Answer:
31/13 could be tested by dividing it and obtaining its decimal expansion and if it has a decimal expansion that is terminating [it has limited decimal places] or repeating[the same number repeat with a pattern till infinity] it will be a rational number. And if it doesnt end or repat with a pattern, 31/13 will be an irrational number.
So lets divide 31 by 13 to get its DECIMAL EXPANSION
31/13 = 2.384615384615..............................
here in the answer we see that decimals 384615 repeats till infinity, so its a NON-TERMINATING[non-stopping or unlimitted] but REPEATING decimal expansion... thus 31/13 is a rational number
NOTE: SEE THE ATTACHMENT TO UNDERSTAND THE DIVISION PART AND I DONT RECOMMEND YOU USE A CALCULATOR FOR THESE SUCH QUESTIONS AS THE CALCULATORS GIVE U EXCAT RESULT BUT NOT THE FULL ONE LIKE IN THIS CASE AND ALL YOU WONT EVEN KNOW IF IT TERMINATES OR REPEATS SO BETTER DO IT IN PAPER AND SEE THE RESULT