TURTLE A turtle is \( 20 \frac{5}{6} \) inches below the surface of a pond. It dives to a depth of \( 32 \frac{1}{4} \) inches. What is the change in the turtle's position?

To find the change in the turtle's position, we need to subtract the initial depth from the final depth. Given: Initial depth = \(20 \frac{5}{6}\) inches Final depth = \(32 \frac{1}{4}\) inches Let's convert the mixed numbers to improper fractions for easier calculation: Initial depth = \(20 \frac{5}{6} = \frac{125}{6}\) inches Final depth = \(32 \frac{1}{4} = \frac{129}{4}\) inches Now, we can calculate the change in the turtle's position by subtracting the initial depth from the final depth: Change in position = Final depth - Initial depth Change in position = \(\frac{129}{4} - \frac{125}{6}\) Let's calculate this: Calculate the value by following steps: - step0: Calculate: \(\frac{129}{4}-\frac{125}{6}\) - step1: Reduce fractions to a common denominator: \(\frac{129\times 3}{4\times 3}-\frac{125\times 2}{6\times 2}\) - step2: Multiply the numbers: \(\frac{129\times 3}{12}-\frac{125\times 2}{6\times 2}\) - step3: Multiply the numbers: \(\frac{129\times 3}{12}-\frac{125\times 2}{12}\) - step4: Transform the expression: \(\frac{129\times 3-125\times 2}{12}\) - step5: Multiply the numbers: \(\frac{387-125\times 2}{12}\) - step6: Multiply the numbers: \(\frac{387-250}{12}\) - step7: Subtract the numbers: \(\frac{137}{12}\) The change in the turtle's position is \(11 \frac{5}{12}\) inches or approximately 11.4166 inches.