Summary
Chapter 5 of Class 8 maths, "Number Play", explores patterns and properties of numbers, focusing on divisibility rules, parity (even and odd numbers), properties of multiples and factors, and number puzzles like cryptarithms and digital roots.
This chapter investigates the mathematical patterns underlying number properties through exploration and reasoning. Students learn divisibility shortcuts for 2, 3, 4, 5, 8, 9, 10, and 11 by understanding how place values relate to remainders. The chapter covers parity rules (how even and odd numbers behave under addition, subtraction, and multiplication), relationships between multiples and factors, and techniques like digital roots (repeatedly summing digits until a single digit remains). Through algebraic proofs and visualization, students discover why these shortcuts work and apply logical reasoning to solve number puzzles.
Key points & formulas
- 01Parity rules: odd ± odd = even; even ± even = even; odd ± even = odd; switching +/- signs between numbers changes the result by an even amount
- 02Divisibility by 10, 5, 2: determined by the units digit (0 for 10; 0 or 5 for 5; even for 2)
- 03Divisibility by 9: a number is divisible by 9 if and only if the sum of its digits is divisible by 9; digital root (repeated digit sum) equals the remainder when divided by 9
- 04Divisibility by 3: a number is divisible by 3 if the sum of its digits is divisible by 3
- 05Divisibility by 11: alternating digit sums — add digits in odd places, subtract digits in even places; if difference is 0 or multiple of 11, the number is divisible by 11
- 06Multiples of 4: two groups of even numbers — multiples of 4 (remainder 0) and non-multiples of 4 (remainder 2); sum of two multiples of 4 is always a multiple of 4; sum of two non-multiples of 4 is also a multiple of 4
- 07Cryptarithms: puzzles where letters represent digits; solved using divisibility properties, place values, and logical constraints
Frequently asked questions
01What is Number Play about?
Number Play (Chapter 5, Class 8 Maths) is about discovering and understanding patterns in numbers. It teaches how to quickly check if a number is divisible by other numbers using shortcuts, why those shortcuts work through algebra, and how to solve number puzzles using logic and divisibility rules.
02What are divisibility rules and why do they work?
Divisibility rules are shortcuts to check if one number divides another without doing the full division. For example, a number is divisible by 9 if the sum of its digits is divisible by 9. These work because place values (10, 100, 1000, ...) have predictable remainders when divided by certain numbers — for 9, every place value leaves remainder 1, so only the sum of digits matters.
03What is a digital root and how is it used?
A digital root is found by repeatedly adding the digits of a number until a single digit remains. For example, 489710 has digital root 2 (4+8+9+7+1+0=29, then 2+9=11, then 1+1=2). The digital root equals the remainder when the number is divided by 9 (or 9 itself if the number is a multiple of 9). It's useful for checking divisibility and verifying arithmetic calculations.
04How do I check if a number is divisible by 11?
Place alternating + and − signs before each digit starting from the units digit (right to left), then evaluate. For example, for 328105: −3+2−8+1−0+5 = −3. If the result is 0 or a multiple of 11, the number is divisible by 11. Otherwise, the result is the remainder.
05Is the Class 8 Maths Number Play PDF free to download?
Yes, the NCERT Class 8 Maths textbook Chapter 5 (Number Play) is free to download. No sign-up or payment is required — it's part of the official NCERT curriculum provided by the Government of India.
More chapters in Ganita Prakash
This is the complete Ganita Prakash Chapter 5 as published by NCERT — every diagram, solved example, and exercise included, free. Browse all NCERT Class 8 textbooks.
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