Question
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.
(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.
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.
Answers
GPT-4o mini
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:
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 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:
1. **Over half the students found a finch.**
Over half of 168 is 84. Since 144 students found a finch, this statement is **True**.
2. **More students found a blackbird than a finch.**
56 students found a blackbird and 144 found a finch. This statement is **False**.
3. **More students found a blue jay than an owl.**
21 students found a blue jay while 77 found an owl. This statement is **False**.
4. **More students found a finch than a blackbird.**
144 found a finch and 56 found a blackbird. This statement is **True**.
5. **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
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:
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 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:
1. **Over half the students found a finch.**
Over half of 168 is 84. Since 144 students found a finch, this statement is **True**.
2. **More students found a blackbird than a finch.**
56 students found a blackbird and 144 found a finch. This statement is **False**.
3. **More students found a blue jay than an owl.**
21 students found a blue jay while 77 found an owl. This statement is **False**.
4. **More students found a finch than a blackbird.**
144 found a finch and 56 found a blackbird. This statement is **True**.
5. **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