Question

Find a rational number(fraction to simplest form) between 6 and 6 1/4?

Answer 1

To find a rational number (fraction) between 6 and \( 6 \frac{1}{4} \), we first convert \( 6 \frac{1}{4} \) to an improper fraction.

\[
6 \frac{1}{4} = 6 + \frac{1}{4} = \frac{24}{4} + \frac{1}{4} = \frac{25}{4}
\]

So, we are looking for a fraction between \( 6 \) (which can be expressed as \( \frac{24}{4} \)) and \( \frac{25}{4} \).

One simple way to find a fraction between these two is to take the average:

\[
\text{Average} = \frac{\frac{24}{4} + \frac{25}{4}}{2} = \frac{\frac{49}{4}}{2} = \frac{49}{8}
\]

Now let's check if \( \frac{49}{8} \) is between \( 6 \) and \( 6 \frac{1}{4} \):

1. Convert \( 6 \) into eighths:
\[
6 = \frac{48}{8}
\]
2. Convert \( 6 \frac{1}{4} \) into eighths:
\[
6 \frac{1}{4} = \frac{25}{4} = \frac{50}{8}
\]

Now we can see:
\[
\frac{48}{8} < \frac{49}{8} < \frac{50}{8}
\]

Thus, \( \frac{49}{8} \) is indeed between \( 6 \) and \( 6 \frac{1}{4} \).

In simplest form, the fraction is \( \frac{49}{8} \).