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Grade 5 Math Fraction of Whole Error Analysis Question
Mathematics
Grade 5 (Primary School)
Question Content
Error - prone example: Divide 3 kilograms of apples equally among 5 people. The fraction of the total that each person gets is (______). Wrong answer: 3/5. Error analysis: The mistake in this question is ______. Correct answer: 1/5.
Correct Answer
1/5; Error analysis: Confusing specific quantity with fraction of the whole
Detailed Solution Steps
1
Understand the question: '占总数的' asks for the fraction of the whole (total apples), not the weight each person gets.
2
The total is considered as 1 whole (3 kilograms is the total amount, but the fraction is about the parts of the whole). Divide 1 whole into 5 parts, and each part is 1/5.
3
The wrong answer 3/5 is the weight per person (3 kg ÷ 5 = 3/5 kg), but the question asks for the fraction of the total, so it should be 1/5.
4
Conclusion: the mistake is confusing the specific quantity (weight) with the fraction of the whole (1/5), and the correct answer is 1/5.
Knowledge Points Involved
1
Fraction of Whole vs. Specific Quantity
When asked for the fraction of a total (e.g., the share of apples), it is based on dividing the whole (1) into parts, not the specific quantity (e.g., weight). For example, when 3 kilograms of apples are divided into 5 people, each person gets 3/5 kilograms (specific quantity) but 1/5 of the total (fraction of the whole).
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