEMDAS stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
02

- Calculate the Exponent

First, handle the exponent in the expression. Calculate the value of 4^2 = 16.
03

- Perform Division

Next, perform the division: 16 { 2 = 8.
04

- Perform Subtraction

Finally, subtract: 6 8 = -2.

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Key Concepts

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

PEMDAS
When solving a math problem, the order in which you perform operations is crucial. This is where PEMDAS comes into play. PEMDAS stands for:
  • Parentheses
  • Exponents
  • Multiplication
  • Division
  • Addition
  • Subtraction
Remember, multiplication and division should be done from left to right, as well as addition and subtraction. Failing to follow this order can lead to incorrect answers. By using PEMDAS, you ensure each part of the math problem is handled correctly, making your final answer accurate.
Exponents
Exponents are a key part of many math problems. In the expression given, we had to deal with an exponent first:
\(4^2\).
Exponents tell you how many times to multiply a number by itself. In this case, \(4^2\) means 4 multiplied by 4, which equals 16. Handling exponents correctly is vital for solving expressions accurately. So, always tackle exponents early in the process, right after parentheses, if there are any.
Division
Once exponents are out of the way, division comes next in the order of operations. In our problem, post evaluating the exponent, we have
\(16 \div 2\).
Division is straightforward: here, 16 divided by 2 gives us 8. Always work from left to right when performing division (or multiplication). This rule ensures the accuracy of your calculations.
Subtraction
Finally, we handle subtraction, arriving at the last step of our given expression:
\(6 - 8\).
Subtraction tells us how much one number is less than another. In our case, 6 minus 8 results in -2. This step comes after you have completed all previous operations (PEMDAS). By following the idea of finishing all additions and subtractions last (from left to right), you arrive at the correct solution.

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