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

Question

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.



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(5 points)
True 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.

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Answer 1

To determine the truth value of the statements based on the reported tree findings, let's first convert all the fractions to have a common denominator to facilitate comparison.

The least common multiple of the denominators (7, 9, 4, and 23) is 1,954. We can convert each fraction to have this common denominator:

1. Birch tree:
   \(\frac{1}{7} = \frac{1 \times 279}{7 \times 279} = \frac{279}{1954}\)

2. Pine tree:
   \(\frac{7}{9} = \frac{7 \times 217}{9 \times 217} = \frac{1523}{1954}\)

3. Maple tree:
   \(\frac{1}{4} = \frac{1 \times 488.5}{4 \times 488.5} = \frac{488.5}{1954}\)
   This is not a whole number, hence we actually take it as \(\approx \frac{489}{1954}\), assuming we round to the nearest whole number for comparison.

4. Oak tree:
   \(\frac{11}{23} = \frac{11 \times 85.8}{23 \times 85.8} = \frac{944.4}{1954}\)
   Similarly for oak, we can take it as \(\approx \frac{944}{1954}\).

Now, we have:

• Birch tree: \(279\)
• Pine tree: \(1523\)
• Maple tree: \(489\)
• Oak tree: \(944\)

Now we can evaluate each statement:

1. Over half the students found a pine tree.

   • True: Since \( \frac{1523}{1954} > \frac{1}{2} \).

2. More students found a maple tree than a pine tree.

   • False: \( 489 < 1523 \).

3. More students found a birch tree than an oak tree.

   • False: \( 279 < 944 \).

4. More students found a pine tree than a birch tree.

   • True: \( 1523 > 279 \).

5. More students found a maple tree than an oak tree.

   • False: \( 489 < 944 \).

Summarizing the results:

• Over half the students found a pine tree: True
• More students found a maple tree than a pine tree: False
• More students found a birch tree than an oak tree: False
• More students found a pine tree than a birch tree: True
• More students found a maple tree than an oak tree: False

Here are the final evaluations:

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