Question

Jasmine asked her classmates to name all the types of trees they found while on a field trip at a local park.

1/7
reported finding a birch tree.

7/9
reported finding a pine tree.

1/4
reported finding a maple tree.

11/23
reported finding an oak tree.

Based on the results, determine which statements are true and which statements are false.
Over half the students found a pine tree.


More students found a maple tree than a pine tree.


More students found a birch tree than an oak tree.


More students found a pine tree than a birch tree.


More students found a maple tree than an oak tree.

Answer 1

To determine the truth of the statements, we first need to establish a common denominator for the fractions given for each type of tree. This will allow us to compare the reported findings directly.

The fractions given are:

- Birch tree: \( \frac{1}{7} \)
- Pine tree: \( \frac{7}{9} \)
- Maple tree: \( \frac{1}{4} \)
- Oak tree: \( \frac{11}{23} \)

The least common multiple (LCM) of the denominators (7, 9, 4, and 23) can be found to be 126:

- For Birch: \( \frac{1}{7} = \frac{18}{126} \)
- For Pine: \( \frac{7}{9} = \frac{98}{126} \)
- For Maple: \( \frac{1}{4} = \frac{31.5}{126} \) (which is not possible, so it makes more sense to convert it directly)
- For Oak: \( \frac{11}{23} = \frac{60}{126} \)

Now we can convert each fraction into a comparable number of students based on a hypothetical total (let's assume there are 126 students total). This yields:

- Birch tree: 18 students
- Pine tree: 98 students
- Maple tree: 31.5 shouldn't be used since we can't have half students. Let's round that given the context to 31 (there could be a slight misunderstanding in numbers).
- Oak tree: 60 students

Now, let's assess each statement:

1. **Over half the students found a pine tree.**
- True, because 98 out of 126 is more than half.

2. **More students found a maple tree than a pine tree.**
- False, because 31 is less than 98.

3. **More students found a birch tree than an oak tree.**
- False, because 18 is less than 60.

4. **More students found a pine tree than a birch tree.**
- True, because 98 is greater than 18.

5. **More students found a maple tree than an oak tree.**
- False, because 31 is less than 60.

In summary:

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