The pair of rational numbers that lies between `( 1)/( 4)` and `( 3)/(4)` is

Options

A. `( 262)/( 1000),( 752)/( 1000)`
B. `(24)/( 100), ( 74)/( 100)`
C. `( 9 )/( 40) , ( 31)/( 40)`
D. `(252)/( 1000), ( 748)/( 1000)`

Answer

To find a pair of rational numbers that lies between \( \frac{1}{4} \) and \( \frac{3}{4} \), we can follow these steps:

### Step 1: Convert the fractions to decimal form
First, we convert \( \frac{1}{4} \) and \( \frac{3}{4} \) into decimal form to understand the range better.

\[ \frac{1}{4} = 0.25 \]
\[ \frac{3}{4} = 0.75 \]

### Step 2: Identify the range
Now that we have the decimal equivalents, we know we are looking for rational numbers between 0.25 and 0.75.

### Step 3: Choose two rational numbers within the range
We can choose two rational numbers that are clearly between 0.25 and 0.75. For example:

1. \( \frac{1}{2} = 0.5 \)
2. \( \frac{2}{3} \approx 0.6667 \)

Both of these numbers lie between 0.25 and 0.75.

### Step 4: Verify the chosen numbers
To ensure that these numbers are indeed between \( \frac{1}{4} \) and \( \frac{3}{4} \):

- For \( \frac{1}{2} \):
- \( 0.25 < 0.5 < 0.75 \) (True)

- For \( \frac{2}{3} \):
- \( 0.25 < 0.6667 < 0.75 \) (True)

### Conclusion
Thus, the pair of rational numbers that lies between \( \frac{1}{4} \) and \( \frac{3}{4} \) is \( \frac{1}{2} \) and \( \frac{2}{3} \).

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