A turtle

A turtle is 20 5/6 inches below the surface of a pond. It dives to a depth of 32 1/4 inches. What is the change in the turtle's position? Write your answer as a mixed number.

Correct answer:

x =  11 ⁵⁄₁₂ = 137/12 in

Step-by-step explanation:

$$\begin{gathered} a=20\frac{5}{6}=20+\frac{5}{6}=\frac{20\cdot 6+5}{6}=\frac{120+5}{6}=\frac{125}{6}\doteq 20.8333\text{in} \\ b=32\frac{1}{4}=32+\frac{1}{4}=\frac{32\cdot 4+1}{4}=\frac{128+1}{4}=\frac{129}{4}=32.25\text{in} \\ x=b-a=\frac{129}{4}-\frac{125}{6}=\frac{387}{12}-\frac{250}{12}=\frac{387-250}{12}=\frac{137}{12}=\frac{137}{12}\text{in}=11\frac{5}{12}\text{in}=11.4167\text{in} \end{gathered}$$

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