Download Number Play – NCERT Class 8 Maths Chapter 5 PDF from the new NCERT Class 8 Maths book Ganita Prakash (2026-27). Read the chapter online or download the free PDF. Placing ‘+’ and ‘–’ signs between four numbers gives 8 expressions, and all 8 have the same parity. Switching one sign changes the value by 2 × (that number), an even change — so the parity can never change.
Number Play PDF – Chapter 5 of Ganita Prakash (Part I)
Read the chapter online or download the PDF.
| Chapter | Download | |
|---|---|---|
| Chapter 5 PDF | Number Play | View PDF |
| Full book | NCERT Class 8 Maths – Ganita Prakash | View Book |
Read Online
What Is in Number Play? (Class 8 Maths Chapter 5)
- Placing ‘+’ and ‘–’ signs between four numbers gives 8 expressions, and all 8 have the same parity. Switching one sign changes the value by 2 × (that number), an even change — so the parity can never change.
- The same idea, one level up: even numbers split into 4p and 4p + 2. Two of the same type add to a multiple of 4; one of each type never does. ‘Multiple of 4’ behaves exactly like ‘even’ does inside the whole numbers.
- Four divisibility facts are established and used throughout: if a number divides both M and N, it divides M + N and M – N; if A is divisible by k, then all multiples of A are divisible by k; if A is divisible by k, then A is divisible by every factor of k; and if A is divisible by both k and m, then A is divisible by LCM (k, m).
- Every place value is 1 more than a multiple of 9 (1 = 0 + 1, 10 = 9 + 1, 100 = 99 + 1, …). That single fact is the whole proof of the digit-sum test for 9 — and, since 9, 99, 999 are also multiples of 3, of the test for 3.
- Place values alternate 1 more, 1 less than a multiple of 11 (1, 10, 100, 1000 → +1, –1, +1, –1). So attaching alternating signs to the digits from the units place gives the remainder on division by 11.
- The digital root of a number is its remainder on division by 9, with 9 in place of 0. Cryptarithms are then solved by the same tools — place value, parity, divisibility and elimination.
Quick revision – Number Play
| Divisor | Shortcut | Why it works | Example |
|---|---|---|---|
| 10 | Units digit is 0 | Every place value above the units is a multiple of 10 | 4070 ✓, 4075 ✗ |
| 5 | Units digit is 0 or 5 | 10, 100, 1000 … are all multiples of 5 | 4075 ✓, 4073 ✗ |
| 2 | Units digit is even | 10, 100, 1000 … are all multiples of 2 | 708 ✓, 477 ✗ |
| 4 | Last two digits form a multiple of 4 | 100, 1000, 10000 … are multiples of 4 | 2856 → 56 ✓ |
| 8 | Last three digits form a multiple of 8 | 1000, 10000 … are multiples of 8 | 2856 → 856 = 8 × 107 ✓ |
| 3 | Digit sum is a multiple of 3 | 9, 99, 999 … are multiples of 3, so N and its digit sum leave the same remainder | 429714 → 27 ✓ |
| 9 | Digit sum is a multiple of 9 | 1 = 0 + 1, 10 = 9 + 1, 100 = 99 + 1, … | 405 → 9 ✓, 8888 → 32 ✗ |
| 11 | (sum of digits in the 1, 100, 10000 places) – (sum of digits in the 10, 1000 places) is 0 or a multiple of 11 | Place values are alternately 1 more and 1 less than a multiple of 11 | 462 → 4 – 6 + 2 = 0 ✓ |
| 6 | Divisible by 2 and by 3 | 2 and 3 are coprime, LCM (2, 3) = 6 | 186 ✓, 225 ✗ |
| 24 | Divisible by 3 and by 8 (not by 4 and 6) | 24 = 2³ × 3; LCM (4, 6) is only 12 | 12 passes 4 and 6 but fails 24 |
| Digital root | Add digits repeatedly to one digit | Adding digits never changes the remainder mod 9 | 489710 → 29 → 11 → 2 |
Old NCERT vs New – Class 8 Maths
This chapter is from Ganita Prakash, the new NCERT Class 8 Maths book (NCF-SE 2023, used from 2025-26). It replaced the old book “Mathematics”, so chapter numbers and names differ from older PDFs.
Solutions and All Chapters
Answers to the exercises and the full chapter list of Ganita Prakash:
Number Play – Overview
| Class | Class 8 |
| Subject | Maths |
| Book | Ganita Prakash – new NCERT book |
| Part | Part I |
| Chapter | 5 of 14 – Number Play |
| Book pages | 112 – 135 |
| Edition | NCERT Reprint 2026-27 |
| Session | 2026-27 |
| Free – read online or download |
Class 8 Maths Chapter 5 – FAQs
Where can I download Number Play Class 8 PDF?
From the download table on this page – the chapter PDF is free, and the full book is linked too.
What is Class 8 Maths Chapter 5 about?
Placing ‘+’ and ‘–’ signs between four numbers gives 8 expressions, and all 8 have the same parity. Switching one sign changes the value by 2 × (that number), an even change — so the parity can never change.
Is Number Play from the new NCERT Class 8 Maths book?
Yes. It is chapter 5 of ganita prakash (part i), the new NCERT Class 8 Maths book for 2026-27.
Is this the latest NCERT edition for 2026-27?
Yes – the PDF is NCERT’s latest edition for the 2026-27 session.
Where are the NCERT Solutions for Class 8 Maths Chapter 5?
Open the NCERT Solutions link above for answers to the exercise questions.