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?
-
A+ + + - * =
-
B* + + + - =
-
C+ + - * + =
-
D- + + + * =
Answer
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:+ + + - * =