find a rational number between 2 and 2 1/4 using the method of adding the numbers together and dividing by 2 write answers as mixed numbers

Answer 1

To find a rational number between \(2\) and \(2 \frac{1}{4}\) using the method of averaging, we can follow these steps:

1. Convert \(2\) and \(2 \frac{1}{4}\) into improper fractions:

   • \(2 = \frac{2 \times 4 + 0}{4} = \frac{8}{4}\)
   • \(2 \frac{1}{4} = \frac{2 \times 4 + 1}{4} = \frac{9}{4}\)

2. Add the two numbers together: \[ \frac{8}{4} + \frac{9}{4} = \frac{17}{4} \]

3. Divide by \(2\) to find the average: \[ \frac{17}{4} \div 2 = \frac{17}{4} \times \frac{1}{2} = \frac{17}{8} \]

4. Convert \(\frac{17}{8}\) into a mixed number:

   • Divide \(17\) by \(8\):
     • \(17 \div 8 = 2\) with a remainder of \(1\).
   • This gives us \(2\) whole parts and \(\frac{1}{8}\) as the fractional part.

Therefore, \(\frac{17}{8}\) as a mixed number is: \[ 2 \frac{1}{8} \]

So, a rational number between \(2\) and \(2 \frac{1}{4}\) is: \[ \boxed{2 \frac{1}{8}} \]