Choose the fraction that goes in the blank.
$\frac{1}{2} < \_ < \frac{4}{5}$
To determine which fraction fits in the blank space of the inequality \(\frac{1}{2} < \_\_ < \frac{4}{5}\), we first represent all given fractions as decimal values. The lower bound of the inequality is \(\frac{1}{2} = 0.5\). The upper bound of the inequality is \(\frac{4}{5} = 0.8\). Therefore, we are looking for a fraction \(x\) such that \(0.5 < x < 0.8\).
Next, we evaluate the provided options:
Upon evaluation, neither \(\frac{1}{3}\) nor \(\frac{2}{4}\) strictly satisfies the inequality \(\frac{1}{2} < x < \frac{4}{5}\). In mathematical terms, \(\frac{1}{3} < 0.5\) and \(\frac{2}{4} = 0.5\). If one must choose the "best" fit or assume a potential typo in the original question where the lower bound might be \(\le\), \(\frac{2}{4}\) is the closest possible value. However, strictly speaking, neither option satisfies the provided inequality as stated. Assuming the task is to identify if either satisfies the condition, the conclusion is that neither does. If the inequality were non-strict, \(\frac{2}{4}\) would be a candidate. Assuming this is a standard arithmetic test question where an error in the provided options or the inequality symbol exists, it is important to state the mathematical truth based on the given values. Given the strict inequality requirement, there is no correct option among A and B.
Understanding how to compare and order fractions is essential for everyday tasks, such as adjusting ingredient quantities in a recipe. If a recipe calls for between \(\frac{1}{2}\) and \(\frac{4}{5}\) cups of flour, and you have measuring cups of \(\frac{1}{3}\) or \(\frac{2}{4}\), you would know that neither provides the required amount, helping you avoid mistakes before you start cooking!