Which one of the following will have minimum change in its value if 5 is added to both numerator and the denominator of the fractions 2/3, 3/4, 4/5 and 5/6?

The correct answer is 5/6 (Option 4).

Step-by-Step Explanation:
We are given four fractions: $\frac{2}{3}$, $\frac{3}{4}$, $\frac{4}{5}$, and $\frac{5}{6}$.
We need to find which fraction undergoes the minimum change in its value when 5 is added to both its numerator and denominator.

Step 1: Convert the original fractions to decimals.
1. $\frac{2}{3}=0.6667$
2. $\frac{3}{4}=0.7500$
3. $\frac{4}{5}=0.8000$
4. $\frac{5}{6}=0.8333$

Step 2: Add 5 to both the numerator and denominator of each fraction and calculate the new value.
1. For $\frac{2}{3}$:
$\text{New fraction}=\frac{2+5}{3+5}=\frac{7}{8}=0.8750$
2. For $\frac{3}{4}$:
$\text{New fraction}=\frac{3+5}{4+5}=\frac{8}{9}=0.8889$
3. For $\frac{4}{5}$:
$\text{New fraction}=\frac{4+5}{5+5}=\frac{9}{10}=0.9000$
4. For $\frac{5}{6}$:
$\text{New fraction}=\frac{5+5}{6+5}=\frac{10}{11}=0.9091$

Step 3: Calculate the change (difference) in value for each fraction.
1. For $\frac{2}{3}$:
$\text{Change}=0.8750-0.6667=0.2083$
2. For $\frac{3}{4}$:
$\text{Change}=0.8889-0.7500=0.1389$
3. For $\frac{4}{5}$:
$\text{Change}=0.9000-0.8000=0.1000$
4. For $\frac{5}{6}$:
$\text{Change}=0.9091-0.8333=0.0758$

Conclusion:
Comparing all the changes:
0.0758 < 0.1000 < 0.1389 < 0.2083
Thus, the fraction 5/6 experiences the minimum change (approximately 0.0758).