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id: "69be8085a20d3dd4a91ce2c4"
title: "Operations with Integers"
board: "CBSE"
curriculum: "CBSE"
class: "Class 7"
subject: "Mathematics"
book: "Ganita Prakash II"
chapter: "Operations with Integers"
chapter_slug: "operations-with-integers"
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last_updated: "2026-06-20"
---

# Operations with Integers

This chapter focuses on various operations involving integers, highlighting their properties and applications through engaging puzzles, games, and mathematical reasoning.

---

## Knowledge Snapshot

| Field | Details |
| :--- | :--- |
| Class | Class 7 |
| Subject | Mathematics |
| Book | Ganita Prakash II |
| Chapter | Operations with Integers |
| Pages | 24-46 |

---

## Chapter Summary

### Short Summary
This chapter introduces the concept of integers and explores operations involving addition and subtraction through practical examples and puzzles.

### Detailed Summary
The chapter begins with Rakesh's puzzle to identify pairs of numbers based on their sums and differences. Various integer addition and subtraction strategies, including the use of a number line and the concept of additive inverses, are covered. Practical examples such as the movement of a carrom coin illustrate positive and negative integers along with their computations. The chapter ends with strategies for subtracting integers using tokens to represent numbers visually.

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## Topic-Wise Explanation

### A Quick Recap of Integers
An overview of integers and their properties, emphasizing operations on positive and negative integers.

### Rakesh’s Puzzle: A Number Game
Rakesh challenges the reader to find two numbers based on given sums and differences, illustrating problem-solving with integers. The first challenge involves numbers summing to 25 with a difference of 11, leading to exploration of various integer combinations.

### Figure it Out
Additional practices to find pairs of integers based on similar sums and differences as a way to deepen understanding of the relationship between integers.

### Multiplication of Integers
Discussion of the multiplication properties of integers and how they behave based on the signs of the numbers involved.

### Patterns in Integer Multiplication
Exploration of patterns that emerge when multiplying integers, detailing outcomes based on the signs of the integers.

### Brahmagupta’s Rules for Multiplication and Division
Presentation of foundational rules for multiplying and dividing integers, including examples to demonstrate application.

### Division of Integers
Explanation of how to divide integers, focusing on both positive and negative outcomes with illustrative examples.

---

## Core Ideas

| Idea | Explanation |
| :--- | :--- |
| Addition of Integers | Adding positive and negative integers results in varying outcomes based on their values. |
| Subtraction as Addition of Inverses | Subtracting integers can be viewed as adding their additive inverses. |

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## Key Concepts

| Concept | Meaning |
| :--- | :--- |
| Integer | Whole numbers that can be positive, negative, or zero. |
| Additive Inverse | The opposite of an integer, which when added to the integer yields zero. |

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## Important Points for Revision

* Integers include positive and negative numbers as well as zero.
* Utilization of a number line aids in visualizing integer operations.
* Addition of two positive integers yields a positive integer.
* Addition of two negative integers yields a negative integer.
* The sum of a positive and a negative integer depends on their absolute values.
* Subtraction can be transformed into addition by using the additive inverse.
* Multiplying two integers of the same sign results in a positive integer.
* Multiplying two integers of different signs results in a negative integer.
* Division follows similar rules to multiplication regarding signs.

---

## Practice Questions

### Short Answer Questions
1. What are the two numbers that satisfy Rakesh's first challenge?
2. How do you determine the final position of a carrom coin struck twice?
3. Write the formula for calculating the final position of a carrom coin after two strikes in different directions.
4. Explain what an additive inverse is with an example.
5. Calculate the result of \(7 - 18\).

### Long Answer Questions
1. Derive the final position of a carrom coin after being struck in opposite directions.
2. Discuss how addition and subtraction are performed on integers with examples.
3. Illustrate the rules for multiplying integers with examples highlighting different sign scenarios.

---

## Related Concepts
* Number Line
* Additive Inverses
* Properties of Operations

---

## Source Attribution

| Field | Value |
| :--- | :--- |
| Source | Edzy |
| Reference Type | examSubjectBookChapter |
| Reference ID | 69be8085a20d3dd4a91ce2c4 |
| Canonical URL | https://www.edzy.ai/cbse-class-7-mathematics-ganita-prakash-ii-operations-with-integers |
| Markdown URL | https://www.edzy.ai/okf/chapter/cbse-class-7-mathematics-ganita-prakash-ii-operations-with-integers.md |