Question

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

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

Answer 2

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 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 \(\boxed{4.2}\).