Simplify: $\frac{(120 - 12) \div (24 \div 2) - 12 + 7}{5 \time... | Mathematics MCQ | Examoogle

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Simplify: $\frac{(120 - 12) \div (24 \div 2) - 12 + 7}{5 \times 12 \div 10 - (6 \times 4) \div 12}$

$\frac{2}{3}$

$-1$

$\frac{3}{2}$

$1$

Correct Answer

⚙️ TE • Technical BODMAS RuleMathematicsArithmetic

Option D

$1$

Quick Summary:

Solve the numerator and denominator separately by applying the BODMAS sequence strictly to each segment before final division.

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📐MAMath SolutionBODMAS Rule

📋 Given

A mathematical expression involving division, subtraction, multiplication, and addition.

🔢 Formula Used

BODMAS Rule: B-Brackets, O-Of, D-Division, M-Multiplication, A-Addition, S-Subtraction\text{BODMAS Rule: B-Brackets, O-Of, D-Division, M-Multiplication, A-Addition, S-Subtraction}BODMAS Rule: B-Brackets, O-Of, D-Division, M-Multiplication, A-Addition, S-Subtraction

⚡ Exam Hall Shortcut / Speed Trick

Solve the numerator and denominator separately by applying the BODMAS sequence strictly to each segment before final division.

⚠️ Common Student Trap / Pitfall

Performing operations from left to right without respecting the BODMAS order, specifically prioritizing divisions within brackets first.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Simplify the Numerator

First, solve the brackets: $(120 - 12) = 108$ and $(24 \div 2) = 12$ . Now calculate the numerator: $108 \div 12 - 12 + 7 = 9 - 12 + 7 = 4$ .

108÷12−12+7=9−12+7=4108 \div 12 - 12 + 7 = 9 - 12 + 7 = 4108÷12−12+7=9−12+7=4

Simplify the Denominator

Solve the multiplication inside brackets: $(6 \times 4) = 24$ . Then calculate the whole expression: $5 \times 12 \div 10^{-24} \div 12 = 60 \div 10^{-2} = 6 - 2 = 4$ .

5×12÷10−24÷12=6−2=45 \times 12 \div 10^{-24} \div 12 = 6 - 2 = 45×12÷10−24÷12=6−2=4

Final Calculation

Divide the simplified numerator by the simplified denominator: $4 \div 4 = 1$ .

44=1\frac{4}{4} = 144​=1

✅

D is correct because the result of the expression is 1.

Core Concepts Used

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BODMAS Rule Order of Operations Arithmetic simplification

💡 EXAM TIP

This type of simplification is fundamental in Data Interpretation and Simplification questions in RRB exams; always maintain the order of operations to avoid sign errors.

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