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

Answer 1

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:

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 compare the results:

- Blue jay: 21
- Finch: 144
- Blackbird: 56
- Owl: 77

Now let's evaluate each statement:

1. **Over half the students found a finch.**
- True, because 144 (found a finch) is more than half of 168 (which is 84).

2. **More students found a blackbird than a finch.**
- False, because 56 (found a blackbird) is less than 144 (found a finch).

3. **More students found a blue jay than an owl.**
- False, because 21 (found a blue jay) is less than 77 (found an owl).

4. **More students found a finch than a blackbird.**
- True, because 144 (found a finch) is greater than 56 (found a blackbird).

5. **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:

1. True
2. False
3. False
4. True
5. False