The NCERT Notes for Class 7 Mathematics Part 2 Chapter 2 Operations with Integers cover number-line movement, token models, multiplication, division and integer properties for the 2026-27 textbook. Use these notes to revise sign rules and word-problem models before solving the chapter exercises.
- Resource: Class 7 Maths Part 2 Chapter 2 Notes PDF.
- Chapter focus: additive inverse, multiplication signs, division signs and integer expressions.
- Revision use: quick sign tables, examples and common-trap checks.
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Student Feedback: Students usually improve after they separate two steps: multiply the magnitudes first, then decide the sign.
Operations with Integers Class 7 Notes Overview
Operations with Integers starts from familiar models: number-line movement, token pairs and sums or differences. The chapter then uses these models to build multiplication and division rules for positive and negative numbers.
The main rule is simple. For multiplication and division, same signs give a positive result, while different signs give a negative result. The magnitude is still found by multiplying or dividing the usual positive numbers.
Integer Models and Sign Rules
The number line shows direction. A right movement is positive and a left movement is negative. Token models show cancellation because one positive token and one negative token make a zero pair.
| Idea | Rule | Example |
|---|---|---|
| Additive inverse | Subtract by adding the opposite | 4 - (-12) = 4 + 12 |
| Multiplication | Same signs positive, different signs negative | (-6) x (-3) = 18 |
| Division | Use the same sign rule as multiplication | 36 ÷ (-18) = -2 |
| Many factors | Odd negative count gives negative | (-1) x (-1) x (-1) = -1 |
Operations with Integers Video Lesson
Source: YouTube classroom video
Multiplication, Division and Properties in Operations with Integers
Integer multiplication is commutative and associative. This means factors can be swapped or grouped without changing the product. The distributive property also works for integers.
| Property | Form | Use |
|---|---|---|
| Commutative | a x b = b x a | Swap factors safely |
| Associative | a x (b x c) = (a x b) x c | Group three factors |
| Distributive | a x (b + c) = a x b + a x c | Expand brackets |
| Division as missing factor | b x ? = a | Reframe integer division |
Word Problems in Operations with Integers
Word problems become easier when each quantity is assigned a sign first. Profit, upward movement and correct-answer marks are positive. Loss, downward movement, temperature fall and wrong-answer marks are negative.
- Exam score: correct marks are positive, wrong marks are negative.
- Elevator: upward movement is positive and downward movement is negative.
- Temperature: a fall each hour is repeated negative change.
- Profit-loss: profit is positive and loss is negative.
How to Use These Operations with Integers Notes
Start by revising the sign table. Then solve three examples: one token question, one multiplication question and one word problem. This checks all major ideas in the chapter.
- Rewrite subtraction as addition of the opposite.
- Find magnitudes before deciding signs in multiplication and division.
- Count negative factors in long products.
- State what the answer means in word problems.
Do not skip the final sentence in a word problem. A result of -120 in the elevator question means 120 metres below ground level.
Class 7 Maths Part 2 Chapter 2 Resource Links
Use these related resources when you want the same chapter in another format.
| Resource | Best use | Link |
|---|---|---|
| NCERT Notes | Quick concept revision | Open notes |
| NCERT Solutions | Step-by-step answers for textbook questions | Open solutions |
| Handwritten Notes | Fast visual revision | Open handwritten notes |
| NCERT Book PDF | Official textbook chapter | Open book PDF |
All NCERT Notes for Class 7 Mathematics Part 2 Chapters
| Chapter | Title | Notes link |
|---|---|---|
| Chapter 1 | Geometric Twins | Open Notes |
| Chapter 2 | Operations with Integers | Open Notes |
| Chapter 3 | Finding Common Ground | Open Notes |
| Chapter 4 | Another Peek Beyond the Point | Open Notes |
Operations with Integers Class 7 Maths NCERT Notes FAQs
Ques. What does Class 7 Maths Chapter 2 Operations with Integers explain?
Ans. It explains integer addition, subtraction, multiplication, division, sign rules and properties through token and number-line models.
Ques. What is the rule for multiplying two integers?
Ans. Same signs give a positive product, and different signs give a negative product. Multiply the magnitudes first.
Ques. What is the rule for dividing integers?
Ans. Integer division follows the multiplication sign rule. Same signs give a positive quotient and different signs give a negative quotient.
Ques. Do these notes follow the 2026-27 NCERT textbook?
Ans. Yes. The notes follow the 2026-27 Ganita Prakash Class 7 Mathematics Part 2 chapter on Operations with Integers.
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