Question

Eric rides his bike 4 1/3 hours during the week. His little brother rides his bike 1 3/4 hours during the week.

How many more hours does Eric ride his bike during the week than his little brother?

Enter your answer as a mixed number in simplest form by filling in the boxes.

Answer 1

To find how many more hours Eric rides his bike than his little brother, we will subtract the time his little brother rides from the time Eric rides.

1. **Convert the mixed numbers to improper fractions:**

- Eric rides for \( 4 \frac{1}{3} \) hours. To convert this to an improper fraction:
\[
4 \frac{1}{3} = \frac{4 \cdot 3 + 1}{3} = \frac{12 + 1}{3} = \frac{13}{3}
\]

- His little brother rides for \( 1 \frac{3}{4} \) hours. To convert this to an improper fraction:
\[
1 \frac{3}{4} = \frac{1 \cdot 4 + 3}{4} = \frac{4 + 3}{4} = \frac{7}{4}
\]

2. **Find a common denominator to subtract the fractions.**
The denominators are \( 3 \) and \( 4 \). The least common multiple of \( 3 \) and \( 4 \) is \( 12 \).

- Convert \( \frac{13}{3} \) to a denominator of \( 12 \):
\[
\frac{13}{3} = \frac{13 \cdot 4}{3 \cdot 4} = \frac{52}{12}
\]

- Convert \( \frac{7}{4} \) to a denominator of \( 12 \):
\[
\frac{7}{4} = \frac{7 \cdot 3}{4 \cdot 3} = \frac{21}{12}
\]

3. **Subtract the two fractions:**
\[
\frac{52}{12} - \frac{21}{12} = \frac{52 - 21}{12} = \frac{31}{12}
\]

4. **Convert the improper fraction back to a mixed number:**
- Divide \( 31 \) by \( 12 \):
\[
31 \div 12 = 2 \quad \text{(with a remainder of } 7\text{)}
\]
- This result can be expressed as:
\[
2 \frac{7}{12}
\]

Thus, Eric rides his bike \( 2 \frac{7}{12} \) hours more than his little brother.

The final answer is:
\[
\boxed{2} \quad \text{in the first box, and} \quad \boxed{7} \quad \text{in the second box.}
\]