Answer:
The diver is at a depth of [tex]-5\frac{1}{15}[/tex].
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What we have given:
Initial dive: [tex]1\frac{2}{3}[/tex] = [tex]x[/tex]
Additional dive: [tex]3\frac{2}{5}\\[/tex] = [tex]z[/tex]
Given the context, we can assume that sea level is 0ft.
So we have:
[tex]d=0-1\frac{2}{3}-3\frac{2}{5}[/tex] (d = depth)|
[tex]d=0-\frac{5}{3}-\frac{17}{5}[/tex] <- Convert mixed numbers to improper fractions.
[tex]d=-\frac{5}{3}-\frac{17}{5}[/tex] <- Simplify.
[tex]d=-\frac{25}{15}-\frac{51}{15}[/tex] <- The LCM between 3 and 5 is 15, so adjust the fractions accordingly.
(NOTE: Remember everything you do to the denominator must be replicated on the numerator as well!)
[tex]d=\frac{-25-51}{15}[/tex] <- Since the denominators are equal, combine the fractions.
[tex]d=\frac{-76}{15}[/tex]
[tex]d=-\frac{76}{15}[/tex] <- Apply the following fraction rule = [tex]\frac{-a}{b}=-\frac{a}{b}[/tex]
[tex]d=-5\frac{1}{15}[/tex] <- Convert the improper fraction to a mixed number and there is your final answer.
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