Number System — Compute the exact product: 5358 × 51. Select the correct result.

Introduction / Context:
Multiplying by 51 can be simplified using the identity 51 = 50 + 1. This reduces the problem to one large product plus the original number. Such decomposition helps prevent mistakes and keeps the arithmetic organized.

Given Data / Assumptions:

• We need the exact value of 5358 × 51.
• Use distributive property to simplify mental math.
• All calculations are with integers.

Concept / Approach:
Use 51 = 50 + 1. Then 5358 × 51 = 5358 × 50 + 5358. Compute each term separately and add. This minimizes errors compared to long multiplication done all at once.

Step-by-Step Solution:
1) Compute 5358 × 50 = 5358 × (5 × 10) = (5358 × 5) × 10.2) 5358 × 5 = 26790; then × 10 → 267900.3) Add the remaining 5358: 267900 + 5358 = 273258.4) Therefore, 5358 × 51 = 273258.

Verification / Alternative check:
Long multiplication: 5358 × 51 = 5358 × (1) + 5358 × (50) = 5358 + 267900 = 273258. Matches the distributive method result exactly.

Why Other Options Are Wrong:
273358, 273348, 273268, and 273308 are near-miss transpositions or off-by-10/50 errors that typically arise from misplacing zeros or mis-adding.

Common Pitfalls:
Forgetting the extra zero when multiplying by 50; arithmetic slips when adding the two parts; swapping digits in the thousands and hundreds places.

Final Answer:
273258