What should come in place of $*$ mark in the following equation? $$1*544 \div 148 = 78$$

### Concept & Logic This problem tasks you with finding a missing digit inside a large dividend. Attempting long division with an unknown digit is highly inefficient. The easiest approach is to use the inverse property of division: $\text{Dividend} = \text{Divisor} \times \text{Quotient}$. ### Step-by-Step Solution * **Given:** $1*544 \div 148 = 78$. * **Inverse Operation:** Rewrite the division equation as a multiplication equation to find the full value of the dividend. $$1*544 = 148 \times 78$$ * **Calculation:** Perform the multiplication. $$148 \times (70 + 8)$$ $$= (148 \times 70) + (148 \times 8)$$ $$= 10360 + 1184$$ $$= 11544$$ * **Comparison:** Align the calculated product with the given dividend format. $$11544 = 1*544$$ * By direct comparison, the missing digit indicated by the $*$ is $1$. ### Exam Strategy & Shortcut **Estimation & Structure Matching:** You do not need to perform the exact multiplication if you estimate intelligently. Calculate roughly: $150 \times 80 = 12000$. Since $148$ is slightly less than $150$ and $78$ is slightly less than $80$, the product must be slightly less than $12000$. Look at the dividend structure: $1\_544$. The only number slightly less than $12000$ that fits this exact digit pattern is $11544$. Thus, the missing digit must be $1$. ### Common Pitfall Attempting to set up algebraic long division with $x$ as the missing digit (e.g., $10000 + 1000x + 544$). This creates an unnecessarily complex setup that is prone to arithmetic errors under time pressure. Always convert division with missing dividend digits into multiplication. ### Final Answer Therefore, the correct answer is **1**.