$5358 \times 51 = x$

### Concept & Strategy To multiply a large number by a number close to a multiple of 10 (like 51), we can use the distributive property of multiplication over addition. $$a \times (b + c) = (a \times b) + (a \times c)$$ ### Step-by-Step Solution * Break down 51 into simpler additive components: $$51 = 50 + 1$$ * Apply the distributive property: $$5358 \times 51 = 5358 \times (50 + 1)$$ * Multiply 5358 by 50 and by 1: $$5358 \times 50 = 5358 \times \frac{100}{2} = 267900$$ $$5358 \times 1 = 5358$$ * Add the results together: $$267900 + 5358 = 273258$$ ### Exam Strategy & Shortcut Check the last two digits using the unit digit method for faster elimination. The last two digits of the product will be determined by the last two digits of the multiplicands. $$58 \times 51 \rightarrow 58 \times (50 + 1) = 2900 + 58 = 2958$$ The last two digits must be 58. We can eliminate options (b) and (c) immediately. Since $53 \times 5 = 265$, the answer must be around 270,000, confirming 273258. ### Common Pitfall Students often attempt direct vertical multiplication, which consumes excessive time and increases the risk of carrying errors during addition. Always look for base-10 approximations. ### Final Answer **Therefore, the correct answer is 273258.**