For the expression X = (A + B + 1.2) * (A + B - C), what is the correct left-to-right sequence of operations (operators only) considering parentheses and standard evaluation order?

Difficulty: Medium

Correct Answer: + + + - * =

Explanation:


Introduction / Context:
Operator sequencing questions assess understanding of evaluation order with parentheses. Parentheses force inner expressions first, left-to-right where operators have the same precedence (e.g., + and -). Multiplication of the two parenthesized results occurs next, followed by assignment.


Given Data / Assumptions:

  • Expression: X = (A + B + 1.2) * (A + B - C)
  • Operators involved: +, -, , =
  • Parentheses dictate sub-expression evaluation before multiplication and assignment.


Concept / Approach:
Within each parenthesized group, perform additions/subtractions left-to-right. After both parentheses are resolved to scalar results, multiply them, then assign to X.


Step-by-Step Solution:

First parenthesis: compute A + B → operator '+' #1.Still inside first parenthesis: (A + B) + 1.2 → operator '+' #2.Second parenthesis: compute A + B → operator '+' #3.Still inside second parenthesis: (A + B) - C → operator '-'.Multiply the two parenthesis results → operator ''.Assign to X → operator '='.


Verification / Alternative check:
If you symbolically name sub-results as P = A + B + 1.2 and Q = A + B - C, then X = P * Q; sequence clearly contains two pluses for P, plus then minus for Q, then multiply, then assign.


Why Other Options Are Wrong:

  • * + + + - =: Starts with multiplication before the parentheses are resolved.
  • + + - * + =: Ends with '+' instead of '='; misorders multiplication and assignment.
  • - + + + * =: Begins with '-' which does not match the first required operation.


Common Pitfalls:

  • Ignoring that + and - have equal precedence but evaluate left-to-right within parentheses.
  • Attempting multiplication before evaluating parenthetical sums/differences.


Final Answer:
+ + + - * =

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