Question

A fish is swimming in a lake at −8 3/4 feet. The fish dives down another 1 5/8 feet. What is the current depth of the fish now

Answer 1

To calculate the fish's new depth, convert the initial and additional depths to improper fractions, sum them up, and convert back to a mixed number. The fish's current depth is − 10 3/8 feet.

Step-by-step explanation:

To find the current depth of the fish in the lake after it dives down an additional distance, we simply need to add the depth at which it is initially swimming to the distance it dives down further. Initially, the fish is swimming at − 8 3/4 feet, and then it dives down another 1 5/8 feet.

Step-by-step calculation:

1. Convert the mixed numbers to improper fractions: − 8 3/4 = − (8 × 4 + 3)/4 = − 35/4 and 1 5/8 = (1 × 8 + 5)/8 = 13/8.
2. Add the two depths: − 35/4 (original depth) + − 13/8 (additional depth dived).
3. Find a common denominator for the fractions, which is 8: − 35/4 = − 70/8.
4. Add the fractions: − 70/8 + − 13/8 = − 83/8.
5. Convert the improper fraction back to a mixed number: − 83/8 = − 10 3/8 feet.

Therefore, after diving down an additional 1 5/8 feet, the fish is at a current depth of − 10 3/8 feet.1