Class 9 Maths Ch 3: What "rational" means, and why the denominator cannot be zero

Everyone can recite that you cannot divide by zero. Almost nobody can say why — and “it is not allowed” is a rule with the reason removed. Full topic page, with the transcript and the exact book reference: https://prepshorts.com/learn/class-9/... Everyone can recite that you cannot divide by zero. Almost nobody can say why, and the usual answer - that it is not allowed - is not a reason, it is a rule with the reason removed. This video derives it twice, from a definition, and shows it turning up in three different disguises in one topic. Start with what a rational number is: one integer over another, with the lower one non-zero. That last clause is the whole video. But first, the part people get wrong in the other direction - being rational is not about LOOKING like a fraction. Five is rational, because 5 = 5/1. Minus ten is rational. Every integer from -20 to 20 was searched for a writing and all 41 have one. The word describes what a number CAN be written as, not what it happens to look like on the page. Now the forbidden denominator. Division is meant to undo multiplication: 3/1 asks what number, multiplied by 1, gives 3. Search a thousand and one candidates and exactly one answers. Ask the same of 3/0 - what number, multiplied by 0, gives 3 - and out of the same 1001, none works, because multiplying by nought sends every one of them to the same place, and that place is nought. Then the case people expect to be easier: 0/0. Every single one of the 1001 works. Nothing to give back, or too much to give back; a value that could be anything is not a value. Neither answer was forbidden - both were searched for and found to fail, in opposite directions. CHAPTERS 0:00 One field, three children 0:46 Every fraction has an opposite 1:23 Where the minus may sit 2:06 Five was rational all along 3:11 Nothing to give back 4:06 Too much to give back 4:51 One point, many names 5:33 Choosing one to stand for all 6:28 The cross test 7:30 The four operations 8:19 Three conditions, not two 9:03 Closed, with one asterisk IN THE BOOK Class 9 Mathematics, Chapter 3, "The World of Numbers". NCERT Ganita Manjari, Grade 9 Mathematics, NCF-SE 2023 (Part I), printed pp. 41–67. ABOUT PREPSHORTS One short video per NCERT topic, with the book open beside it. Not worked answers to the exercises — the reason each result has to hold, which is the half that carries into a question you have not seen before. The full library is 708 videos across Classes 6 to 12, about 147 hours in all. 88 are free to watch, one opening every chapter. https://prepshorts.com/?utm_source=yo...