Reverse division — Given divisor = 13, quotient = 30, and remainder = 12, find the dividend using the standard division identity.

Introduction / Context:
Problems that ask for the dividend, given divisor, quotient, and remainder, rely on the basic division identity. Mastering this identity is essential for quick reconstruction of missing parts in division problems.

Given Data / Assumptions:

• Divisor = 13.
• Quotient = 30.
• Remainder = 12, with 0 ≤ remainder < divisor.

Concept / Approach:
Division identity: dividend = divisor * quotient + remainder. This follows directly from Euclidean division, where remainder is what is left after taking the largest multiple of the divisor not exceeding the dividend.

Step-by-Step Solution:
Compute product: 13 * 30 = 390.Add remainder: 390 + 12 = 402.Thus, dividend = 402.

Verification / Alternative check:
Check by direct division: 402 ÷ 13 = 30 remainder 12, since 13*30 = 390 and 402 - 390 = 12, confirming the result.

Why Other Options Are Wrong:

• 436 / 455 / 543 / 396: Do not satisfy dividend = 13*30 + 12; their remainders against 13 are not 12 with quotient 30.

Common Pitfalls:
Multiplying but forgetting to add the remainder; adding the remainder before multiplying; using an incorrect quotient or mixing up divisor and dividend.

Final Answer:
402