The expression in the image asks to compute the following using modular arithmetic:

$[(24 \mod 8) + (15 \mod 8)] \mod 8$

Step-by-step solution:

1. First, compute $24 \mod 8$: $24 \div 8 = 3 \quad \text{(remainder is 0)}$ So, $24 \mod 8 = 0$.

2. Next, compute $15 \mod 8$: $15 \div 8 = 1 \quad \text{(remainder is 7)}$ So, $15 \mod 8 = 7$.

3. Now, add the two results: $0 + 7 = 7$

4. Finally, compute $7 \mod 8$: Since $7 < 8$, the result is $7$.

Final Answer:

$[(24 \mod 8) + (15 \mod 8)] \mod 8 = 7$

Would you like further details or have any questions?

Here are five related questions to deepen your understanding:

1. What is the general formula for calculating the modulus of a number?
2. Can you explain how modular arithmetic is used in computer science?
3. How does modular arithmetic apply to cryptography, such as in RSA encryption?
4. How would the solution change if the modulo was a different number (e.g., 5 instead of 8)?
5. Can you calculate $(45 \mod 12) + (32 \mod 7)$ using modular arithmetic?

Tip: When using modular arithmetic, results are always within the range of $0$ to $n-1$, where $n$ is the modulus.