Examkin

Question

Difficulty: HardOrder of Operations

Determine the correct chronological sequence of steps required to evaluate the following mathematical expression according to the standard order of operations:

−3×[4−(5−23)]−7+4 \frac{ -3 \times \left[ 4 - \left( 5 - 2^3 \right) \right] }{ -7 + 4 }
  1. 1Evaluate the exponent within the innermost parentheses of the numerator.
  2. 2Calculate the difference inside the innermost parentheses.
  3. 3Resolve the subtraction operation inside the square brackets.
  4. 4Perform the multiplication in the numerator and the addition in the denominator.
  5. 5Divide the final value of the numerator by the final value of the denominator.

Answer

The correct sequence begins with the innermost exponent, resolves the nested grouping symbols outward, simplifies the numerator and denominator independently, and finishes with division.
The correct evaluation sequence strictly follows the order of operations (PEMDAS). It begins by isolating the innermost grouping symbols and addressing the exponent. Once the innermost parentheses are reduced to a single value, the surrounding brackets are resolved, carefully tracking negative signs. The large fraction bar acts as an invisible grouping symbol, requiring the entire numerator and denominator to be independently simplified before performing the final division.

Step-by-Step Solution

1
Identify innermost grouping symbols and evaluate exponents.
The expression (5−23)(5 - 2^3) becomes (5−8)(5 - 8).
Parentheses and Exponents have the highest priority in the order of operations.
2
Complete operations inside the innermost parentheses.
The expression (5−8)(5 - 8) evaluates to −3-3.
The innermost group must be resolved to a single number before moving outward to the next level of grouping.
3
Evaluate operations inside the outer square brackets.
The expression [4−(−3)][4 - (-3)] becomes [4+3][4 + 3], which simplifies to 77.
Square brackets function as the next level of grouping and must be completely simplified before multiplying.
4
Simplify the remainder of the numerator and the denominator.
The numerator becomes −3×7=−21-3 \times 7 = -21. The denominator becomes −7+4=−3-7 + 4 = -3.
A fraction bar acts as a grouping symbol, meaning the top and bottom expressions must be fully evaluated independently before division occurs.
5
Perform the final division.
−21÷−3=7-21 \div -3 = 7.
Division is the final operation combining the fully simplified numerator and denominator.

Key Concept

Order of Operations (PEMDAS) with nested grouping symbols, negative numbers, and fraction bars.
Rate this question

Topics

Order of Operations

More questions from this topic