a diver dives $17\frac{2}{3}$ yards and then comes back to the surface. then, she dives $9\frac{3}{8}$ yards…

Answer:

A. $- 27\frac{7}{24}$

Explanation:

Step1: Convert mixed - numbers to improper fractions

The first dive is $17\frac{2}{3}=\frac{17\times3 + 2}{3}=\frac{51+2}{3}=\frac{53}{3}$ yards. The second dive is $9\frac{3}{8}=\frac{9\times8 + 3}{8}=\frac{72 + 3}{8}=\frac{75}{8}$ yards deeper than the first dive.

Step2: Find the depth of the second dive

The depth of the second dive is the sum of the depth of the first dive and the additional depth. So we need to calculate $\frac{53}{3}+\frac{75}{8}$. First, find a common denominator. The least common multiple of 3 and 8 is 24. $\frac{53}{3}\times\frac{8}{8}=\frac{53\times8}{24}=\frac{424}{24}$ and $\frac{75}{8}\times\frac{3}{3}=\frac{75\times3}{24}=\frac{225}{24}$. Then $\frac{424}{24}+\frac{225}{24}=\frac{424 + 225}{24}=\frac{649}{24}$. Converting $\frac{649}{24}$ back to a mixed - number: $649\div24 = 27$ with a remainder of 1. So $\frac{649}{24}=27\frac{1}{24}$. But since it is a depth below the surface, the value is negative, so the depth is $-27\frac{7}{24}$ yards.