Consider the extension of the Gumulgal number system beyond 6 in the same way of counting by 2s. Come up with ways Class 8

Consider the extension of the Gumulgal number system beyond 6 in the same way of counting by 2s. Come up with ways Class 8

Question 1.

Consider the extension of the Gumulgal number system beyond 6 in the same way of counting by 2s. Come up with ways of performing the different arithmetic operations (+, –, ×, ÷) for numbers occurring in this system, without using Hindu numerals. Use this to evaluate the following: Class 8

(i) (ukasar-ukasar-ukasar-ukasar- urapon) + (ukasar-ukasar-ukasar-urapon)

(ii) (ukasar-ukasar-ukasar-ukasar- urapon) – (ukasar-ukasar-ukasar)

(iii) (ukasar-ukasar-ukasar-ukasar- urapon) × (ukasar-ukasar)

(iv) (ukasar-ukasar-ukasar-ukasar- ukasar-ukasar-ukasar-ukasar) ÷ (ukasar- ukasar)

Solution:

(i) (ukasar-ukasar-ukasar-ukasar-urapon) + (ukasar-ukasar-ukasar-urapon) = ukasar-ukasar-ukasar-ukasar-ukasar -ukasar-ukasar-ukasar

= 16.

(ii) ukasar-ukasar-ukasar- ukasar-urapon– (ukasar-ukasar-ukasar)

= ukasar-urapon

= 3.

(iii) (ukasar-ukasar-ukasar-ukasar-urapon) × (ukasar-ukasar)

= ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar

= 36.

Here, ukasar × ukasar = ukasar-ukasar- ukasar-ukasar and urapon × ukasar = ukasar

(iv) = (ukasar-ukasar-ukasar-ukasar

ukasar-ukasar-ukasar-ukasar) ÷ (ukasar-ukasar)

= ukasar-ukasar = 4.

(8 ukasar divided in two groups of 4 ukasar) In Hindu numerals,

(i) 9 + 7 = 16

(ii) 9 – 6 = 3

(iii) 9 × 4 = 36

(iv) 16 ÷ 4 = 4.