Chapter 6: Integers
Standard NCERT & CBSE aligned study curriculum. Master concepts, track accuracy, revise weak areas, and challenge yourself with 9 customized practice modes.
This topic is taught in multiple grades. Switch classes to see specific curriculum details:
Syllabus Sections
Chapter Overview
Welcome to Class VI Mathematics: Integers. This chapter forms a core structural component of the math syllabus, designed to build analytical rigor and key formula models.
Use the detailed subtopic guide below to review standard definitions, key mathematical rules, and study guidelines.
Prerequisite Concepts
About This Chapter
This comprehensive study guide for Integers is designed for Class VI students following the CBSE and NCERT Mathematics curriculum. It covers 4 key subtopics including Negative numbers concept, Integers set definition, Ordering of integers on number line, and 1 more essential concepts. Whether you are preparing for school examinations, CBSE board exams, or competitive tests, this resource provides everything you need to build a strong conceptual foundation and achieve mastery.
The chapter includes 1 key formulas and equations, 1 fully worked step-by-step example problems, interactive practice exercises across 9 difficulty categories, timed mock quizzes, and downloadable worksheets. Each topic is explained with detailed concept definitions, mathematical representations, and expert study guidelines to help you understand not just the "how" but the "why" behind every formula and method.
Mathematics is a subject that rewards consistent practice and conceptual clarity over rote memorization. As you work through this chapter on Integers, focus on understanding the underlying principles first, then gradually increase problem difficulty. Use the practice sections to identify and strengthen weak areas, and refer to the common mistakes section to avoid the pitfalls that most students encounter.
What You'll Learn in This Chapter
By the end of studying Integers for Class VI, you will have developed proficiency in the following learning outcomes as outlined by the NCERT syllabus:
Locate negative integers on a standard number line.
Compare negative integers using inequality signs.
Add and subtract positive and negative integers.
Prerequisites for This Chapter
Before studying Integers, make sure you are comfortable with the following prerequisite concepts. A strong foundation in these areas will help you understand new topics faster and solve problems more confidently:
If any of these prerequisites feel unfamiliar, consider reviewing them first using the Related Chapters section at the bottom of this page. Building a solid base ensures you can tackle Integers with full confidence.
Real-World Applications of Integers
Students often wonder “Where will I use Integersin real life?” The answer is: everywhere. The mathematical concepts you learn in this chapter have practical applications across science, engineering, technology, medicine, finance, and everyday problem-solving. Here are some notable examples:
Temperature Readings
Below-zero temperatures (-5°C, -20°C) require understanding of negative integers and integer operations.
Bank Transactions
Deposits (positive) and withdrawals (negative) are integer operations that determine account balances.
Altitude & Depth Measurement
Measuring heights above sea level (+8848 m for Everest) and ocean depths (-10,994 m for Mariana Trench) uses integers.
Game Score Tracking
Many games feature positive points for correct answers and negative penalties for wrong answers, requiring integer arithmetic.
Understanding the real-world relevance of Integers not only makes learning more engaging but also helps you appreciate how mathematical thinking is a superpower that opens doors in virtually every career path — from engineering and medicine to finance and technology.
Study Tips for Integers
Follow these expert study strategies to maximize your understanding and exam performance in this chapter. These tips are specifically tailored for the type of content covered in Integers:
Practice Step-by-Step
Write out every intermediate step when solving problems. Skipping steps is the most common source of errors in calculation-heavy chapters. Build speed only after achieving consistent accuracy.
Verify by Back-Substitution
After finding your answer, substitute it back into the original equation to verify correctness. This simple habit catches most arithmetic and sign errors before they cost you marks.
Maintain an Error Log
Keep a dedicated notebook of mistakes you make during practice. Review it weekly to identify patterns — you will notice the same types of errors recurring and can actively work to eliminate them.
Pro Tip: Consistency beats intensity. Studying Integers for 30 minutes daily is far more effective than cramming for 5 hours before the exam. Use the practice sections below to build muscle memory through regular problem-solving.
Detailed Subtopics Study Guide
Review detailed conceptual explanations, mathematical equations, and guidelines for each subtopic in this chapter:
1Negative numbers concept
Concept Explanation
Negative numbers represent values below zero, used for negative temperatures, depths, or financial debts.
Mathematical Representation
2Integers set definition
Concept Explanation
Integers are the set containing all whole numbers and their negative opposites.
Mathematical Representation
3Ordering of integers on number line
Concept Explanation
Arranging integers sequentially: numbers to the right are larger; numbers to the left are smaller.
Mathematical Representation
4Addition and subtraction of integers
Concept Explanation
Rules for adding and subtracting signed numbers: adding negatives is subtracting; subtracting negatives is adding.