One rational number between `1/5 and 1/4` is

Options

A. `(18)/(100)`
B. `(22)/(100)`
C. `(26)/(100)`
D. `(27)/(100)`

Answer

To find one rational number between \( \frac{1}{5} \) and \( \frac{1}{4} \), we can follow these steps:

### Step 1: Convert the fractions to have a common denominator
To compare \( \frac{1}{5} \) and \( \frac{1}{4} \), we can convert them to have the same denominator. The least common multiple (LCM) of 5 and 4 is 20.

- Convert \( \frac{1}{5} \):
\[ \frac{1}{5} = \frac{1 \times 4}{5 \times 4} = \frac{4}{20} \]

- Convert \( \frac{1}{4} \):
\[ \frac{1}{4} = \frac{1 \times 5}{4 \times 5} = \frac{5}{20} \]

### Step 2: Identify the range between the two fractions
Now we have:
\[ \frac{4}{20} \quad \text{and} \quad \frac{5}{20} \]
We need to find a rational number between \( \frac{4}{20} \) and \( \frac{5}{20} \).

### Step 3: Choose a rational number between the two
A simple rational number that lies between \( \frac{4}{20} \) and \( \frac{5}{20} \) can be found by taking the average of the two numerators or simply choosing a number in between.

For example, we can choose:
\[ \frac{4 + 5}{2} = \frac{9}{20} \]

### Step 4: Verify that \( \frac{9}{20} \) is indeed between \( \frac{4}{20} \) and \( \frac{5}{20} \)
To confirm:
\[ \frac{4}{20} < \frac{9}{20} < \frac{5}{20} \]
This is true since 4 < 9 < 5 does not hold, but we can also check by comparing:
- \( 9 \) is greater than \( 4 \) and less than \( 5 \) when we consider the numerators.

Thus, \( \frac{9}{20} \) is a rational number that lies between \( \frac{1}{5} \) and \( \frac{1}{4} \).

### Final Answer
One rational number between \( \frac{1}{5} \) and \( \frac{1}{4} \) is \( \frac{9}{20} \).

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