NCERT Solutions for Class 7th Maths Chapter 2 Operations with Integers
Updated on 2026-09-19
About this chapter
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
- A Quick Recap of Integers
- Multiplication of Integers
Quick revision
| 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 count → +, odd count → – | (–2)(–1)(–5)(–3) = 30 |
| Distributive | a × (b + c) = a × b + a × c | (–5) × (18 + (–3)) = –75 | Splits a hard product into two easy ones |
Exercises
- In-text Questions — A Quick Recap of Integers Page 25
- Figure it Out — A Quick Recap of Integers Page 26
- In-text Questions — A Quick Recap of Integers Page 26–27
- Try This — A Quick Recap of Integers Page 27
- In-text Questions — A Quick Recap of Integers Page 28
- In-text Questions — Multiplication of Integers Page 29–30
- Figure it Out — Multiplication of Integers Page 31
- Math Talk — Multiplication of Integers Page 31
- In-text Questions — Multiplication of Integers Page 32–33
- Figure it Out — Multiplication of Integers Page 33–34
- In-text Questions — Multiplication of Integers Page 34–35
- Brahmagupta’s Rules for Multiplication and Division · Examples 1 and 2 — In-text Questions Page 35–36
- A Magic Grid of Integers — Multiplication of Integers Page 37–38
- In-text Questions — Multiplication of Integers Page 38–39
- Figure it Out — Multiplication of Integers Page 39
- In-text Questions — Multiplication of Integers Page 39–41
- Try This — Multiplication of Integers Page 41
- Pick the Pattern — Multiplication of Integers Page 41–42
- Figure it Out — Multiplication of Integers Page 42–44
- Puzzle Time