five rational number between 2/3 and 3
Answers
I think you’ve been misled. There are a few more than 5 rational numbers between those two numbers - there are an infinite number. In fact there are an infinite number of rational numbers between any two numbers.
Here are some lists of rational numbers between 23 and 32 :
3/4, 4/5, 5/6, 6/7, 7/8, 8/9, 9/10, 10/11, 11/12, 12/13…
4/3, 5/4, 6/5, 7/6, 8/7, 9/8, 10/9, 11/10, 12/11, 13/12…
You can easily find many many more!
EDIT:
I hope you noticed the pattern/algorithm I used there. I love that about mathematics!
I did think of another way of generating lists of rational numbers between those two limits. Any finite decimal can be written as a fraction, eg 65.873 = 65873/100000. Now 23 is less than 0.7, and 32 is of course 1.5.
So, how about this list of rational numbers, that are between those limits:
7/10, 8/10, 9/10, 10/10, 11/10, 12/10, 13/10, 14/10.
And going down one level further:
71/100, 72/100, 73/100, …, 78/100, 79/100, 81/100, …, 138/100, 139/100
The next level down starts with 701/1000 and ends with 1399/1000.
Hopefully you can see how we can generate an infinite number of rationals in this way!
I know some of those fractions can be simplified, but I’m just trying to show the process.
That's what you needed.
