Question 1 - Figure it out (Page 54) - The Mechanism of Counting - Chapter 3 Class 8 - A Story of Numbers (Ganita Prakash)

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Question 1 - Figure it out (Page 54) Suppose you are using the number system that uses sticks to represent numbers, as in Method 1. Without using either the number names or the numerals of the Hindu number system, give a method for adding, subtracting, multiplying and dividing two numbers or two collections of sticks. We have two groups of sticks. Let's call them Group A & Group B. Let’s check them one by one Addition (A + B): To add two groups of sticks, we simply combine all the sticks from the first group with all the sticks from the second group and count the total. Subtraction (A – B): A – B means we need to find out what's left of Group A after "taking away" Group B. To subtract, we follow these steps Take one stick from Group B and one stick from Group A and set them aside. Repeat this one-to-one mapping: take another stick from B and another from A and discard them. Continue until Group B is completely gone. The sticks that remain in Group A are the answer. Multiplication (A × B) This is "repeated addition”. You want to find out what you get if you add Group A to itself, B times. Start with an empty space for your "Result Group." Take one stick from Group B. In your Result Group, create an exact copy of Group A. Take another stick from Group B. Add another exact copy of Group A to your Result Group. Repeat this process until you have used every stick in Group B. The final, large collection of sticks in the Result Group is the answer. Division (A ÷ B) This is "repeated subtraction". You want to find out how many times Group B can "fit into" Group A. Start with Group A. Have an empty space for your "Quotient Group" (the answer). From Group A, remove a group of sticks that is the same size as Group B. For successfully doing this one time, place one stick into your Quotient Group. Look at the sticks remaining in Group A. If you can, remove another group of sticks the same size as Group B. When you do, place another one stick into your Quotient Group. Keep repeating this until Group A is either empty or has fewer sticks than Group B (this would be the "remainder"). The final collection of sticks in your Quotient Group is the answer.