Question

rob owns \\( \frac{1}{7} \\) of the stock in a local bread company. his sister talia owns half as much stock as rob. what part of the stock is owned by neither rob nor talia?
there is \\( \square \\) of the stock that is owned by neither rob nor talia.
(type an integer or a simplified fraction.)

Explanation:

Step1: Find Talia's stock fraction

Rob owns $\frac{1}{7}$ of the stock. Talia owns half as much as Rob, so Talia's fraction is $\frac{1}{2} \times \frac{1}{7} = \frac{1}{14}$.

Step2: Find total fraction owned by Rob and Talia

Add Rob's and Talia's fractions: $\frac{1}{7} + \frac{1}{14}$. Convert to common denominator (14): $\frac{2}{14} + \frac{1}{14} = \frac{3}{14}$.

Step3: Find fraction owned by neither

The total stock is 1 (or $\frac{14}{14}$). Subtract the fraction owned by Rob and Talia: $1 - \frac{3}{14} = \frac{14}{14} - \frac{3}{14} = \frac{11}{14}$.

Answer:

$\frac{11}{14}$