A diver dives 17 and two-thirds yards and then comes back to the surface. Then, she dives 9 and StartFraction 3 over 8 EndFraction yards deeper than her first dive. What is her depth, in yards, in relation to the surface of the water?
Negative 27 and StartFraction 7 over 24 EndFraction
Negative 27 and StartFraction 1 over 24 EndFraction
Negative 8 and StartFraction 7 over 24 EndFraction
Negative 8 and StartFraction 1 over 24 EndFraction

Question

Mercury · Answer

The first dive is $$-17\frac{ 2 }{ 3 }$$(negative because it's underneath sea level)

she dove another $$9\frac{ 3 }{ 8 }$$
which means her depth is now

$$-17\frac{ 2 }{ 3 }-9\frac{ 3 }{ 8 }$$

now, ignore the negative signs for now, and just focus on converting the mixed numbers to improper fractions. multiply the denominator * the whole number part, then add the numerator, then put the result over the original denominator (easier to see through an example)

|dw:1625973863777:dw|

Mercury · Answer

repeating this logic with 9 and 3/8, we get 75/8

now we have

53/3 and 75/8

to convert these both to the same denominator, we find the LCM of 3 and 8 (which is 24)

so we multiply 53/3 by 8/8 to get 424/24
and 75/8 by 3/3 to get 225/24

then adding in the original signs we have

-424/24 - 225/24 = -649/24

24 goes into 649, 27 times with 1 leftover ----> -649/24 = -27 and 1/24