Answer:
[tex](-\frac{7}{6} )[/tex]
Step-by-step explanation:
From the question the emerald was located at a depth which is between -1/2 and -1 2/3 meters
This statement can be written as
[tex](-1\frac{2}{3}) -(-\frac{1}{2} )[/tex]
To get the depth, you find the depth of the emerald location, you find difference between the two mentioned depths
[tex]-(1\frac{2}{3} )-(-\frac{1}{2} )\\\\[/tex]
Change first term to improper fraction
[tex]=-(\frac{5}{3} )-(-\frac{1}{2} )\\\\[/tex]
Find the LCM to solve the operation the involves the fractions.The Least common multiple here is 6 i.e 3*2
[tex]=(-\frac{5}{3} )-(-\frac{1}{2})\\[/tex]
[tex]=\frac{-5}{3} +\frac{1}{2} =\frac{-10+3}{6} =\frac{-7}{6}[/tex]
The number that could represent the depth at which the emerald was located is
[tex]=\frac{-7}{6}[/tex]
