$60840 \div 234 = x$

Concept & Strategy This is a direct division problem involving large numbers. The goal is to simplify the division by estimating or using the unit digit to verify the quotient quickly. Step-by-Step Solution * We need to find the value of $x$ in the equation: $$60840 \div 234 = x$$ * Let's perform long division. Divide the first three digits ($608$) by $234$. * $234 \times 2 = 468$. * Subtract $468$ from $608$: $608 - 468 = 140$. * Bring down the next digit ($4$) to make $1404$. * Divide $1404$ by $234$. Since $4 \times 6 = 24$, let's test $6$. * $234 \times 6 = 1404$. * The remainder is $0$. Bring down the final $0$, making the quotient $260$. Exam Strategy & Shortcut Use option elimination. The dividend $60840$ ends in $0$. Since $234$ does not end in $5$ or $0$, the quotient must end in $0$ or $5$ to produce a $0$ in the dividend. $234 \times 200 = 46800$ and $234 \times 300 = 70200$. The answer must be between $200$ and $300$, but closer to $250$. Looking at the options ending in $0$ or $5$: $255$ and $260$. Check the unit digit of $234 \times 26 = 6084$. Add the zero, giving $260$. Common Pitfall Getting bogged down in massive long division without using the options as a guide. Estimating first prevents calculation errors from going unnoticed. Final Answer **Therefore, the correct answer is 260.**