The World of Numbers • Class 9 Mathematics • Ganita Manjari
Practice Mode: पहले question खुद solve करें। समझ न आए तो 🇮🇳 हिंदी में समझें दबाएँ। उसके बाद Solution देखें से diagram और पूरा solution check करें।
Exercise Focus: Lothal trade, prime numbers, natural numbers की closure property और base-12 counting.
Question 1
Lothal Trade and Ratio
A merchant in the port city of Lothal receives 15 copper ingots for every 2 bags of spices. If he brings 12 bags of spices to the market, how many copper ingots will he receive?
हिंदी में समझें:
Given: 2 bags → 15 ingots. 12 bags = 6 groups of 2 bags. Therefore ingots = 6 × 15 = 90.
Step-by-Step Solution:
Visual: Diagram को देखकर question की quantity, pattern या number operation को समझें।
Look at the sequence 11, 13, 17, 19. What do these numbers have in common? List the next three numbers that fit this pattern.
हिंदी में समझें:
All four numbers are prime numbers. The next prime numbers after 19 are 23, 29 and 31.
Step-by-Step Solution:
Visual: Diagram को देखकर question की quantity, pattern या number operation को समझें।
All four numbers are prime numbers. The next prime numbers after 19 are 23, 29 and 31.
✅ Final Answer: 23, 29 and 31
Question 3
Closure Property of Natural Numbers
Natural numbers are closed under addition. Are they closed under subtraction? Give a couple of examples to justify your answer.
हिंदी में समझें:
No. For example, 7 − 3 = 4, which is natural, but 3 − 7 = −4, which is not a natural number. Since subtraction can take us outside the set of natural numbers, natural numbers are not closed under subtraction.
Step-by-Step Solution:
Visual: Diagram को देखकर question की quantity, pattern या number operation को समझें।
No. For example, 7 − 3 = 4, which is natural, but 3 − 7 = −4, which is not a natural number. Since subtraction can take us outside the set of natural numbers, natural numbers are not closed under subtraction.
✅ Final Answer: No, natural numbers are not closed under subtraction.
Question 4
Ancient Base-12 Counting
Ancient Indians used the joints of their fingers to count, with the thumb acting as a pointer. If each of the four fingers has 3 joints, how many positions can be counted on one hand? What base does this suggest?
हिंदी में समझें:
There are 4 fingers and each has 3 joints. Number of positions = 4 × 3 = 12. Therefore the method suggests a base-12 number system.
Step-by-Step Solution:
Visual: Diagram को देखकर question की quantity, pattern या number operation को समझें।
There are 4 fingers and each has 3 joints. Number of positions = 4 × 3 = 12. Therefore the method suggests a base-12 number system.