Question

Derek has walked his dog 3\4 miles during the neighborhood doggie walk the whole course is 3 1\2 miles long so how much of the course has Derek finished??

Answer 1

To find out how much of the course Derek has finished, we can set up the fraction of the distance he has walked over the total distance of the course.

Derek has walked \( \frac{3}{4} \) miles, and the total course is \( 3 \frac{1}{2} \) miles. First, we need to convert \( 3 \frac{1}{2} \) into an improper fraction.

1. Convert \( 3 \frac{1}{2} \) to an improper fraction:
\[
3 \frac{1}{2} = 3 + \frac{1}{2} = \frac{6}{2} + \frac{1}{2} = \frac{7}{2}
\]

2. Now, we find the fraction of the course that Derek has completed:
\[
\text{Fraction completed} = \frac{\text{Distance walked}}{\text{Total distance}} = \frac{\frac{3}{4}}{\frac{7}{2}}
\]

3. To divide fractions, we multiply by the reciprocal:
\[
\frac{3}{4} \div \frac{7}{2} = \frac{3}{4} \times \frac{2}{7} = \frac{3 \times 2}{4 \times 7} = \frac{6}{28}
\]

4. We can simplify \( \frac{6}{28} \):
\[
\frac{6 \div 6}{28 \div 6} = \frac{3}{14}
\]

Thus, Derek has finished \( \frac{3}{14} \) of the course.