Chapter 5: Number PlayClass 8 Mathematics — summary, notes, extra questions & MCQ quiz

Summary

Number Play uses algebra, visualisation and reasoning to explore parity, divisibility and number puzzles. Beginning with sums of consecutive numbers and the parities of expressions \(a \pm b \pm c \pm d\), it shows all such combinations share the same parity. Algebra explains when expressions are always even — for example \(4m + 2q = 2(2m+q)\) is always even. The chapter develops general divisibility rules and proves why they work: divisibility by \(2, 5, 10\) from the units digit; by \(9\) and \(3\) from the digit sum (since each place value is one more than a multiple of \(9\)); and by \(11\) from the alternating digit sum (since place values alternate one more and one less than a multiple of \(11\)). Key divisibility laws are established: if \(a\) divides \(M\) and \(N\), it divides \(M+N\) and \(M-N\); if \(a\) is divisible by \(k\) then so are all multiples of \(a\); and if a number is divisible by both \(k\) and \(m\), it is divisible by their LCM. Digital roots and cryptarithms — puzzles where letters stand for digits — round out the playful but rigorous tour.

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