$7777 \div 77 \div 5 = x$

### Concept & Formula When a mathematical expression contains multiple consecutive divisions, evaluate them strictly from left to right. A helpful rule for continuous division is: $$ a \div b \div c = \frac{a}{b \times c} $$ ### Step-by-Step Solution * **Given:** $$ 7777 \div 77 \div 5 = x $$ * **Calculation:** Perform the first division on the left. $$ \frac{7777}{77} = 101 $$ * Now perform the second division using the result. $$ \frac{101}{5} = 20.2 $$ * Check the given options. The value $20.2$ is not among (a), (b), (c), or (d). ### Exam Strategy & Shortcut Using the continuous division rule: $$ x = \frac{7777}{77 \times 5} $$ Simplify the fraction by canceling $77$ from the numerator and denominator: $$ x = \frac{101}{5} $$ To divide any number by $5$ quickly, multiply the number by $2$ and divide by $10$: $$ 101 \times 2 = 202 $$ $$ 202 \div 10 = 20.2 $$ Since $20.2$ is not listed, the answer is "None of these". ### Common Pitfall A very common mistake is calculating $77 \div 5$ first, or improperly grouping the terms. Division is not associative; $a \div (b \div c)$ is NOT equal to $(a \div b) \div c$. Always work left-to-right. Another error is dividing $7777$ by $77$ and getting $11$ instead of $101$. ### Final Answer **Therefore, the correct answer is None of these (20.2).**