Find a rational number between 2 and 2 1/4 using the method of adding the numbers together and dividing by 2. Write the answer as a mixed number.

Answer 1

To find a rational number between \( 2 \) and \( 2 \frac{1}{4} \), we first convert \( 2 \frac{1}{4} \) to an improper fraction.

\[ 2 \frac{1}{4} = 2 + \frac{1}{4} = \frac{8}{4} + \frac{1}{4} = \frac{9}{4} \]

Now we have the two numbers \( 2 \) and \( \frac{9}{4} \). To find a rational number between them using the method of adding the numbers together and dividing by 2, we do the following:

1. Convert \( 2 \) to a fraction: \[ 2 = \frac{8}{4} \]

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

3. Now divide by \( 2 \) (which is the same as multiplying by \( \frac{1}{2} \)): \[ \frac{17}{4} \div 2 = \frac{17}{4} \times \frac{1}{2} = \frac{17}{8} \]

Now, convert \( \frac{17}{8} \) back to a mixed number. To do this, divide \( 17 \) by \( 8 \):

• \( 8 \) goes into \( 17 \) two times.
• \( 2 \times 8 = 16 \), and the remainder is \( 17 - 16 = 1 \).

Thus, \[ \frac{17}{8} = 2 \frac{1}{8} \]

So, a rational number between \( 2 \) and \( 2 \frac{1}{4} \) is

\[ \boxed{2 \frac{1}{8}} \]

Answer 2

what is the answer

Answer 3

The rational number between \( 2 \) and \( 2 \frac{1}{4} \) that we calculated using the method of adding the two numbers together and dividing by \( 2 \) is

\[ \boxed{2 \frac{1}{8}}. \]

Answer 4

no it not

Answer 5

Let's go through the calculation step-by-step again to ensure we find a rational number between \(2\) and \(2 \frac{1}{4}\):

1. Convert \(2\) and \(2 \frac{1}{4}\) to improper fractions: \[ 2 = \frac{4}{2} \quad \text{and} \quad 2 \frac{1}{4} = 2 + \frac{1}{4} = \frac{8}{4} + \frac{1}{4} = \frac{9}{4} \]

2. Find the average by adding the two fractions and dividing by \(2\): \[ \text{Average} = \frac{\frac{8}{4} + \frac{9}{4}}{2} \] This can be simplified: \[ \frac{\frac{8 + 9}{4}}{2} = \frac{\frac{17}{4}}{2} = \frac{17}{4} \times \frac{1}{2} = \frac{17}{8} \]

3. Convert \(\frac{17}{8}\) back to a mixed number:

   • \(17\) divided by \(8\) gives \(2\) (since \(8 \times 2 = 16\)), with a remainder of \(1\).
   • So, \(\frac{17}{8} = 2 \frac{1}{8}\).

If you are looking for a different rational number between \(2\) and \(2 \frac{1}{4}\), there are infinitely many numbers. For example, \(2.1\), \(2.2\), \(2.125\), etc., are all rational numbers that fit between these two values.

But according to the calculation we've done based on the method you provided, the answer is \( \boxed{2 \frac{1}{8}} \). If you meant a different method or approach, please clarify!