To compute \((-133 \mod 23) + (26 \mod 23)\), we follow these steps:

### Step 1: Compute \(-133 \mod 23\)
The modulus operation gives the remainder when dividing a number by another. To find \(-133 \mod 23\), we first compute:
\[
-133 \div 23 = -5.7826 \quad (\text{truncate to } -6)
\]
Now, multiply \(-6\) by 23:
\[
-6 \times 23 = -138
\]
Subtract \(-133 - (-138)\):
\[
-133 - (-138) = 5
\]
Thus, \(-133 \mod 23 = 5\).

### Step 2: Compute \(26 \mod 23\)
Now compute:
\[
26 \div 23 = 1.1304 \quad (\text{truncate to } 1)
\]
Multiply \(1\) by 23:
\[
1 \times 23 = 23
\]
Subtract \(26 - 23 = 3\).
Thus, \(26 \mod 23 = 3\).

### Step 3: Add the two results
Now, add the two results from steps 1 and 2:
\[
5 + 3 = 8
\]

So, the final result is:
\[
\boxed{8}
\]

Would you like more details on any step? 

Here are some related questions:
1. What is the general formula for computing \( a \mod b \)?
2. How do negative numbers behave under modulo operations?
3. Can the modulus operation be used to solve linear congruences?
4. What is the difference between modulo and remainder?
5. How is the modulus operation applied in cryptography?

**Tip:** When working with negative numbers and the modulus operation, it can be helpful to convert them into positive equivalents for simpler calculations.

Learn how to compute (−133 mod 23) + (26 mod 23) with a step-by-step explanation. This problem focuses on modulus operations, dealing with negative numbers, and division with remainders. Suitable for students in Grades 9-11.

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