Complete the table. (a) (b) (c) (d) \begin{tabular}{|c|c|c|c|} \hline A & B & C & D \\ \hline $5 \frac{1}{2} \mathrm{in.}$ & $2 \frac{3}{4} \mathrm{in.}$ & $1 \frac{5}{6} \mathrm{in.}$ & \\ \hline & $23.6 \mathrm{~cm}$ & $23.4 \mathrm{~cm}$ & $15.6 \mathrm{~cm}$ \\ \hline $15 \mathrm{ft}$ & & $6 \mathrm{ft}$ & $4 \mathrm{ft}$ \\ \hline $4 \mathrm{~m}$ & $3.2 \mathrm{~m}$ & & $2.4 \mathrm{~m}$ \\ \hline \end{tabular} (a) $D=\frac{11}{12}$ in. (Type a whole number or a simplified fraction.) (b) $A=\square \mathrm{cm}$ (Type a whole number or a decimal.)
Solution
Step 1 ：Set up a proportion using the given values in the first row and solve for D. The proportion is \(\frac{A}{B} = \frac{C}{D}\). Substitute the given values to get \(\frac{5.5}{2.75} = \frac{1.8333333333333335}{D}\). Solving for D gives \(D = 0.9166666666666667\) inches.
Step 2 ：Convert the decimal to a fraction to get \(D = \frac{11}{12}\) inches.
Step 3 ：Set up a proportion using the given values in the second row and solve for A. The proportion is \(\frac{A}{B} = \frac{C}{D}\). Substitute the given values to get \(\frac{A}{23.6} = \frac{23.4}{15.6}\). Solving for A gives \(A = 15.733333333333336\) cm.
Step 4 ：The final answers are: For part (a), the value of D in inches is \(\boxed{\frac{11}{12}}\). For part (b), the value of A in cm is \(\boxed{15.73}\).
