Difficulty: Easy
Correct Answer: 12
Explanation:
Introduction / Context:
This is a straightforward arithmetic expression designed to check whether you correctly apply the order of operations in a situation where the same number, 3, appears several times. Even simple expressions can produce errors if multiplication is not carried out before addition and subtraction.
Given Data / Assumptions:
Concept / Approach:
The only operation with higher precedence here is the multiplication 3 × 3. After computing this product, we are left with a sequence of additions and subtractions that can be evaluated from left to right. The key is to ensure that we do not treat all operations as if they have the same priority.
Step-by-Step Solution:
First perform the multiplication: 3 × 3 = 9.Substitute back into the expression to obtain 9 + 3 − 3 + 3.Now evaluate left to right: 9 + 3 = 12.Next, 12 − 3 = 9.Finally, 9 + 3 = 12.
Verification / Alternative check:
We can also group the terms: 3 × 3 + (3 − 3) + 3.Here, 3 × 3 = 9 and (3 − 3) = 0, so the expression becomes 9 + 0 + 3 = 12.This grouping again confirms the value 12.
Why Other Options Are Wrong:
An answer of 9 would result from stopping the evaluation at 3 × 3 or from miscalculating one of the addition or subtraction steps.An answer of 3 might come from grouping 3 × (3 + 3 − 3 + 3) incorrectly instead of respecting the original structure.A negative result such as −3 clearly conflicts with the fact that most terms are positive and the net effect is an increase in value.
Common Pitfalls:
One common mistake is to perform 3 + 3 first and then multiply by 3, which effectively changes the expression and leads to a different result.Another pitfall is to rush through the plus and minus operations and miscount them, for example, canceling the wrong pair of 3s.
Final Answer:
Correctly applying the order of operations, the value of the expression is 12.
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