Class 8 Maths Ch 5 Number Play | Writing "leaves remainder r" as an algebraic expression

“Leaves 3 when you divide by 5” is not a fact about a number. It names an endless, evenly spaced family. Full topic page, with the transcript and the exact book reference: https://prepshorts.com/learn/class-8/... "LEAVES 3 WHEN YOU DIVIDE BY 5" IS NOT A FACT ABOUT A NUMBER. It names an endless, evenly spaced FAMILY - the multiples of 5 pushed 3 steps along - and once you see that, the reason for writing it as 5k + 3 stops being notation and becomes the point. Ask for one such number and you get 8; ask for another and you do not search, you add 5, because adding 5 cannot move the leftover. 3, 8, 13, 18, 23, and it runs backwards too: -2 leaves 3 under 5 just as 3 does. FIRST, WHAT A REMAINDER IS ALLOWED TO BE. 23 is 4 fives and 3 more; you could also say 23 is 2 fives and 13 more and be arithmetically right and useless, because 13 still has fives inside it. A remainder is never negative and never reaches the divisor - across a sweep of 1991 divisions here, in a range that runs below zero, that holds every time. SIX EXPRESSIONS ARE OFFERED AND EXACTLY 2 SURVIVE, and the video argues the rejections the source does not. 3k + 5 gives 5, 8, 11, 14 - it steps by 3, and a family stepping by 3 is not the family stepping by 5 whatever you add on the end, so the number in FRONT of the letter is the divisor and not decoration. 5k - 3 steps by 5 correctly and still fails: it gives 2, 7, 12, so right step, wrong family. What passes has to produce every member of the family AND nothing else - a test that only looks one way lets 10k + 3 through, which produces nothing but family members and misses most of them. THE TWO SURVIVORS ARE THE SAME FAMILY UNDER TWO NAMES. CHAPTERS 0:00 Find one, then another, and watch the step 0:48 What a leftover actually is 1:37 The multiples of 5, pushed 3 along 2:15 Six expressions, and how to test one 3:20 The number in front sets the step 4:10 The same family under a second name 5:08 Complete rows, and one short row 5:52 Two conditions at once, not added together 6:50 Adding without dividing 7:50 When the answer lands outside the range 8:50 A riddle that is only a list of conditions 9:42 One short of everything IN THE BOOK Class 8 Mathematics, Chapter 5, "Number Play". NCERT Ganita Prakash, Textbook of Mathematics for Grade 8, Part I (NCF-SE 2023). 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...