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.
Addition: Combine both collections of sticks together. Count the total number of sticks by making a one-to-one mapping with a standard sequence.
Subtraction: Remove sticks from the larger collection equal to the number of sticks in the smaller collection. The remaining sticks represent the difference.
Multiplication: Create multiple collections of sticks, each equal to one number. Repeat as many times as the other number. Combine all collections.
Division: Distribute the sticks of the larger collection equally into groups of the size of the smaller number. Count how many groups are formed.
Explanation
The chapter explains that in Method 1, sticks are used to represent numbers through one-to-one mapping. Each stick corresponds to one object being counted. Arithmetic operations can be performed physically with sticks without using number names or Hindu numerals. Addition involves combining collections, subtraction involves removing sticks, multiplication involves creating repeated collections, and division involves distributing sticks into equal groups.
Solution Steps
Addition: Combine both collections of sticks together and count the total using one-to-one mapping with a standard sequence.
Subtraction: Remove sticks from the larger collection equal to the smaller collection; remaining sticks represent the difference.
Multiplication: Create multiple collections of sticks (each equal to one number), repeat as many times as the other number, then combine all collections.
Division: Distribute sticks of the larger collection equally into groups of the size of the smaller number, then count how many groups are formed.