Find two rational numbers between `-(1)/(4)and(2)/(5)`.

Explanation

To find two rational numbers between \(-\frac{1}{4}\) and \(\frac{2}{5}\), we will follow these steps:

### Step 1: Convert the fractions to have a common denominator
We need to find a common denominator for \(-\frac{1}{4}\) and \(\frac{2}{5}\). The denominators are 4 and 5. The least common multiple (LCM) of 4 and 5 is 20.

### Step 2: Convert \(-\frac{1}{4}\) to have a denominator of 20
To convert \(-\frac{1}{4}\) to a fraction with a denominator of 20, we multiply both the numerator and denominator by 5:
\[ -\frac{1}{4} = -\frac{1 \times 5}{4 \times 5} = -\frac{5}{20} \]

### Step 3: Convert \(\frac{2}{5}\) to have a denominator of 20
To convert \(\frac{2}{5}\) to a fraction with a denominator of 20, we multiply both the numerator and denominator by 4:
\[ \frac{2}{5} = \frac{2 \times 4}{5 \times 4} = \frac{8}{20} \]

### Step 4: Identify the rational numbers between \(-\frac{5}{20}\) and \(\frac{8}{20}\)
Now we have the two fractions:
\[ -\frac{5}{20} \quad \text{and} \quad \frac{8}{20} \]
We need to find rational numbers between these two fractions. The rational numbers can be found by choosing any two fractions that lie between \(-5\) and \(8\) when expressed with a denominator of \(20\).

### Step 5: Choose two rational numbers
We can choose:
1. \(-\frac{4}{20}\) (which is \(-\frac{1}{5}\))
2. \(-\frac{3}{20}\) (which is \(-\frac{3}{20}\))

Thus, the two rational numbers between \(-\frac{1}{4}\) and \(\frac{2}{5}\) are:
\[ -\frac{4}{20} \quad \text{and} \quad -\frac{3}{20} \]

### Summary
The two rational numbers between \(-\frac{1}{4}\) and \(\frac{2}{5}\) are \(-\frac{4}{20}\) and \(-\frac{3}{20}\).

---