Simplify: 150 ÷ [25 ÷ 5 × {12 + 8 - (4 + 2)}] | Mathematics MCQ | Examoogle

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Simplify: 150 ÷ [25 ÷ 5 × {12 + 8 - (4 + 2)}]

2.14

3.57

4.25

5.12

Correct Answer

⚙️ TE • Technical BODMAS RuleMathematicsArithmetic

Option B

Quick Summary:

Solve strictly from the innermost brackets (parentheses, braces, then square brackets) outwards, executing division and multiplication from left to right.

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📐MAMath SolutionBODMAS Rule

📋 Given

Expression: 150 $\div [25 \div 5 \times \{12 + 8 - (4 + 2)\}]$

🔢 Formula Used

Order of Operations: B→O→D→M→A→S\text{Order of Operations: } \text{B} \rightarrow \text{O} \rightarrow \text{D} \rightarrow \text{M} \rightarrow \text{A} \rightarrow \text{S}Order of Operations: B→O→D→M→A→S

⚡ Exam Hall Shortcut / Speed Trick

Solve strictly from the innermost brackets (parentheses, braces, then square brackets) outwards, executing division and multiplication from left to right.

⚠️ Common Student Trap / Pitfall

Failing to follow left-to-right precedence for division and multiplication or making arithmetic errors inside brackets.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Step 1: Simplify Parentheses

Evaluate the innermost parentheses term $(4 + 2)$ first.

(4+2)=6(4 + 2) = 6(4+2)=6

Step 2: Simplify Braces

Substitute the parenthesis result into the braces $\{12 + 8 - 6\}$ and perform addition and subtraction.

12+8−6=1412 + 8 - 6 = 1412+8−6=14

Step 3: Evaluate Square Brackets

Substitute the braces result into the square brackets $[25 \div 5 \times 14]$ and simplify.

25÷5×14=4225 \div 5 \times 14 = 4225÷5×14=42

Step 4: Final Division and Calculation

Divide the outer number $150$ by the evaluated bracket result to obtain the final decimal value.

150÷42≈3.57150 \div 42 \approx 3.57150÷42≈3.57

✅

B is correct because the step-by-step simplification of the given expression using the BODMAS rule results in 3.57.

Core Concepts Used

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BODMAS Rule Bracket Precedence Arithmetic Simplification

💡 EXAM TIP

Accurate application of the BODMAS rule prevents silly mistakes in numerical ability sections across various competitive exams.

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