Question

What is the sum of the biggest and the smallest fraction among the given fractions \(\frac{2}{3}, \frac{3}{4}, \frac{4}{5} \text{ and } \frac{5}{6}?\)

• A. \(\frac{1}{6}\)
• B. \(\frac{2}{5}\)
• C. \(\frac1{1}{2}\)
• D. \(\frac1{2}{3}\)

Answer 1

The Correct Option is C

Finding the Sum of the Largest and Smallest Fractions 

Step 1: Convert the Fractions to Decimal Form

• \[ \frac{2}{3} \approx 0.6667 \]
• \[ \frac{3}{4} = 0.75 \]
• \[ \frac{4}{5} = 0.8 \]
• \[ \frac{5}{6} \approx 0.8333 \]

Step 2: Identify the Smallest and Largest Fractions

From the decimal values, we see that:

• Smallest fraction: \( \frac{2}{3} \)
• Largest fraction: \( \frac{5}{6} \)

Step 3: Add the Largest and Smallest Fractions

\[ \frac{5}{6} + \frac{2}{3} \]

Convert \( \frac{2}{3} \) to have a denominator of 6:

\[ \frac{2}{3} = \frac{4}{6} \]

Now, add the fractions:

\[ \frac{5}{6} + \frac{4}{6} = \frac{9}{6} = \frac{3}{2} \]

Final Answer:

Thus, the correct answer is (C) \(1 \frac{1}{2} \).