Final answer:
The correct addition problem from the given options that results in a sum of -4 3/5 with both addends having the same sign is option c) -3 1/5 + (-1 2/3).
Step-by-step explanation:
The student is asked to find an addition problem that results in a sum of -4 3/5 and where both addends have the same sign. We need to remember that when two negative numbers are added together, the sum carries a negative sign, which aligns with the target sum in this case. After testing given options, we can use the rules of addition for negative numbers to identify the correct problem.
- Option a) -2 1/4 + (-2 2/5) does not yield the correct sum.
- Option b) -1 2/3 + (-2 5/15) does not yield the correct sum after converting and simplifying.
- Option c) -3 1/5 + (-1 2/3) does yield the correct sum of -4 3/5 after finding a common denominator and combining the fractions.
- Option d) is not suitable because the addends have different signs.
Through this evaluation, we can conclude that option c) -3 1/5 + (-1 2/3) is the correct addition problem that satisfies the given conditions.