find a rational number between 2 and 2 and 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 \(2 \frac{1}{4}\) using the method of adding the two numbers together and dividing by \(2\), we can follow these steps:

1. Convert the mixed number \(2 \frac{1}{4}\) into an improper fraction. \[ 2 \frac{1}{4} = \frac{2 \times 4 + 1}{4} = \frac{8 + 1}{4} = \frac{9}{4} \]

2. Add the two numbers together: \[ 2 + 2 \frac{1}{4} = 2 + \frac{9}{4} \] We need to express \(2\) as a fraction with a common denominator: \[ 2 = \frac{8}{4} \] Thus, \[ 2 + \frac{9}{4} = \frac{8}{4} + \frac{9}{4} = \frac{17}{4} \]

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

4. Now we will convert \(\frac{17}{8}\) back to a mixed number: \[ 17 \div 8 = 2 \quad \text{remainder } 1 \] So, \[ \frac{17}{8} = 2 \frac{1}{8} \]

Thus, a rational number between \(2\) and \(2 \frac{1}{4}\) is \(\boxed{2 \frac{1}{8}}\).

Answer 2

find a rational number with one decimal place that is between the square root of 17 and the square root of 18.

Answer 3

To find a rational number with one decimal place that is between \(\sqrt{17}\) and \(\sqrt{18}\), we first need to calculate approximate values for these square roots.

1. Calculate \(\sqrt{17}\): \[ \sqrt{17} \approx 4.1231 \]

2. Calculate \(\sqrt{18}\): \[ \sqrt{18} = \sqrt{9 \times 2} = 3\sqrt{2} \approx 4.2426 \]

Now that we have the approximate values:

• \(\sqrt{17} \approx 4.1231\)
• \(\sqrt{18} \approx 4.2426\)

We are looking for a rational number with one decimal place that lies between these two values.

A number that is between \(4.1231\) and \(4.2426\) could be:

• \(4.2\)

Since \(4.2\) is greater than \(4.1231\) and less than \(4.2426\), it fits the requirement.

Thus, a rational number with one decimal place that is between \(\sqrt{17}\) and \(\sqrt{18}\) is \(\boxed{4.2}\).