Three rational numbers lying between `(-3)/(4) and (1)/(2)` are

Options

A. `-(1)/(2), 0, (3)/(4)`
B. `(-1)/(4), (1)/(4), (3)/(4)`
C. `(-1)/(4),0,(1)/(4)`
D. `(-5)/(4),0,(1)/(4)`

Answer

To find three rational numbers lying between \(-\frac{3}{4}\) and \(\frac{1}{2}\), we can follow these steps:

### Step 1: Convert \(\frac{1}{2}\) to a fraction with a denominator of 4
To compare the two fractions easily, we can convert \(\frac{1}{2}\) to a fraction with a denominator of 4.

\[ \frac{1}{2} = \frac{1 \times 2}{2 \times 2} = \frac{2}{4} \]

### Step 2: Identify the range of fractions
Now we have two fractions:
- \(-\frac{3}{4}\)
- \(\frac{2}{4}\)

We need to find three rational numbers that lie between \(-\frac{3}{4}\) and \(\frac{2}{4}\).

### Step 3: Choose a common denominator
Since we are working with fractions that have a denominator of 4, we can choose rational numbers that also have a denominator of 4.

### Step 4: List the rational numbers
The rational numbers that lie between \(-\frac{3}{4}\) and \(\frac{2}{4}\) can be:
- \(-\frac{2}{4}\)
- \(-\frac{1}{4}\)
- \(0\) (which can be written as \(\frac{0}{4}\))

### Step 5: Write the final answer
Thus, three rational numbers lying between \(-\frac{3}{4}\) and \(\frac{1}{2}\) are:
1. \(-\frac{2}{4}\)
2. \(-\frac{1}{4}\)
3. \(0\) (or \(\frac{0}{4}\))

### Summary
The three rational numbers between \(-\frac{3}{4}\) and \(\frac{1}{2}\) are:
- \(-\frac{2}{4}\)
- \(-\frac{1}{4}\)
- \(0\)

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