Download Operations with Integers – NCERT Class 7 Maths Chapter 10 PDF from the new NCERT Class 7 Maths book Ganita Prakash (2026-27). Read the chapter online or download the free PDF. A movement on a number line carries two pieces of information — magnitude (how far) and direction (left or right). Writing it as a positive or negative integer stores both, so two strikes of a carrom coin always land at P = a + b.
Operations with Integers PDF – Chapter 10 of Ganita Prakash (Part II)
Read the chapter online or download the PDF.
| Chapter | Download | |
|---|---|---|
| Chapter 10 PDF | Operations with Integers | View PDF |
| Full book | NCERT Class 7 Maths – Ganita Prakash | View Book |
Read Online
What Is in Operations with Integers? (Class 7 Maths Chapter 10)
- A movement on a number line carries two pieces of information — magnitude (how far) and direction (left or right). Writing it as a positive or negative integer stores both, so two strikes of a carrom coin always land at P = a + b.
- In the token model, a green token is +1 and a red token is –1. A green and a red together make a zero pair, so you may drop as many zero pairs into the bag as you like without changing its value.
- The multiplier says what to do and how often; the multiplicand says what to do it with. A positive multiplier puts tokens in, a negative multiplier takes tokens out. That single idea gives all four sign cases.
- The four results are 4 × 2 = 8, 4 × (–2) = –8, (–4) × 2 = –8 and (–4) × (–2) = 8. So the magnitudes multiply as usual, and the product is positive for like signs, negative for unlike signs. Division follows the same rule.
- Brahmagupta stated these rules in the Brāhmasphuṭasiddhānta (628 CE) using dhana (fortune) for positive and ṛṇa (debt) for negative — the first time anyone wrote them down.
- Integer multiplication is commutative (a × b = b × a), associative (a × (b × c) = (a × b) × c) and distributive over addition (a × (b + c) = a × b + a × c) — exactly as for whole numbers.
Quick revision – Operations with Integers
| Idea | Rule | Example | What it means |
|---|---|---|---|
| Sum and difference | First = (sum + difference) ÷ 2 | Sum 25, difference 11 → 18 and 7 | One guess-and-check table finds any such pair |
| Two strikes | P = a + b | 5 + (–7) = –2 | Right is +, left is –; P is the final position |
| Zero pair | 1 green + 1 red = 0 | Add 11 zero pairs to take 18 from 7 | Lets you remove more than the bag holds |
| Subtraction | A – b = a + (–b) | 7 – 18 = 7 + (–18) = –11 | Subtracting is adding the additive inverse |
| Positive × positive | Positive | 4 × 2 = 8 | Put 2 greens in, 4 times |
| Positive × negative | Negative | 4 × (–2) = –8 | Put 2 reds in, 4 times |
| Negative × positive | Negative | (–4) × 2 = –8 | Take 2 greens out, 4 times |
| Negative × negative | Positive | (–4) × (–2) = 8 | Take 2 reds out, 4 times |
| Division | A ÷ (–b) = –(a ÷ b), (–a) ÷ (–b) = a ÷ b | (–100) ÷ 25 = –4 | Turn it into 25 × ? = –100 |
| –1 × a | –1 × a = –a | –1 × (–31) = 31 | Multiplying by –1 gives the additive inverse |
| Many factors | Count the negative factors: even → +, odd → – | (–2) × (–1) × (–5) × (–3) = 30 | Four negative factors, so the product is positive |
| Distributive | A × (b + c) = a × b + a × c | (–5) × (18 + (–3)) = –75 | Splits a hard product into two easy ones |
Old NCERT vs New – Class 7 Maths
This chapter is from Ganita Prakash, the new NCERT Class 7 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:
Operations with Integers – Overview
| Class | Class 7 |
| Subject | Maths |
| Book | Ganita Prakash – new NCERT book |
| Part | Part II |
| Chapter | 10 of 15 – Operations with Integers |
| Book pages | Part II, 25 – 45 |
| Edition | NCERT Reprint 2026-27 |
| Session | 2026-27 |
| Free – read online or download |
Class 7 Maths Chapter 10 – FAQs
Where can I download Operations with Integers Class 7 PDF?
From the download table on this page – the chapter PDF is free, and the full book is linked too.
What is Class 7 Maths Chapter 10 about?
A movement on a number line carries two pieces of information — magnitude (how far) and direction (left or right). Writing it as a positive or negative integer stores both, so two strikes of a carrom coin always land at P = a + b.
Is Operations with Integers from the new NCERT Class 7 Maths book?
Yes. It is chapter 10 of ganita prakash (part ii), the new NCERT Class 7 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 7 Maths Chapter 10?
Open the NCERT Solutions link above for answers to the exercise questions.