Simplify: $\left( \frac{15}{24} \div \frac{15}{2} \right) \div... | Mathematics MCQ | Examoogle

MathematicsArithmetic

Simplify: $\left( \frac{15}{24} \div \frac{15}{2} \right) \div \left( \frac{1}{8} \times \frac{16}{3} + \frac{1}{8} \right) + \frac{2}{11} \div \frac{19}{23} \text{ of } \frac{23}{11}$

$-\frac{4}{24}$

$\frac{4}{19}$

$\frac{7}{18}$

$-\frac{5}{23}$

Correct Answer

⚙️ TE • Technical BODMAS RuleMathematicsArithmetic

Option B

$\frac{4}{19}$

Quick Summary:

Focus on solving parts separately: first parenthesis is (15/24 * 2/15) = 1/12. Second is (2/3 + 1/8) = 19/24. Third part is 2/11 ÷ (19/23 * 23/11) = 2/11 ÷ 19/11 = 2/19.

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📐MAMath SolutionBODMAS Rule

📋 Given

A fractional expression: (15/24 ÷ 15/2) ÷ (1/8 × 16/3 + 1/8) + 2/11 ÷ 19/23 of 23/11

🔢 Formula Used

BODMAS:Brackets,Of,Division,Multiplication,Addition,SubtractionBODMAS: \text{Brackets}, Of, \text{Division}, \text{Multiplication}, \text{Addition}, \text{Subtraction}BODMAS:Brackets,Of,Division,Multiplication,Addition,Subtraction

⚡ Exam Hall Shortcut / Speed Trick

Focus on solving parts separately: first parenthesis is (15/24 * 2/15) = 1/12. Second is (2/3 + 1/8) = 19/24. Third part is 2/11 ÷ (19/23 * 23/11) = 2/11 ÷ 19/11 = 2/19.

⚠️ Common Student Trap / Pitfall

Confusing the priority of 'of' over division; 'of' must be calculated before the division operator.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Simplify first bracket

Evaluate $\frac{15}{24} \div \frac{15}{2} = \frac{15}{24} \times \frac{2}{15} = \frac{1}{12}$ .

1524×215=112\frac{15}{24} \times \frac{2}{15} = \frac{1}{12}2415​×152​=121​

Simplify second bracket

Calculate $(\frac{1}{8} \times \frac{16}{3}) + \frac{1}{8} = \frac{2}{3} + \frac{1}{8}$ . Finding the LCM (24), we get $\frac{16+3}{24} = \frac{19}{24}$ .

23+18=1924\frac{2}{3} + \frac{1}{8} = \frac{19}{24}32​+81​=2419​

Simplify third part

Calculate $\frac{2}{11} \div (\frac{19}{23} \text{ of } \frac{23}{11})$ . The 'of' becomes $\frac{19}{23} \times \frac{23}{11} = \frac{19}{11}$ . Then $\frac{2}{11} \div \frac{19}{11} = \frac{2}{11} \times \frac{11}{19} = \frac{2}{19}$ .

211÷1911=219\frac{2}{11} \div \frac{19}{11} = \frac{2}{19}112​÷1119​=192​

Combine parts

The full expression is $(\frac{1}{12} \div \frac{19}{24}) + \frac{2}{19}$ . Calculate division first: $\frac{1}{12} \times \frac{24}{19} = \frac{2}{19}$ . Finally, $\frac{2}{19} + \frac{2}{19} = \frac{4}{19}$ .

219+219=419\frac{2}{19} + \frac{2}{19} = \frac{4}{19}192​+192​=194​

✅

B is correct because the result of the entire expression is 4/19.

Core Concepts Used

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BODMAS order of operations Fractional arithmetic Precedence of 'of' operator

💡 EXAM TIP

Always treat 'of' as multiplication but with higher precedence than standard division/multiplication operators in competitive exams.

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