To find a rational number between \( 2 \) and \( 2\frac{1}{4} \) using the method of averaging, we can follow these steps:
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Convert \( 2 \frac{1}{4} \) to an improper fraction: \[ 2 \frac{1}{4} = 2 + \frac{1}{4} = \frac{8}{4} + \frac{1}{4} = \frac{9}{4} \]
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Add the two numbers together: \[ 2 + 2 \frac{1}{4} = 2 + \frac{9}{4} = \frac{8}{4} + \frac{9}{4} = \frac{17}{4} \]
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Divide by 2 to find the average: \[ \text{Average} = \frac{\frac{17}{4}}{2} = \frac{17}{4} \times \frac{1}{2} = \frac{17}{8} \]
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Convert \(\frac{17}{8}\) back to a mixed number: \[ \frac{17}{8} = 2 \frac{1}{8} \]
Thus, a rational number between \( 2 \) and \( 2 \frac{1}{4} \) is \( 2 \frac{1}{8} \).