Question

rational number between 5 and 5 and 1/4

Answer 1

To find a rational number between 5 and \( 5 \frac{1}{4} \), you can first express \( 5 \frac{1}{4} \) as an improper fraction:

\[
5 \frac{1}{4} = 5 + \frac{1}{4} = \frac{20}{4} + \frac{1}{4} = \frac{21}{4}
\]

Now you have two numbers: \( 5 \) (which can be written as \( \frac{20}{4} \)) and \( \frac{21}{4} \). A rational number between them can be found by taking the average:

\[
\text{Average} = \frac{\frac{20}{4} + \frac{21}{4}}{2} = \frac{\frac{41}{4}}{2} = \frac{41}{8}
\]

To convert \( \frac{41}{8} \) back to a mixed number, divide 41 by 8:

- 8 goes into 41 five times (since \( 8 \times 5 = 40 \)), with a remainder of 1.

Thus, \( \frac{41}{8} = 5 \frac{1}{8} \).

Therefore, \( 5 \frac{1}{8} \) is a rational number that lies between 5 and \( 5 \frac{1}{4} \).

Alternatively, you could just choose any fraction within that range, such as \( 5.1 \), \( \frac{41}{40} \), or any other value between 5 and \( 5.25 \) (the decimal equivalent of \( 5 \frac{1}{4} \)).

Answer 2

so the answer is 5 1/8?

Answer 3

Yes, \( 5 \frac{1}{8} \) is one rational number between 5 and \( 5 \frac{1}{4} \). However, there are many other rational numbers you could also find in that range, such as \( 5.1 \), \( 5.2 \), or different fractions like \( \frac{41}{40} \).

But specifically, \( 5 \frac{1}{8} \) is a valid answer!