Which of the following rational numbers does not lie between `(1)/(4)` and `(2)/(3)` ?

Options

A. `(1)/(2)`
B. `(1)/(3)`
C. `(14)/(24)`
D. `(18)/(24)`

Answer

To determine which of the following rational numbers does not lie between \( \frac{1}{4} \) and \( \frac{2}{3} \), we can follow these steps:

### Step 1: Convert the fractions to decimal form
First, we convert \( \frac{1}{4} \) and \( \frac{2}{3} \) into decimal form for easier comparison.

- \( \frac{1}{4} = 0.25 \)
- \( \frac{2}{3} \approx 0.67 \) (more precisely, it is \( 0.6666... \))

### Step 2: Identify the range
Now we know that the range we are interested in is between \( 0.25 \) and \( 0.67 \).

### Step 3: Convert the options to decimal
Next, we need to convert the given options into decimal form to see if they lie within this range. Let's assume the options are:

1. \( \frac{1}{2} \)
2. \( \frac{1}{3} \)
3. \( \frac{14}{24} \)
4. \( \frac{18}{24} \)

Now, we convert each of these fractions to decimal:

1. \( \frac{1}{2} = 0.5 \)
2. \( \frac{1}{3} \approx 0.33 \)
3. \( \frac{14}{24} \approx 0.5833 \)
4. \( \frac{18}{24} = 0.75 \)

### Step 4: Compare the decimals with the range
Now we compare each decimal with the range \( 0.25 \) to \( 0.67 \):

- \( 0.5 \) lies between \( 0.25 \) and \( 0.67 \).
- \( 0.33 \) lies between \( 0.25 \) and \( 0.67 \).
- \( 0.5833 \) lies between \( 0.25 \) and \( 0.67 \).
- \( 0.75 \) does not lie between \( 0.25 \) and \( 0.67 \).

### Conclusion
Thus, the rational number that does not lie between \( \frac{1}{4} \) and \( \frac{2}{3} \) is \( \frac{18}{24} \).