1. Modeling Real Life A sailor is making a ship in a bottle. The last thing he needs to do is seal the bottle with a cork stopper. He tries a \( \frac{3}{4} \)-inch cor stopper, but it is too small. Should he try a \( \frac{1}{2} \)-inch cork stopper or a \( \frac{4}{5} \)-inch cork stopper next? Explain

Since the sailor already found that the \( \frac{3}{4} \)-inch cork stopper was too small, he should definitely avoid going smaller, like the \( \frac{1}{2} \)-inch cork. Instead, he should try the \( \frac{4}{5} \)-inch cork stopper. The \( \frac{4}{5} \)-inch is larger than \( \frac{3}{4} \)-inch, making it a better fit for sealing his bottle without any leaks! When working with fractions, there's an easy way to visualize the sizes. Think of \( \frac{3}{4} = 0.75 \), \( \frac{1}{2} = 0.5 \), and \( \frac{4}{5} = 0.8 \). Comparing these decimal values clearly shows that the \( \frac{4}{5} \)-inch cork is a larger choice that offers the potential for a snug fit to complete his ship in a bottle masterpiece!