Question

Choose a rational number that lie between 1/6 and -1/5. *
7/30
-7/30
-3/30
-11/30

Answer 1

explaining what a rational number is and how there is an actually an infinite number of rational numbers that satisfy this question. I am going to assume the reader understands what a rational number is and just give a simpler, more practical method of answering the question.

We are looking for any rational number between 1.5 and 1.6. I have noticed that if you take fractions of any numerator over the denominator of 9, you get a simple infinitely repeating decimal.

For example: 1/9 = 0.111…

You may note that 5/9 gives us the repeating fraction 0.555…

We also know that if you have the same number in both the denominator and the numerator the answer is equal to 1. Hence, 9/9 = 1.

So it should be apparent that if you had 5/9 + 9/9 = 14/9, then we get a number that clearly comes between 1.5 and 1.6.

14/9 = 1.555 ….

I also like using 11 as a denominator as it also gives simple repeating decimal answers. For example 6/11 = 0.5454… Thus another good option is 11/11 + 6/11 = 17/11.

17/11 = 1.5454… which is also clearly between 1.5 and 1.6.

So those are two types of fractions to look at when looking for an easy example.