Suppose you are using the number system that uses sticks to represent numbers, as in Method 1. Class 8

Suppose you are using the number system that uses sticks to represent numbers, as in Method 1. Class 8

Question 1.

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. Class 8

Solution:

Adding : Combined the sticks of both the groups and then count them. This will give the sum of the number of sticks of the two groups.

Subtracting : Take the sticks of the two groups and match one-to-one sticks of one group with the sticks of the other group. The remaining unmatched sticks of the larger group will give the difference of the two numbers.

Multiplication : Count the sticks of one group as many times as the number of sticks in the other group. The final count will give the product of two numbers.

Division : Repeatedly match the sticks of the smaller group with those of the larger group, setting aside the matched sticks of the larger group. When the remaining sticks of the larger group become less than that of the smaller group, then these remaining sticks will give the remainder. The number of times of matchings will give the quotient.

Question 2.

One way of extending the number system in Method 2 is by using strings with more than one letter — for example, we could use 'aa' for 27. How can you extend this system to represent all the numbers? There are many ways of doing it! Class 8

Solution:

One of the ways may be ‘bb’ for 28, ‘cc’ for 29, ‘dd’ for 30, and so on, finding ‘zz’ for 52, ‘acta’ for 53, ‘bbb’ for 54, ..., ‘zzz’ for 81, and so on.

Question 3.

Try making your own number system. Class 8

Solution:

Note : Do as directed.