Which of the following fractions is greater than $\frac{2}{3}$ and less than $\frac{4}{5}$?

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Examoogle · Accepted Answer

The correct answer is Option A: $\frac{3}{4}$. Convert all fractions to decimal equivalents or make denominators equal by finding the LCM. \frac{2}{3} \approx 0.667 and \frac{4}{5} = 0.80. Check the options: \frac{3}{4} = 0.75, which lies between 0.667 and 0.80.

Step-by-Step Solution & Concepts:
Shortcut Trick: Convert all fractions to decimal equivalents or make denominators equal by finding the LCM. \frac{2}{3} \approx 0.667 and \frac{4}{5} = 0.80. Check the options: \frac{3}{4} = 0.75, which lies between 0.667 and 0.80.

Formula Used: $$\frac{a}{b}

Given: Fractions to compare: \frac{2}{3} and \frac{4}{5}. Options provided: \frac{3}{4}, \frac{1}{2}, \frac{5}{6}, \frac{9}{11}.

Steps: Step 1: Convert given boundaries to decimal form: Convert \frac{2}{3} and \frac{4}{5} to decimals to easily compare values: $$\frac{2}{3} \approx 0.667$$ and $$\frac{4}{5} = 0.80$$. Step 2: Evaluate Option A (\frac{3}{4}): Convert \frac{3}{4} into a decimal value: $$\frac{3}{4} = 0.75$$. Step 3: Verify the condition: Since $0.75$ is strictly greater than $0.667$ (\frac{2}{3}) and less than $0.80$ (\frac{4}{5}), \frac{3}{4} is the correct fraction.

Answer: A is correct because \frac{3}{4} equals 0.75, which lies strictly between \frac{2}{3} \approx 0.667 and \frac{4}{5} = 0.80.

Exam Tip: Converting fractions to decimals or common denominators is a fundamental technique for comparing rational numbers quickly in quantitative aptitude tests.

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