Question

mike used the computation \\(\frac{7}{(6+8+7)} \approx 0.33 = 33\\%\\) to find the percentage of eighth-grade band members who can play more than one instrument. what error did mike make?

• mike included 7 when finding a sum to use as the denominator of his fraction.
• mike used the total of the column containing 7 as his denominator instead of the total of the row containing 7.
• mike should have used the sum of all the cell values as his denominator.
• mike should have used the number of eighth-grade students who can only play one instrument as the denominator of his fraction.

Explanation:

Identify the target percentage and correct values

The target is the percentage of eighth-grade band members who can play more than one instrument.

• Number of eighth-grade band members who can play more than one instrument: \(7\)
• Total number of eighth-grade band members (the row containing \(7\)): \(18 + 7 = 25\)
• Correct calculation: \(\frac{7}{25} = 0.28 = 28\%\)

Analyze Mike's calculation and error

• Mike's calculation: \(\frac{7}{6 + 8 + 7} \approx 0.33 = 33\%\)
• The denominator used by Mike is \(6 + 8 + 7 = 21\), which is the sum of the column "Can Play More than One Instrument".
• Therefore, Mike used the total of the column containing \(7\) as his denominator instead of the total of the row containing \(7\).

Answer:

• Mike included 7 when finding a sum to use as the denominator of his fraction.
• Mike used the total of the column containing 7 as his denominator instead of the total of the row containing 7. (Correct answer)
• Mike should have used the sum of all the cell values as his denominator.
• Mike should have used the number of eighth-grade students who can only play one instrument as the denominator of his fraction.