Question

a scuba diver descended $12\frac{5}{12}$ feet below sea level. then, he descended another $3\frac{4}{5}$ feet. which of the following is true about the scuba diver after both descents?\
a. the location of the scuba diver in relation to sea level was $16\frac{13}{60}$ feet.\
b. the location of the scuba diver in relation to sea level was $8\frac{37}{60}$ feet.\
c. the location of the scuba diver in relation to sea level was $-8\frac{37}{60}$ feet.\
d. the location of the scuba diver in relation to sea level was $-16\frac{13}{60}$ feet.

Explanation:

Step1: Convert mixed numbers to improper fractions

First, convert \( 12\frac{5}{12} \) to an improper fraction. \( 12\frac{5}{12}=\frac{12\times12 + 5}{12}=\frac{144+5}{12}=\frac{149}{12} \). Then, convert \( 3\frac{4}{5} \) to an improper fraction: \( 3\frac{4}{5}=\frac{3\times5 + 4}{5}=\frac{15 + 4}{5}=\frac{19}{5} \).

Step2: Find a common denominator

The common denominator of 12 and 5 is 60. Rewrite the fractions with the common denominator: \( \frac{149}{12}=\frac{149\times5}{12\times5}=\frac{745}{60} \) and \( \frac{19}{5}=\frac{19\times12}{5\times12}=\frac{228}{60} \).

Step3: Add the two fractions

Since the diver is descending (below sea level, represented by negative numbers), we add the two distances: \( -\frac{745}{60}-\frac{228}{60}=-\frac{745 + 228}{60}=-\frac{973}{60} \). Now, convert \( -\frac{973}{60} \) back to a mixed number. Divide 973 by 60: \( 60\times16 = 960 \), so \( 973-960 = 13 \). Thus, \( -\frac{973}{60}=-16\frac{13}{60} \).

Answer:

D. The location of the scuba diver in relation to sea level was \( -16\frac{13}{60} \) feet.