To determine which statements are true or false, we first need to express each fraction in terms of a common denominator so we can compare them easily. The least common multiple of the denominators (8, 7, 3, and 24) is 168.
Now, we'll convert each fraction to have a denominator of 168:
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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 can compare the results:
- Blue jay: 21
- Finch: 144
- Blackbird: 56
- Owl: 77
Now let's evaluate each statement:
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Over half the students found a finch.
- True, because 144 (found a finch) is more than half of 168 (which is 84).
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More students found a blackbird than a finch.
- False, because 56 (found a blackbird) is less than 144 (found a finch).
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More students found a blue jay than an owl.
- False, because 21 (found a blue jay) is less than 77 (found an owl).
-
More students found a finch than a blackbird.
- True, because 144 (found a finch) is greater than 56 (found a blackbird).
-
More students found a blackbird than an owl.
- False, because 56 (found a blackbird) is less than 77 (found an owl).
So the final assessment is:
- True
- False
- False
- True
- False