B. \( 2 \frac{5}{8} t=14 \frac{1}{2} ; t=\square \)

To solve the equation \(2 \frac{5}{8} t = 14 \frac{1}{2}\) for \(t\), we first need to convert the mixed numbers to improper fractions. Given: \[2 \frac{5}{8} t = 14 \frac{1}{2}\] Convert the mixed numbers to improper fractions: \[2 \frac{5}{8} = \frac{2 \times 8 + 5}{8} = \frac{21}{8}\] \[14 \frac{1}{2} = \frac{14 \times 2 + 1}{2} = \frac{29}{2}\] Now, the equation becomes: \[\frac{21}{8} t = \frac{29}{2}\] To solve for \(t\), we can multiply both sides of the equation by the reciprocal of \(\frac{21}{8}\) to isolate \(t\). \[\frac{8}{21} \times \frac{21}{8} t = \frac{8}{21} \times \frac{29}{2}\] Simplifying: \[t = \frac{8}{21} \times \frac{29}{2}\] Now, we can calculate the value of \(t\). Calculate the value by following steps: - step0: Calculate: \(\frac{\frac{8}{21}\times 29}{2}\) - step1: Multiply the numbers: \(\frac{\frac{232}{21}}{2}\) - step2: Multiply by the reciprocal: \(\frac{232}{21}\times \frac{1}{2}\) - step3: Reduce the numbers: \(\frac{116}{21}\times 1\) - step4: Multiply: \(\frac{116}{21}\) The value of \(t\) is \(5 \frac{11}{21}\) or approximately \(5.5\).