The rational number between `1//2` and `1//3` is

Options

A. `2//5`
B. `1//5`
C. `3//5`
D. `4//5`

Answer

To find a rational number between \( \frac{1}{2} \) and \( \frac{1}{3} \), we can follow these steps:

### Step 1: Convert the fractions to decimal form
- Convert \( \frac{1}{2} \) to decimal:
\[ \frac{1}{2} = 0.5 \]
- Convert \( \frac{1}{3} \) to decimal:
\[ \frac{1}{3} \approx 0.3333\ldots \text{ (or } 0.3\overline{3}\text{)} \]

### Step 2: Identify the range
- We need to find a rational number between \( 0.3333\ldots \) and \( 0.5 \).

### Step 3: Check the options
- The options provided are:
- \( \frac{2}{5} \)
- \( \frac{1}{5} \)
- \( \frac{3}{5} \)
- \( \frac{4}{5} \)

### Step 4: Convert the options to decimal form
- Convert \( \frac{2}{5} \):
\[ \frac{2}{5} = 0.4 \]
- Convert \( \frac{1}{5} \):
\[ \frac{1}{5} = 0.2 \]
- Convert \( \frac{3}{5} \):
\[ \frac{3}{5} = 0.6 \]
- Convert \( \frac{4}{5} \):
\[ \frac{4}{5} = 0.8 \]

### Step 5: Identify the rational number between \( 0.3333\ldots \) and \( 0.5 \)
- From the converted options:
- \( 0.2 \) (from \( \frac{1}{5} \)) is less than \( 0.3333\ldots \)
- \( 0.4 \) (from \( \frac{2}{5} \)) is between \( 0.3333\ldots \) and \( 0.5 \)
- \( 0.6 \) (from \( \frac{3}{5} \)) is greater than \( 0.5 \)
- \( 0.8 \) (from \( \frac{4}{5} \)) is also greater than \( 0.5 \)

### Conclusion
- The only rational number that lies between \( \frac{1}{2} \) and \( \frac{1}{3} \) is \( \frac{2}{5} \).

### Final Answer
The rational number between \( \frac{1}{2} \) and \( \frac{1}{3} \) is \( \frac{2}{5} \).

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