Chaining division and multiplication (left-to-right) Evaluate: 171 ÷ 19 * 9 exactly.

Introduction / Context:
Problems like this reward noticing exact cancellations. If the first division yields an integer, the remaining multiplication is quick and prevents rounding errors.

Given Data / Assumptions:

• Expression: 171 ÷ 19 * 9.
• Division and multiplication evaluated left to right.
• All values are integers; no rounding needed.

Concept / Approach:
Check whether 171 is a multiple of 19. If so, perform the exact division to simplify the expression, then multiply by 9. This is faster than turning to decimals too early.

Step-by-Step Solution:
Observe 19 * 9 = 171, hence 171 ÷ 19 = 9.Then compute 9 * 9 = 81.Thus, the final value is 81.

Verification / Alternative check:
Reverse grouping: (171/19)*9 = 9*9 = 81. Direct computation without simplification would also yield 81 but with more steps, so the factor observation is preferred.

Why Other Options Are Wrong:
0 or 1 ignore the multiplication; 18 comes from stopping after the first division and forgetting the final multiplication.

Common Pitfalls:
Converting 171/19 to a decimal approximation and introducing rounding; losing the left-to-right flow by multiplying 19 * 9 first in the denominator mentally.

Final Answer:
81