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.


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Answer 1

To determine which statements are true and which are false, we'll convert the fractions reported for each bird into a common denominator so we can compare them directly.

The findings:
- Blue jay: \( \frac{1}{8} \)
- Finch: \( \frac{6}{7} \)
- Blackbird: \( \frac{1}{3} \)
- Owl: \( \frac{11}{24} \)

The least common multiple (LCM) of the denominators (8, 7, 3, and 24) is 168. Now, we'll convert each fraction to have a denominator of 168.

1. **Blue jay:**
\[
\frac{1}{8} = \frac{1 \times 21}{8 \times 21} = \frac{21}{168}
\]

2. **Finch:**
\[
\frac{6}{7} = \frac{6 \times 24}{7 \times 24} = \frac{144}{168}
\]

3. **Blackbird:**
\[
\frac{1}{3} = \frac{1 \times 56}{3 \times 56} = \frac{56}{168}
\]

4. **Owl:**
\[
\frac{11}{24} = \frac{11 \times 7}{24 \times 7} = \frac{77}{168}
\]

Now we have the following counts for each type of bird, expressed as follows:
- Blue jay: \( 21 \)
- Finch: \( 144 \)
- Blackbird: \( 56 \)
- Owl: \( 77 \)

Now we can evaluate the statements:

1. **Over half the students found a finch.**
- True: \( 144 > \frac{1}{2} \times 168 = 84 \)

2. **More students found a blackbird than a finch.**
- False: \( 56 < 144 \)

3. **More students found a blue jay than an owl.**
- False: \( 21 < 77 \)

4. **More students found a finch than a blackbird.**
- True: \( 144 > 56 \)

5. **More students found a blackbird than an owl.**
- False: \( 56 < 77 \)

In summary, the truth values of the statements are:
- **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**