To determine the truthfulness of each statement, let's first find a common denominator for the fractions representing the students who found each type of bird.
The fractions are:
- Blue Jay: \( \frac{1}{8} \)
- Finch: \( \frac{6}{7} \)
- Blackbird: \( \frac{1}{3} \)
- Owl: \( \frac{11}{24} \)
The least common multiple of the denominators (8, 7, 3, 24) is 168. We'll convert each fraction to have this common denominator:
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Blue Jay: \[ \frac{1}{8} = \frac{21}{168} \]
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Finch: \[ \frac{6}{7} = \frac{144}{168} \]
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Blackbird: \[ \frac{1}{3} = \frac{56}{168} \]
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Owl: \[ \frac{11}{24} = \frac{77}{168} \]
Now we have the following results in terms of the number of students:
- Blue Jay: 21 students
- Finch: 144 students
- Blackbird: 56 students
- Owl: 77 students
Now we can evaluate each statement:
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Over half the students found a finch.
Over half of 168 is 84. Since 144 students found a finch, this statement is True. -
More students found a blackbird than a finch.
56 students found a blackbird and 144 found a finch. This statement is False. -
More students found a blue jay than an owl.
21 students found a blue jay while 77 found an owl. This statement is False. -
More students found a finch than a blackbird.
144 found a finch and 56 found a blackbird. This statement is True. -
More students found a blackbird than an owl.
56 students found a blackbird while 77 found an owl. This statement is False.
To summarize:
- Statement 1: True
- Statement 2: False
- Statement 3: False
- Statement 4: True
- Statement 5: False
1 answer