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

Question

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.

(5 points)
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.

Answer 1

To analyze the statements, let's first convert the reported fractions into a common denominator so we can easily compare the number of students who found each type of bird. The common denominator for 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 summarize the number of students who found each bird in terms of the same denominator:

• Blue Jay: 21 students
• Finch: 144 students
• Blackbird: 56 students
• Owl: 77 students

Now, let's evaluate each statement:

1. Over half the students found a finch.

   • True, because \(144 > 84\) (half of 168).

2. More students found a blackbird than a finch.

   • False, because \(56 < 144\).

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

   • False, because \(21 < 77\).

4. More students found a finch than a blackbird.

   • True, because \(144 > 56\).

5. More students found a blackbird than an owl.

   • False, because \(56 < 77\).

Summary of Statements:

• Over half the students found a finch. True
• More students found a blackbird than a finch. False
• More students found a blue jay than an owl. False
• More students found a finch than a blackbird. True
• More students found a blackbird than an owl. False