Question

progress:
question id: 706441
the movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer.
dilma is on a $10\frac{1}{2}$ mile hike. she has hiked $\frac{2}{3}$ of the total distance already. how many miles has she already hiked?
\bigcirc 7
\bigcirc 8
\bigcirc 6\frac{2}{3}
\bigcirc 3\frac{1}{2}

Explanation:

Step1: Convert mixed number to improper fraction

The total distance is \(10\frac{1}{2}\) miles. To convert this mixed number to an improper fraction, we use the formula \(a\frac{b}{c}=\frac{a\times c + b}{c}\). So, \(10\frac{1}{2}=\frac{10\times2 + 1}{2}=\frac{21}{2}\) miles.

Step2: Multiply by the fraction of distance hiked

She has hiked \(\frac{2}{3}\) of the total distance. So we multiply the total distance by \(\frac{2}{3}\): \(\frac{21}{2}\times\frac{2}{3}\). The 2 in the numerator and denominator cancels out, and we have \(\frac{21}{3}=7\) miles.

Answer:

7