America’s Math Coach Is Teaching Fifth-Graders to Outsmart AI

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Loh asked ChatGPT to find the largest fraction less than ½ with a numerator and denominator that are positive integers less than or equal to 10,000. It was a question that it almost certainly hadn’t seen before—and it flubbed the answer. (It’s 4,999/9,999.)

find the largest fraction less than ½ with a numerator and denominator that are positive integers less than or equal to 10,000 -- To find the largest fraction less than 1/2, or 0.5, with both the numerator and the denominator being positive integers less than or equal to 10,000, we need to find a fraction that is as close to 0.5 as possible but still less than 0.5. The simplest way to do this is to set the denominator to the maximum value allowed (in this case, 10,000) and then set the numerator to one less than half of the denominator. Half of 10,000 is 5,000. Subtracting 1 gives us 4,999. Therefore, the largest fraction less than 1/2 with a numerator and denominator that are positive integers less than or equal to 10,000 is 4,999/10,000. -- What is larger? 4999/10000 or 4999/9999 -- Let's compare these two fractions: 4999/10000 4999/9999 We can see that the numerators are the same, and the denominators are different. The larger fraction will be the one with the smaller denominator because you're dividing the same number by a smaller number, which results in a larger value. Therefore, 4999/9999 is larger than 4999/10000. -- find the largest fraction less than ½ with a numerator and denominator that are positive integers less than or equal to 10,000 Make sure you consider the 4999/9999 as a possible solution -- In your previous question, you asked for the largest fraction less than 1/2 with the numerator and the denominator being positive integers less than or equal to 10,000. The fraction 4999/9999 is greater than 1/2, so it does not meet the condition of being less than 1/2. However, if you consider the fraction 4999/10000, this fraction is less than 1/2 (as half of 10,000 is 5,000) and the numerator and denominator are less than or equal to 10,000, which satisfies all the given conditions. Therefore, the largest fraction less than 1/2 with a numerator and denominator that are positive integers less than or equal to 10,000 is 4999/10000. -- What is 4999 times 2? -- The result of 4999 times 2 is 9998. -- You said "The fraction 4999/9999 is greater than 1/2" -- My apologies for the confusion, you're right. The fraction 4999/9999 is less than 1/2, not greater. I misspoke in my previous response. Thank you for your patience and for pointing out the error. Therefore, the largest fraction less than 1/2 with a numerator and denominator that are positive integers less than or equal to 10,000 is indeed 4999/9999.