Question
Which is a rational number between 5 and 5 1/4
Answers
GPT-4o mini
To find a rational number between 5 and \( 5 \frac{1}{4} \), we first convert \( 5 \frac{1}{4} \) to an improper fraction:
\[
5 \frac{1}{4} = \frac{5 \times 4 + 1}{4} = \frac{20 + 1}{4} = \frac{21}{4}
\]
Now we know that \( 5 \) can also be written as \( \frac{20}{4} \). We are looking for a rational number between \( \frac{20}{4} \) and \( \frac{21}{4} \).
One simple rational number to consider is the average of these two fractions:
\[
\text{Average} = \frac{\frac{20}{4} + \frac{21}{4}}{2} = \frac{\frac{41}{4}}{2} = \frac{41}{8}
\]
Now let's convert \( \frac{41}{8} \) back to a mixed number:
\[
\frac{41}{8} = 5 \frac{1}{8}
\]
Thus, a rational number between \( 5 \) and \( 5 \frac{1}{4} \) is \( 5 \frac{1}{8} \), or in improper fraction form, it is \( \frac{41}{8} \).
Other rational numbers could also work, such as \( 5.1 \) or \( \frac{21}{4} \), but \( 5 \frac{1}{8} \) is one specific example.
\[
5 \frac{1}{4} = \frac{5 \times 4 + 1}{4} = \frac{20 + 1}{4} = \frac{21}{4}
\]
Now we know that \( 5 \) can also be written as \( \frac{20}{4} \). We are looking for a rational number between \( \frac{20}{4} \) and \( \frac{21}{4} \).
One simple rational number to consider is the average of these two fractions:
\[
\text{Average} = \frac{\frac{20}{4} + \frac{21}{4}}{2} = \frac{\frac{41}{4}}{2} = \frac{41}{8}
\]
Now let's convert \( \frac{41}{8} \) back to a mixed number:
\[
\frac{41}{8} = 5 \frac{1}{8}
\]
Thus, a rational number between \( 5 \) and \( 5 \frac{1}{4} \) is \( 5 \frac{1}{8} \), or in improper fraction form, it is \( \frac{41}{8} \).
Other rational numbers could also work, such as \( 5.1 \) or \( \frac{21}{4} \), but \( 5 \frac{1}{8} \) is one specific example.