Question

blake lives \\(\frac{3}{4}\\) miles from school. he walks \\(\frac{2}{9}\\) of the distance to school before he stops to tie his shoe. how many more feet does blake walk to reach school?

Explanation:

Step1: Find remaining distance fraction

Blake walks $\frac{2}{9}$ of the distance, so remaining fraction is $1 - \frac{2}{9} = \frac{7}{9}$.

Step2: Calculate remaining distance in miles

Total distance is $\frac{3}{4}$ miles. Remaining distance: $\frac{3}{4} \times \frac{7}{9} = \frac{7}{12}$ miles.

Step3: Convert miles to feet (1 mile = 5280 feet)

Distance in feet: $\frac{7}{12} \times 5280 = 7 \times 440 = 3080$ feet. Wait, no—wait, the question is "how many more feet does Blake walk to reach school?" Wait, maybe I misread. Wait, he walks $\frac{2}{9}$ then stops, so the distance left is what he needs to walk more. Wait, original total distance: $\frac{3}{4}$ miles. Distance walked: $\frac{3}{4} \times \frac{2}{9} = \frac{1}{6}$ miles? No, no—wait, the question is "how many more feet does Blake walk to reach school?" So first, find the distance he still needs to walk. Total distance: $\frac{3}{4}$ miles. He walked $\frac{2}{9}$ of the distance, so remaining distance is $\frac{3}{4} \times (1 - \frac{2}{9}) = \frac{3}{4} \times \frac{7}{9} = \frac{7}{12}$ miles. Now convert $\frac{7}{12}$ miles to feet. Since 1 mile = 5280 feet, $\frac{7}{12} \times 5280 = 7 \times 440 = 3080$ feet. Wait, but maybe the question is "how many feet does he walk to reach school" (total? No, "how many more"—so after walking $\frac{2}{9}$, how much more to reach. Wait, maybe I made a mistake. Let's re-express:

Wait, total distance $d = \frac{3}{4}$ miles. Distance walked: $d_1 = \frac{3}{4} \times \frac{2}{9} = \frac{1}{6}$ miles. Distance remaining: $d - d_1 = \frac{3}{4} - \frac{1}{6} = \frac{9 - 2}{12} = \frac{7}{12}$ miles. Convert to feet: $\frac{7}{12} \times 5280 = 7 \times 440 = 3080$ feet. Wait, but let's check again. 5280 divided by 12 is 440, times 7 is 3080. So the answer is 3080? Wait, maybe the question was "how many feet does he walk to reach school" (total), but no, "how many more"—so after walking $\frac{2}{9}$, the remaining is what he needs to walk more. So yes, 3080 feet. Wait, but let's confirm the steps again.

Alternative approach:

1. Convert total distance to feet first: $\frac{3}{4}$ miles $\times 5280$ feet/mile = $\frac{3}{4} \times 5280 = 3960$ feet.

1. Find the fraction of distance remaining: $1 - \frac{2}{9} = \frac{7}{9}$.

1. Distance remaining in feet: $3960 \times \frac{7}{9} = 440 \times 7 = 3080$ feet.

Yes, that's correct. So the steps are:

Step1: Convert total miles to feet

Total distance: $\frac{3}{4}$ miles. $1$ mile = $5280$ feet. So $\frac{3}{4} \times 5280 = 3960$ feet.

Step2: Find remaining distance fraction

Blake walked $\frac{2}{9}$, so remaining fraction: $1 - \frac{2}{9} = \frac{7}{9}$.

Step3: Calculate remaining distance in feet

Remaining distance: $3960 \times \frac{7}{9} = 440 \times 7 = 3080$ feet.

Answer:

3080