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Jasmine asked her classmates to name all the types of birds they found on a field trip to a local aviary.

1/8 reported finding a blue jay.
6/7 reported finding a finch.
1/3 reported finding a blackbird.
11/24 reported finding an owl.
Based on the results, determine which statements are true and which statements are false.

True - False

Over half the students found a finch. -
More students found a blackbird than a finch. -
More students found a blue jay than an owl. -
More students found a finch than a blackbird. -
More students found a blackbird than an owl. -

1 answer

To determine the truth of the statements, we will first convert the fractions of students who reported finding each type of bird into a common denominator. The least common multiple of the denominators (8, 7, 3, and 24) is 168.

Now, let's convert each fraction:

  1. Blue Jay: \( \frac{1}{8} = \frac{21}{168} \)
  2. Finch: \( \frac{6}{7} = \frac{144}{168} \)
  3. Blackbird: \( \frac{1}{3} = \frac{56}{168} \)
  4. Owl: \( \frac{11}{24} = \frac{77}{168} \)

Now we can evaluate each statement:

  1. Over half the students found a finch.

    • \( \frac{144}{168} \) is indeed greater than \( \frac{84}{168} \), which represents half.
    • True

  2. More students found a blackbird than a finch.

    • \( \frac{56}{168} \) (blackbird) is not greater than \( \frac{144}{168} \) (finch).
    • False

  3. More students found a blue jay than an owl.

    • \( \frac{21}{168} \) (blue jay) is not greater than \( \frac{77}{168} \) (owl).
    • False

  4. More students found a finch than a blackbird.

    • \( \frac{144}{168} \) (finch) is indeed greater than \( \frac{56}{168} \) (blackbird).
    • True

  5. More students found a blackbird than an owl.

    • \( \frac{56}{168} \) (blackbird) is not greater than \( \frac{77}{168} \) (owl).
    • False

So, summarizing the results:

  1. Over half the students found a finch. - True
  2. More students found a blackbird than a finch. - False
  3. More students found a blue jay than an owl. - False
  4. More students found a finch than a blackbird. - True
  5. More students found a blackbird than an owl. - False