Ch 16 explores number properties using algebra. Students learn to write numbers in generalised form, prove divisibility rules algebraically, and solve number puzzles using logical reasoning.
A 2-digit number with digits a, b is written as 10a + b. A 3-digit number with digits a, b, c is 100a + 10b + c. This representation helps prove divisibility properties algebraically.
By 2: last digit is even (0,2,4,6,8). By 3: sum of digits is divisible by 3. By 5: last digit is 0 or 5. By 9: sum of digits is divisible by 9. By 11: difference between sum of digits at odd and even positions is 0 or divisible by 11.
Puzzles involve finding missing digits in addition, subtraction, or multiplication where letters replace digits. Use divisibility rules and logical deduction to solve these.
Download: https://ncert.nic.in/textbook/pdf/hemh116.pdf | Complete book: https://ncert.nic.in/textbook/pdf/hemh1ps.zip
Any number can be written as a sum of multiples of powers of 10. Since 10 ≡ 1 (mod 3), each power of 10 leaves remainder 1. So the number's remainder when divided by 3 equals the sum of its digits mod 3.
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