Question

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

Answer 1

Alrite, so their change is just their difference, namely 32 1/4 - 20 5/6.

let's change those to "improper" fractions first.

$\bf 20\frac{5}{6}\implies \cfrac{20\cdot 6+5}{6}\implies \cfrac{125}{6} \\\\\\ 32\frac{1}{4}\implies \cfrac{32\cdot 4+1}{4}\implies \cfrac{129}{4}\impliedby \textit{let's use an LCD of \underline{12}}\\\\ -------------------------------$

$\bf \cfrac{129}{4}-\cfrac{125}{6}\implies \cfrac{(3\cdot 129)+(2\cdot 125)}{12}\implies \cfrac{387-250}{12}\implies \cfrac{137}{12} \\\\\\ \textit{hmmm 12 goes into 137, 11 times, thus}\quad \boxed{11\frac{5}{12}} \\\\\\ \textit{because}\qquad \cfrac{11\cdot 12+5}{12}\implies \cfrac{132+5}{12}\implies \cfrac{137}{12}$