Question

is 5 1/8 a rational number between 5 and 5 1/4

Answer 1

To determine if \( 5 \frac{1}{8} \) is a rational number between \( 5 \) and \( 5 \frac{1}{4} \), we first convert \( 5 \frac{1}{4} \) to an improper fraction:

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

Now we need to express \( 5 \frac{1}{8} \) as an improper fraction as well:

\[
5 \frac{1}{8} = 5 + \frac{1}{8} = \frac{40}{8} + \frac{1}{8} = \frac{41}{8}
\]

Next, we can compare \( 5 \) (as a fraction, \( \frac{40}{8} \)), \( 5 \frac{1}{8} \) (as \( \frac{41}{8} \)), and \( 5 \frac{1}{4} \) (as \( \frac{21}{4} \)). To compare \( \frac{41}{8} \) and \( \frac{21}{4} \), we convert \( \frac{21}{4} \) to have a common denominator of 8:

\[
\frac{21}{4} = \frac{21 \times 2}{4 \times 2} = \frac{42}{8}
\]

Now we can easily compare the fractions:

- \( \frac{40}{8} = 5 \)
- \( \frac{41}{8} = 5 \frac{1}{8} \)
- \( \frac{42}{8} = 5 \frac{1}{4} \)

Since \( \frac{40}{8} < \frac{41}{8} < \frac{42}{8} \), we see that:

\[
5 < 5 \frac{1}{8} < 5 \frac{1}{4}
\]

Thus, \( 5 \frac{1}{8} \) is indeed a rational number between \( 5 \) and \( 5 \frac{1}{4} \).

Answer 2

are you sure thats the right answer?

Answer 3

Let’s verify the details again step by step:

1. **Convert the mixed numbers to improper fractions:**
- For \( 5 \frac{1}{8} \):
\[
5 \frac{1}{8} = 5 + \frac{1}{8} = \frac{40}{8} + \frac{1}{8} = \frac{41}{8}
\]

- For \( 5 \frac{1}{4} \):
\[
5 \frac{1}{4} = 5 + \frac{1}{4} = \frac{20}{4} + \frac{1}{4} = \frac{21}{4}
\]
We can convert \( \frac{21}{4} \) to have a common denominator with \( \frac{41}{8} \) (which is 8):
\[
\frac{21}{4} = \frac{21 \times 2}{4 \times 2} = \frac{42}{8}
\]

2. **Compare the fractions:**
- We have:
- \( 5 = \frac{40}{8} \)
- \( 5 \frac{1}{8} = \frac{41}{8} \)
- \( 5 \frac{1}{4} = \frac{42}{8} \)

3. **Establish the order:**
- Now let’s put those in order:
- \( \frac{40}{8} < \frac{41}{8} < \frac{42}{8} \)
- This translates to \( 5 < 5 \frac{1}{8} < 5 \frac{1}{4} \).

Conclusion: Yes, \( 5 \frac{1}{8} \) is indeed a rational number that falls between \( 5 \) and \( 5 \frac{1}{4} \).

So, the answer is correct: **Yes, \( 5 \frac{1}{8} \) is a rational number between \( 5 \) and \( 5 \frac{1}{4} \).**