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.

1 answer

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