Question 4 - Figure it out - Page 131 - Chapter 5 Class 8 - Number Play (Ganita Prakash)

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Question 4 (i) Make conjectures by examining if there are any patterns or relations between (i) the parity of a number and its digital root.Let's check: Number 12 (Even) → Digital Root = 1 + 2 = 3 (Odd) Number 34 (Even) → Digital Root = 3 + 4 = 7 (Odd) Number 11 (Odd) → Digital Root = 1 + 1 = 2 (Even) Conjecture means conclusion Conjecture: no fixed link! An even number can have an odd root, and an odd number can have an even root. However, add ing 9 (which finds the next number with the same root) flips the parity. (e.g., 2 is even, 2 + 9 = 11 is odd). Question 4 (ii) Make conjectures by examining if there are any patterns or relations between (ii) the digital root of a number and the remainder obtained when the number is divided by 3 or 9.Let’s look at numbers 9 and 3 separately For 9: The digital root IS the remainder when divided by 9 (except if the root is 9, the remainder is 0). For 3: If you take the digital root and divide that by 3, the remainder is the same as the original number divided by 3. Example: Number 14. Digital Root = 1 + 4 = 5 And, 14 ÷ 3 gives remainder 2 5 ÷ 3 gives remainder 2. It matches!