Question

During Primrose School’s annual Walk for Education, Reba walked 5 5/6 laps around the track. Holt walked 1 3/5 more laps than Reba did. How many laps did Holt walk?

Answer 1

To find out how many laps Holt walked, we need to first convert the mixed numbers into improper fractions so we can easily perform the arithmetic.

1. Convert Reba's laps (5 5/6) into an improper fraction:
- \( 5 \) can be written as \( \frac{5 \times 6}{6} = \frac{30}{6} \).
- Adding the fractional part:
\[
\frac{30}{6} + \frac{5}{6} = \frac{35}{6}
\]
So, Reba walked \( \frac{35}{6} \) laps.

2. Convert Holt's additional laps (1 3/5) into an improper fraction:
- \( 1 \) can be written as \( \frac{1 \times 5}{5} = \frac{5}{5} \).
- Adding the fractional part:
\[
\frac{5}{5} + \frac{3}{5} = \frac{8}{5}
\]
So, Holt walked \( \frac{8}{5} \) more laps than Reba.

3. Now, we calculate the number of laps Holt walked:
\[
\text{Holt's laps} = \text{Reba's laps} + \text{additional laps} = \frac{35}{6} + \frac{8}{5}
\]

4. To add the fractions \( \frac{35}{6} \) and \( \frac{8}{5} \), we need a common denominator. The least common multiple of \( 6 \) and \( 5 \) is \( 30 \).

5. Convert each fraction to have the common denominator of \( 30 \):
- For \( \frac{35}{6} \):
\[
\frac{35}{6} = \frac{35 \times 5}{6 \times 5} = \frac{175}{30}
\]
- For \( \frac{8}{5} \):
\[
\frac{8}{5} = \frac{8 \times 6}{5 \times 6} = \frac{48}{30}
\]

6. Now we can add the two fractions:
\[
\frac{175}{30} + \frac{48}{30} = \frac{175 + 48}{30} = \frac{223}{30}
\]

The improper fraction \( \frac{223}{30} \) can be converted back to a mixed number:
- \( 223 \div 30 = 7 \) remainder \( 13 \).
Thus, \( \frac{223}{30} = 7 \frac{13}{30} \).

In conclusion, Holt walked \(\frac{223}{30}\) laps, or \( 7 \frac{13}{30} \) laps, which is approximately \( 7.43 \) laps.