Answer :
Certainly! Let's go through a detailed analysis of the problem described by the statements.
Understanding the Question:
The question provides several options about what could be a mistake in an algebraic process. The goal is to identify the correct observation regarding potential errors made during an algebraic operation.
Analyzing Each Statement:
1. "The work was completed correctly."
- This statement suggests that there were no mistakes. If this were true, there would be no need for analyzing potential errors.
2. "Both sides needed to be multiplied by 3, rather than divided by 3."
- This implies there was a misunderstanding regarding whether multiplication or division by 3 was appropriate. However, without further context, it's unclear if multiplying was indeed necessary.
3. "When dividing 36 by 3, the answer should have been [tex]$1 / 12$[/tex], not 12."
- This statement contains a calculation error. Dividing 36 by 3 actually results in 12, not [tex]$1 / 12$[/tex]. Thus, this statement is incorrect.
4. "Both terms on the right side need to be divided by 3, not just the 36."
- This highlights a common mistake in algebra where an operation like division isn't applied uniformly across all terms of an expression. It's important that every relevant term gets divided to maintain the equality or transformation correctly.
Conclusion:
The correct conclusion here is that "Both terms on the right side need to be divided by 3, not just the 36." This statement accurately identifies a typical algebra error where an operation such as division should be consistently applied to each term across the equation or expression.
Therefore, the observation in this statement about the algebraic error is the most accurate one, making it the correct choice.
Understanding the Question:
The question provides several options about what could be a mistake in an algebraic process. The goal is to identify the correct observation regarding potential errors made during an algebraic operation.
Analyzing Each Statement:
1. "The work was completed correctly."
- This statement suggests that there were no mistakes. If this were true, there would be no need for analyzing potential errors.
2. "Both sides needed to be multiplied by 3, rather than divided by 3."
- This implies there was a misunderstanding regarding whether multiplication or division by 3 was appropriate. However, without further context, it's unclear if multiplying was indeed necessary.
3. "When dividing 36 by 3, the answer should have been [tex]$1 / 12$[/tex], not 12."
- This statement contains a calculation error. Dividing 36 by 3 actually results in 12, not [tex]$1 / 12$[/tex]. Thus, this statement is incorrect.
4. "Both terms on the right side need to be divided by 3, not just the 36."
- This highlights a common mistake in algebra where an operation like division isn't applied uniformly across all terms of an expression. It's important that every relevant term gets divided to maintain the equality or transformation correctly.
Conclusion:
The correct conclusion here is that "Both terms on the right side need to be divided by 3, not just the 36." This statement accurately identifies a typical algebra error where an operation such as division should be consistently applied to each term across the equation or expression.
Therefore, the observation in this statement about the algebraic error is the most accurate one, making it the correct choice.
