Question
5. Find a rational number (fraction in simplest form) between 6 and 6 1/4?
Answers
GPT-4o mini
To find a rational number (a fraction in simplest form) between 6 and \( 6 \frac{1}{4} \), we first convert \( 6 \frac{1}{4} \) to an improper fraction.
\[
6 \frac{1}{4} = 6 + \frac{1}{4} = \frac{24}{4} + \frac{1}{4} = \frac{25}{4}
\]
Now, we need to find a rational number between 6, which can also be expressed as a fraction:
\[
6 = \frac{24}{4}
\]
So, we are looking for a fraction between \( \frac{24}{4} \) and \( \frac{25}{4} \). One possible fraction that lies between these two fractions is:
\[
\frac{24 + 25}{2} = \frac{49}{8}
\]
To verify, we can compare:
- The decimal of \( \frac{24}{4} \) is 6.
- The decimal of \( \frac{25}{4} \) is 6.25.
- The decimal of \( \frac{49}{8} \) is \( 6.125 \).
Since \( 6 < 6.125 < 6.25 \), the fraction \( \frac{49}{8} \) is indeed between 6 and \( 6 \frac{1}{4} \).
Thus, a rational number between 6 and \( 6 \frac{1}{4} \) is:
\[
\frac{49}{8}
\]
\[
6 \frac{1}{4} = 6 + \frac{1}{4} = \frac{24}{4} + \frac{1}{4} = \frac{25}{4}
\]
Now, we need to find a rational number between 6, which can also be expressed as a fraction:
\[
6 = \frac{24}{4}
\]
So, we are looking for a fraction between \( \frac{24}{4} \) and \( \frac{25}{4} \). One possible fraction that lies between these two fractions is:
\[
\frac{24 + 25}{2} = \frac{49}{8}
\]
To verify, we can compare:
- The decimal of \( \frac{24}{4} \) is 6.
- The decimal of \( \frac{25}{4} \) is 6.25.
- The decimal of \( \frac{49}{8} \) is \( 6.125 \).
Since \( 6 < 6.125 < 6.25 \), the fraction \( \frac{49}{8} \) is indeed between 6 and \( 6 \frac{1}{4} \).
Thus, a rational number between 6 and \( 6 \frac{1}{4} \) is:
\[
\frac{49}{8}
\]