Ex. 3.1 The World of Numbers | Ch-3 Class 9 Maths Ganita Manjari | Sanyam Bhayana

Complete solutions for Ex. 3.1 of Class 9 Maths Ganita Manjari Chapter 3 — The World of Numbers. Covers the Lothal merchant proportion problem, the Ishango bone prime number pattern, closure property of natural numbers under addition and subtraction, and the ancient base-12 counting system. New NCERT 2026-27 syllabus. 📌 TELEGRAM (NOTES): https://t.me/+cbiN5dwvTSNkZTg1 📲 INSTAGRAM:   / sanyambhayanaclass9and10   ___________________________________________ ✅ QUESTIONS COVERED IN THIS LECTURE: Q1. A merchant in the port city of Lothal is exchanging bags of spices for copper ingots. He receives 15 ingots for every 2 bags of spices. If he brings 12 bags of spices to the market, how many copper ingots will he leave with? Q2. Look at the sequence of numbers on one column of the Ishango bone: 11, 13, 17, 19. What do these numbers have in common? List the next three numbers that fit this pattern. Q3. We know that natural numbers are closed under addition — the sum of any two natural numbers is always a natural number. Are they closed under subtraction? Provide a couple of examples to justify your answer. Q4. Ancient Indians used the joints of their fingers to count, a practice still seen today. Each finger has three joints, and the thumb is used to count them. How many can you count on one hand? How does this relate to the ancient base-12 counting system? ___________________________________________ 📚 This lecture is useful for Class 9 students of CBSE, ICSE, UP Board, Bihar Board, MP Board, Haryana Board, Punjab Board, and all other state boards following the Ganita Manjari / NCERT syllabus for Session 2026-27. ___________________________________________ 👨‍🏫 ABOUT THE TEACHER: Sanyam Bhayana is a Class 12 State Topper (99.8%) and Gold Medalist from Shri Ram College of Commerce (SRCC), New Delhi. He has helped hundreds of students score 100/100 in board exams. ___________________________________________ ⏱ CHAPTERS: 0:00 Introduction to Chapter 3 — The World of Numbers 0:31 Q1 — Lothal Merchant Proportion Problem 4:01 Q2 — Ishango Bone Prime Number Pattern 6:47 Q3 — Closure of Natural Numbers Under Subtraction 9:32 Q4 — Finger Joints and the Base-12 Counting System ___________________________________________ 💬 Got a doubt? Drop it in the comments — Sanyam Sir answers personally. ___________________________________________ 📂 CLASS 9 MATHS COMPLETE NCERT PLAYLIST: Class 9 Maths Ganita Manjari:    • CLASS 10 MATHS FULL COURSE (2026-2027)   ___________________________________________ Ex. 3.1 of Class 9 Maths Ganita Manjari Chapter 3 — The World of Numbers — introduces the history of counting through the Lothal merchant problem, the Ishango bone, closure properties of natural numbers, and the ancient base-12 counting system. Essential for CBSE, UP Board, Haryana Board, and all state boards using the new NCERT 2026-27 textbook. Ex 3.1 Class 9 Maths The World of Numbers, Ganita Manjari chapter 3 exercise 3.1, class 9 maths chapter 3 solutions, the world of numbers class 9 Ganita Manjari, Lothal merchant problem class 9 maths, Ishango bone class 9 maths, closure property natural numbers class 9, base 12 counting system class 9, Ganita Manjari class 9 new NCERT 2026-27, class 9 maths chapter 3 new chapter, class 9 maths CBSE 2026, class 9 maths in Hindi, Sanyam Bhayana