Question

which fraction represents paiges speed in miles per minute?\\(\frac{\frac{2}{3}}{16}\\)\
which division expression can be used to represent the ratio \\(\frac{\frac{2}{3}}{16}\\)?\
\\(16 \div \frac{2}{3}\\) \\(\frac{2}{3} \div \frac{1}{16}\\) \\(\frac{2}{3} \div 16\\) \\(\frac{1}{16} \div \frac{2}{3}\\)

Explanation:

First Sub - Question (Paige's speed)

To find speed in miles per minute, we use the formula \( \text{speed}=\frac{\text{distance}}{\text{time}} \). If the distance is \( \frac{2}{3} \) miles and the time is 16 minutes, then the speed is \( \frac{\frac{2}{3}}{16} \) (which is equivalent to \( \frac{2}{3}\div16 \), but for the first sub - question, the fraction representing speed is \( \frac{\frac{2}{3}}{16}=\frac{2}{3\times16}=\frac{2}{48}=\frac{1}{24} \), but the given fraction is \( \frac{\frac{2}{3}}{16} \) (or \( \frac{2}{3}\div16 \) in division form, but the first sub - question asks for the fraction. So the fraction is \( \frac{\frac{2}{3}}{16} \) (which can be written as \( \frac{2}{3\times16} \) or simplified, but based on the problem's context, the fraction is \( \frac{2}{3}\div16=\frac{2}{3\times16}=\frac{2}{48}=\frac{1}{24} \), but the given option - like fraction is \( \frac{\frac{2}{3}}{16} \))

Recall that \( \frac{a}{b}=a\div b \). So if \( a = \frac{2}{3} \) and \( b = 16 \), then \( \frac{\frac{2}{3}}{16}=\frac{2}{3}\div16 \).

Answer:

\( \frac{\frac{2}{3}}{16} \) (or \( \frac{2}{3\times16}=\frac{1}{24} \))

Second Sub - Question (Division expression for \( \frac{\frac{2}{3}}{16} \))