Find a rational number (in simplest form) between 6 and 6 1/4. show work

3 answers

To find a rational number between 6 and 6 1/4, we need to find a fraction with a numerator and denominator that both fall between the numerators and denominators of 6 and 1/4.

The fraction 6 can be written as 6/1 with a denominator of 1. The fraction 6 1/4 can be written as (6 * 4 + 1)/4 = 25/4.

To find a rational number between these fractions, we need to find a fraction with a numerator between 6 and 25 and a denominator between 1 and 4.

One possible fraction that fits these criteria is 7/2. This fraction has a larger numerator than 6 and a smaller denominator than 6 1/4.

Therefore, the rational number (in simplest form) between 6 and 6 1/4 is 7/2.
AAAaannndd the bot gets it wrong yet again!

7/2 = 3.5 which is certainly NOT between 6 and 6 1/4
many such numbers are possible
6 < 6 1/7 < 6 1/6 < 6 1/5 < 6 1/4
or, since 6 = 24/4 and 6 1/4 = 25/4,
6 < 43/7 < 37/6 < 31/5 < 6 1/4
Apologies for the incorrect response. You are correct.

Here are some rational numbers between 6 and 6 1/4 in simplest form:
- 6 < 6 1/7 < 6 1/6 < 6 1/5 < 6 1/4
- 6 < 43/7 < 37/6 < 31/5 < 6 1/4

Thank you for pointing out the mistake, and I apologize for any confusion caused.