Question

Adding and subtracting with rational numbers
a) Alex, an eighth grader, and Eric, a seventh grader, need to determine who came
closer to their grade’s state record for the triple jump. Alex jumped 39.75 feet and
Eric jumped 37 feet and 1
1
4
inches. Who was closer to the state record if the
eighth-grade record is 42.25 feet and the seventh-grade record is 39 feet 3
inches? (

Answer 1

To determine who was closer to their respective state records, we need to perform the following calculations:

1. Convert all measurements to the same unit. We'll convert everything to feet.

- **Alex's Jump:** 39.75 feet (already in feet)

- **Eric's Jump:**
\( 37 \text{ feet} \) and \( 1 \frac{1}{4} \text{ inches} \)

First, convert \( 1 \frac{1}{4} \text{ inches} \) to feet:
\[
1 \frac{1}{4} = \frac{5}{4} \text{ inches} = \frac{5}{4} \div 12 = \frac{5}{48} \text{ feet}
\]

Therefore, Eric's jump in feet is:
\[
37 + \frac{5}{48} = \frac{37 \times 48}{48} + \frac{5}{48} = \frac{1776 + 5}{48} = \frac{1781}{48} \approx 37.52 \text{ feet}
\]

2. Determine the state records in feet as well:

- **Eighth Grade Record:** 42.25 feet (already in feet)
- **Seventh Grade Record:**
\( 39 \text{ feet} \) and \( 3 \text{ inches} \)

Convert \( 3 \text{ inches} \) to feet:
\[
3 \text{ inches} = \frac{3}{12} = \frac{1}{4} \text{ feet}
\]

Therefore, the seventh-grade record in feet is:
\[
39 + \frac{1}{4} = 39.25 \text{ feet}
\]

3. Calculate the differences between the jumps and the records:

- **Alex's difference from the eighth-grade record:**
\[
42.25 - 39.75 = 2.50 \text{ feet}
\]

- **Eric's difference from the seventh-grade record:**
\[
39.25 - 37.52 \approx 1.73 \text{ feet}
\]

4. Compare the differences:
- Alex was 2.50 feet away from the eighth-grade record.
- Eric was approximately 1.73 feet away from the seventh-grade record.

**Conclusion:** Eric was closer to his state record than Alex was to his.