Custom operator evaluation — apply the rule a * b = a + b + a/b Using the defined operation, compute the numerical value of 12 * 4.

Introduction / Context:
Algebraic operator questions define a nonstandard operation and require direct substitution. Here, a * b is not multiplication; it is defined as a + b + a/b. The goal is to accurately apply this rule to the pair (12, 4).

Given Data / Assumptions:

• Custom definition: a * b = a + b + a/b.
• We must evaluate 12 * 4.
• Standard arithmetic conventions apply inside the right-hand side.

Concept / Approach:
Replace a by 12 and b by 4 in the given definition, then compute using normal precedence: perform the division a/b before the final addition to avoid mistakes.

Step-by-Step Solution:
Start with a * b = a + b + a/b.Substitute: 12 * 4 = 12 + 4 + 12/4.Compute the division: 12/4 = 3.Sum: 12 + 4 + 3 = 19.

Verification / Alternative check:
Break into parts: (12 + 4) = 16, then add (12/4) = 3 to get 19. Both routes confirm the same value.

Why Other Options Are Wrong:
48 and 20 come from mistaking * for ordinary multiplication or partial sums; 21 results from adding an extra 2; 16 ignores the a/b term entirely.

Common Pitfalls:
Assuming * means multiply; forgetting the division a/b; or doing 12/(4 + 12) instead of 12/4 as defined.

Final Answer:
19