Which fraction is the smallest among `2//3,3//4,4//5and5//6` ?

Options

A. `2//3`
B. `3//4`
C. `4//5`
D. `5//6`

Answer

To determine which fraction is the smallest among \( \frac{2}{3}, \frac{3}{4}, \frac{4}{5}, \) and \( \frac{5}{6} \), we can follow these steps:

### Step 1: Convert each fraction to decimal form
- Calculate \( \frac{2}{3} \):
\[ \frac{2}{3} = 0.6667 \quad (\text{approximately}) \]

- Calculate \( \frac{3}{4} \):
\[ \frac{3}{4} = 0.75 \]

- Calculate \( \frac{4}{5} \):
\[ \frac{4}{5} = 0.8 \]

- Calculate \( \frac{5}{6} \):
\[ \frac{5}{6} = 0.8333 \quad (\text{approximately}) \]

### Step 2: Compare the decimal values
Now we compare the decimal values:
- \( 0.6667 \) (for \( \frac{2}{3} \))
- \( 0.75 \) (for \( \frac{3}{4} \))
- \( 0.8 \) (for \( \frac{4}{5} \))
- \( 0.8333 \) (for \( \frac{5}{6} \))

### Step 3: Identify the smallest value
From the comparison, we see:
- \( 0.6667 < 0.75 < 0.8 < 0.8333 \)

Thus, the smallest fraction is \( \frac{2}{3} \).

### Final Answer
The smallest fraction among \( \frac{2}{3}, \frac{3}{4}, \frac{4}{5}, \) and \( \frac{5}{6} \) is \( \frac{2}{3} \).

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