To identify Fernando's error, let's evaluate the expression step by step:
The original expression is: \[ \frac{5(9 - 5)}{2} + (-2)(-5) + (-3)^2 \]
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Calculate \(9 - 5\): \[ 9 - 5 = 4 \]
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Calculate \(\frac{5(4)}{2}\): \[ \frac{5(4)}{2} = \frac{20}{2} = 10 \]
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Calculate \((-2)(-5)\): \[ (-2)(-5) = 10 \]
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Calculate \((-3)^2\): \[ (-3)^2 = 9 \]
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Combine the results: \[ 10 + 10 + 9 = 29 \]
Now, looking at Fernando's evaluation:
- He calculated: \[ \frac{5(4)}{2} - 10 + 9 \] But he mistakenly evaluated it as: \[ 10 - 10 + 9 = 9 \]
Now, let's look at each possible explanation for the error:
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"Fernando evaluated the numerator of the fraction incorrectly." - He correctly calculated \(5(9 - 5) = 5(4) = 20\).
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"Fernando simplified \(\frac{20}{2}\) incorrectly." - He simplified it correctly as \(\frac{20}{2} = 10\).
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"Fernando incorrectly found the product of \(-2\) and \(-5\)." - He calculated that correctly as \(10\).
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"Fernando evaluated \((-3)^2\) incorrectly." - He evaluated that correctly as \(9\).
Fernando's mistake was in the final step where he combined the results. The calculations leading to the combination were actually correct, but in combining them, he went from:
\[ 10 + 10 + 9 = 29 \] to \[ 10 - 10 + 9 = 9 \] which is not the right combination.
Since all components were evaluated correctly before combining, his error was clearly in incorrectly combining the results at the end.
Based on the provided options, the most relevant explanation would be:
Fernando simplified \(\frac{20}{2}\) incorrectly.
This option can imply he made an error with the final arithmetic which led to his final answer being incorrect. The other options have been confirmed as incorrect evaluations of the separate terms.