Evaluate: $\frac{1}{(\frac{2}{3}) + (\frac{4}{5})} \div \frac... | Mathematics MCQ | Examoogle

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Evaluate: $\frac{1}{(\frac{2}{3}) + (\frac{4}{5})} \div \frac{5}{22}$

Correct Answer

📐 MA • Math Fraction ArithmeticMathematicsMathematics

Option B

Quick Summary:

Calculate the sum in the denominator using cross-multiplication: $\frac{2}{3} + \frac{4}{5} = \frac{10+12}{15} = \frac{22}{15}$ . Then, replace division by the reciprocal to get $\frac{15}{22} \times \frac{22}{5}$ .

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📐MAMath SolutionFraction Arithmetic

📋 Given

An arithmetic expression involving addition of fractions in the denominator and division by another fraction.

🔢 Formula Used

1ab+cd÷ef\frac{1}{\frac{a}{b} + \frac{c}{d}} \div \frac{e}{f}ba​+dc​1​÷fe​

⚡ Exam Hall Shortcut / Speed Trick

⚠️ Common Student Trap / Pitfall

Many students fail to invert the fraction in the denominator correctly or misinterpret the precedence of operations, leading to division errors.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Simplify the denominator

Calculate the sum of fractions $\frac{2}{3} + \frac{4}{5}$ by finding the common denominator $15$ .

23+45=10+1215=2215\frac{2}{3} + \frac{4}{5} = \frac{10 + 12}{15} = \frac{22}{15}32​+54​=1510+12​=1522​

Evaluate the reciprocal

Substitute the result into the expression: $\frac{1}{\frac{22}{15}} = \frac{15}{22}$ .

1(2215)=1522\frac{1}{(\frac{22}{15})} = \frac{15}{22}(1522​)1​=2215​

Perform final division

Divide the result $\frac{15}{22}$ by $\frac{5}{22}$ by multiplying with the reciprocal.

1522÷522=1522×225=155=3\frac{15}{22} \div \frac{5}{22} = \frac{15}{22} \times \frac{22}{5} = \frac{15}{5} = 32215​÷225​=2215​×522​=515​=3

✅

B is correct because the final calculated value of the expression is 3.

Core Concepts Used

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Fraction addition Reciprocals Order of operations

💡 EXAM TIP

Understanding reciprocal multiplication is essential for mastering ratio and proportion questions where variables often appear in fractional forms.

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