Question
provide an explanation of how to correctly evaluate the following expression use academic vocab in your answer
Answers
GPT-4o mini
To evaluate an expression correctly, it is essential to adhere to a systematic approach that ensures accuracy and clarity. Below are the steps typically involved in the evaluation process:
1. **Understand the Expression**: Begin by carefully examining the expression to identify its components, such as numbers, variables, operators (e.g., addition, subtraction, multiplication, division), and any parentheses.
2. **Apply the Order of Operations**: Utilize the established order of operations, commonly represented by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)). This hierarchy is crucial for determining the sequence in which calculations should be performed.
3. **Simplify Inside Parentheses**: If the expression contains parentheses, begin by evaluating the expressions enclosed within them. This step may involve further simplification of the expressions inside, following the same order of operations.
4. **Calculate Exponents**: If there are any exponents in the expression, compute these next, again adhering to the order of operations.
5. **Perform Multiplication and Division**: Proceed with any multiplication and division operations from left to right. In the event that multiple operations of the same rank are present, execute them sequentially from left to right.
6. **Execute Addition and Subtraction**: Finally, perform any addition and subtraction operations, again from left to right, to arrive at the final result.
7. **Verify Your Work**: Upon obtaining a solution, it is prudent to review each step meticulously to ensure that the operations were conducted accurately and that no errors were made in the application of the order of operations.
By methodically adhering to these guidelines, one can effectively evaluate mathematical expressions with precision and confidence.
1. **Understand the Expression**: Begin by carefully examining the expression to identify its components, such as numbers, variables, operators (e.g., addition, subtraction, multiplication, division), and any parentheses.
2. **Apply the Order of Operations**: Utilize the established order of operations, commonly represented by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)). This hierarchy is crucial for determining the sequence in which calculations should be performed.
3. **Simplify Inside Parentheses**: If the expression contains parentheses, begin by evaluating the expressions enclosed within them. This step may involve further simplification of the expressions inside, following the same order of operations.
4. **Calculate Exponents**: If there are any exponents in the expression, compute these next, again adhering to the order of operations.
5. **Perform Multiplication and Division**: Proceed with any multiplication and division operations from left to right. In the event that multiple operations of the same rank are present, execute them sequentially from left to right.
6. **Execute Addition and Subtraction**: Finally, perform any addition and subtraction operations, again from left to right, to arrive at the final result.
7. **Verify Your Work**: Upon obtaining a solution, it is prudent to review each step meticulously to ensure that the operations were conducted accurately and that no errors were made in the application of the order of operations.
By methodically adhering to these guidelines, one can effectively evaluate mathematical expressions with precision and confidence.