What is $348$ times $265$?

Concept & Strategy This is a direct three-digit multiplication problem. To solve it efficiently without a calculator, you can split one of the numbers into hundreds, tens, and units (distributive property) to make the calculations easier to manage. Step-by-Step Solution * We need to find the product: $$348 \times 265$$ * Expand $265$ into $(200 + 60 + 5)$: $$348 \times (200 + 60 + 5)$$ * Multiply $348$ by each part: $$348 \times 200 = 69600$$ $$348 \times 60 = 20880$$ $$348 \times 5 = 1740$$ * Sum the partial products: $$69600 + 20880 + 1740 = 92220$$ Exam Strategy & Shortcut Use the unit digit and tens digit to eliminate options rapidly. First, the unit digit is $8 \times 5 = 40$, which ends in $0$. All options end in $0$. Next, find the last two digits by multiplying the last two digits of the numbers: $48 \times 65$. $48 \times 65 = 48 \times (60 + 5) = 2880 + 240 = 3120$. The product must end in $20$. Looking at the given options, only $92220$ ends in $20$. Common Pitfall Attempting standard column multiplication for large numbers can easily lead to carrying errors. Splitting into partial products or checking the last two digits is much safer and faster. Final Answer **Therefore, the correct answer is 92220.**