Question 2 - Figure it out - Page 60, 61 - Chapter 3 Class 8 - A Story of Numbers (Ganita Prakash)

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Question 2 (i) 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: Let’s remember are Gumulgal number system Gumulgal (Australia) urapon ukasar ukasar-urapon ukasar-ukasar ukasar-ukasar-urapon ukasar-ukasar-ukasarWe note that it uses two words urapon = 1 ukasar = 2 And the rest of the words are formed using these two To answer our questions, we need to translate the words into values, do the math, and then translate the answer back into Gumulgal words. Let’s start Question 2 (i) (i) (ukasar-ukasar-ukasar-ukasar-urapon) + (ukasar-ukasar-ukasar-urapon)Now, (ukasar-ukasar-ukasar-ukasar-urapon) = 2 + 2 + 2 + 2 + 1 = 9 (ukasar-ukasar-ukasar-urapon) = 2 + 2 + 2 + 1 = 7 Now, 9 + 7 = 16 Converting back 16 = 8 × 2 = 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 = ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar Thus, answer is ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar Question 2 (ii) (ii) (ukasar-ukasar-ukasar-ukasar-urapon) – (ukasar-ukasar-ukasar)Now, (ukasar-ukasar-ukasar-ukasar-urapon) = 2 + 2 + 2 + 2 + 1 = 9 (ukasar-ukasar-ukasar) = 2 + 2 + 2 = 6 Now, 9 – 6 = 3 Now, (ukasar-ukasar-ukasar-ukasar-urapon) = 2 + 2 + 2 + 2 + 1 = 9 (ukasar-ukasar-ukasar) = 2 + 2 + 2 = 6 Now, 9 – 6 = 3 Converting back 3 = 2 + 1 = ukasar-urapon Thus, answer is ukasar-urapon Question 2 (iii) (iii) (ukasar-ukasar-ukasar-ukasar-urapon) × (ukasar-ukasar)Now, (ukasar-ukasar-ukasar-ukasar-urapon) = 2 + 2 + 2 + 2 + 1 = 9 (ukasar-ukasar) = 2 + 2 = 4 Now, 9 × 4 = 36 Converting back 36 = 18 × 2 = (2 + 2 + 2 + 2) + (2 + 2 + 2 + 2) + (2 + 2 + 2 + 2) + (2 + 2 + 2 + 2) + (2 + 2 + 2 + 2) + (2 + 2 + 2 + 2) + (2 + 2 + 2 + 2) + (2 + 2 + 2 + 2) + (2 + 2 + 2 + 2) = ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar Thus, this is the answer Question 2 (iv) (iv) (ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar) ÷ (ukasar-ukasar)Now, (ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar) = 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 = 8 × 2 = 16 (ukasar-ukasar) = 2 + 2 = 4 Now, 16 ÷ 4 = 4 Converting back 4 = 2 + 2 = ukasar-ukasar Thus, answer is ukasar-ukasar