Find a rational number between `(1)/(4) and (1)/(3)`.

Options

A. `(9)/(24) `
B. `(7)/(24) `
C. `(5)/(24) `
D. `(11)/(24) `

Answer

To find a rational number between \( \frac{1}{4} \) and \( \frac{1}{3} \), we can follow these steps:

### Step 1: Identify the two rational numbers
We have:
- \( x = \frac{1}{4} \)
- \( y = \frac{1}{3} \)

### Step 2: Find a common denominator
To compare these two fractions, we need a common denominator. The denominators are 4 and 3. The least common multiple (LCM) of 4 and 3 is 12.

### Step 3: Convert the fractions to have the common denominator
Convert \( \frac{1}{4} \) and \( \frac{1}{3} \) to fractions with a denominator of 12:
- \( \frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12} \)
- \( \frac{1}{3} = \frac{1 \times 4}{3 \times 4} = \frac{4}{12} \)

### Step 4: Find a rational number between the two fractions
Now, we can find a rational number between \( \frac{3}{12} \) and \( \frac{4}{12} \). A simple way to find a number between two fractions is to take their average:
\[ \text{Average} = \frac{\frac{3}{12} + \frac{4}{12}}{2} = \frac{\frac{7}{12}}{2} = \frac{7}{24} \]

### Step 5: Conclusion
Thus, a rational number between \( \frac{1}{4} \) and \( \frac{1}{3} \) is \( \frac{7}{24} \).

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