To evaluate the truth of the statements given, we first need to establish the fractions of students who reported finding each bird and then relate these fractions to a common denominator for clear comparison.
The fractions of students who reported finding each bird are:
- Blue Jay: \( \frac{1}{8} \)
- Finch: \( \frac{6}{7} \)
- Blackbird: \( \frac{1}{3} \)
- Owl: \( \frac{11}{24} \)
To compare these fractions easily, we’ll convert them to a common denominator. The least common multiple (LCM) of 8, 7, 3, and 24 is 168. We can convert each fraction as follows:
- Blue Jay: \[ \frac{1}{8} = \frac{21}{168} \]
- Finch: \[ \frac{6}{7} = \frac{144}{168} \]
- Blackbird: \[ \frac{1}{3} = \frac{56}{168} \]
- Owl: \[ \frac{11}{24} = \frac{77}{168} \]
Now we have:
- Blue Jay: \( 21 \)
- Finch: \( 144 \)
- Blackbird: \( 56 \)
- Owl: \( 77 \)
Now let's evaluate each statement one by one:
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Less than half of the students found a finch.
- Half of 168 is 84. Since 144 students found a finch, this statement is False.
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More students found a finch than a blackbird.
- Students who found a finch: 144, students who found a blackbird: 56. Thus, this statement is True.
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More students found an owl than a blue jay.
- Students who found an owl: 77, students who found a blue jay: 21. Thus, this statement is True.
-
More students found a blackbird than a finch.
- Students who found a blackbird: 56, students who found a finch: 144. Thus, this statement is False.
-
More students found an owl than a blackbird.
- Students who found an owl: 77, students who found a blackbird: 56. Thus, this statement is True.
Summary of Results:
- Less than half of the students found a finch. False
- More students found a finch than a blackbird. True
- More students found an owl than a blue jay. True
- More students found a blackbird than a finch. False
- More students found an owl than a blackbird. True
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