find a rational number between-2 and 1/2
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Answer:
How can I find 5 rational numbers between 1 and 2?
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I presume you mean a system to generate ALL rational numbers between 1 and 2.
Start by listing all fractions which sum to greater than or equal to 1, less than or equal to 2 with natural numbers that sum to 2. 0/2 is crossed out because it’s less than 1. 1/1 is your first number. 2/0 is infinite, greater than 2, so it’s crossed off your list
second step, list all fractions which sum to greater than or equal to 1, less than or equal to 2 with natural numbers that sum to 3. 0/3 and 1/2 are crossed off because less than 1. 2/1 is included in your list.
Third step, list all fractions which sum to greater than or equal to 1, less than or equal to 2 with natural numbers that sum to 4. 0/4 and 1/3 are crossed off, 2/2 makes your list, and 3/1 is crossed off.
Fourth step, list all fractions which sum to greater than or equal to 1, less than or equal to 2 with natural numbers that sum to 5. 0/5, 1/4, 2/3 and 4/1 are crossed off, but 3/2 makes your list.
In general , for step n, list all fractions which sum to greater than or less than 1, less than or equal to 2, with the sum of digits equal to n.
0/n, 1/(n-1), 2/(n-2)….. , x/(n-x) etc., and cross off all numbers less than 1 and greater than 2.
Using this system , you’re BOUND to hit every possible rational number sooner or later. For the fraction, 103/101, it will be the second number NOT crossed off in step 204, right after 102/102 which will have been duplicated previously when you hit 1/2, 2/2, 3/3, etc.
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