Evaluate: $\frac{1}{(\frac{2}{3}) + (\frac{3}{4})} \div \frac... | Mathematics MCQ | Examoogle

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Evaluate: $\frac{1}{(\frac{2}{3}) + (\frac{3}{4})} \div \frac{8}{17}$

0.5

1.5

Correct Answer

📐 MA • Math Fraction ArithmeticMathematicsMathematics

Option A

Quick Summary:

Calculate the sum in the denominator first by cross-multiplying ( $2 \times 4 + 3 \times 3 = 17$ ) over the product of denominators ( $3 \times 4 = 12$ ). The expression becomes $12/17 \times 17/8$ , where 17 cancels out immediately.

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📐MAMath SolutionFraction Arithmetic

📋 Given

An expression containing a sum of two fractions in the denominator divided by a fraction: 1 / (2/3 + 3/4) / (8/17)

🔢 Formula Used

1ab+cd÷ef=1ad+bcbd×fe\frac{1}{\frac{a}{b} + \frac{c}{d}} \div \frac{e}{f} = \frac{1}{\frac{ad+bc}{bd}} \times \frac{f}{e}ba​+dc​1​÷fe​=bdad+bc​1​×ef​

⚡ Exam Hall Shortcut / Speed Trick

⚠️ Common Student Trap / Pitfall

Many students try to divide the expression in the wrong order or invert the sum part before completing the addition inside the bracket.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Simplify the denominator sum

To add $\frac{2}{3}$ and $\frac{3}{4}$ , find the common denominator, which is $12$ . The sum is $\frac{8+9}{12}$ .

23+34=8+912=1712\frac{2}{3} + \frac{3}{4} = \frac{8+9}{12} = \frac{17}{12}32​+43​=128+9​=1217​

Calculate the reciprocal

The expression is $\frac{1}{\frac{17}{12}}$ , which simplifies to the reciprocal of the fraction.

11712=1217\frac{1}{\frac{17}{12}} = \frac{12}{17}1217​1​=1712​

Perform the final division

Now divide the result by $\frac{8}{17}$ , which is equivalent to multiplying by the reciprocal $\frac{17}{8}$ .

1217×178=128=32=1.5\frac{12}{17} \times \frac{17}{8} = \frac{12}{8} = \frac{3}{2} = 1.51712​×817​=812​=23​=1.5

✅

C is correct because the step-by-step simplification leads to $1.5$ . Note: The official provided answer key stated A(2), but the correct mathematical evaluation is $1.5$ .

Core Concepts Used

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Fractional Addition Reciprocal properties Order of Operations

💡 EXAM TIP

Always simplify compound fractions from the inside out; this approach is vital in complex algebra and calculus problems involving nested rational functions.

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