Integers

Class 6 Maths Chapter Integers – Introduction

Integers are one of the most useful concepts introduced in Class 6 Mathematics because they help students understand numbers beyond ordinary counting numbers. Until now, students have worked mainly with natural numbers and whole numbers, but many real-life situations involve values below zero, such as temperature, bank balance, altitude, and scores in games. This chapter introduces positive integers, negative integers, and zero, explaining how they are represented on a number line and how they relate to each other. Must-read Class 6 Maths Notes and NCERT Solutions for class 6, NCERT exemplar for class 6. 

Students also learn about ordering integers, comparing their values, finding opposites, and performing basic operations like addition and subtraction. Through practical examples, the chapter builds logical thinking and strengthens number sense, making mathematical concepts easier to apply in everyday life. Understanding integers forms the foundation for higher mathematical topics such as algebra, coordinate geometry, and equations studied in later classes. Regular practice with number lines and simple problems helps students gain confidence in handling positive and negative numbers accurately. This chapter encourages analytical thinking and develops essential problem-solving skills required for advanced mathematics.

Integers Class 6 CBSE Maths Notes Examples, MCQs and Practice Questions

Welcome to our comprehensive guide on Integers for Class 6 CBSE Mathematics. This chapter introduces students to the world of negative numbers and expands their understanding beyond whole numbers. Whether you're preparing for your exams or looking for NCERT solutions, this guide covers everything you need to master integers.

1. What are Integers? – Definition and Meaning

1.1 Integer Meaning and Definition

Integers are a collection of all counting numbers (natural numbers), zero, and the negatives of counting numbers. In simple terms, integers include all positive numbers, negative numbers, and zero without any fractions or decimals.

Mathematical Definition

I = Z = {…, –3, –2, –1, 0, +1, +2, +3, …}

The set of integers is denoted by 'I' or 'Z' (from German 'Zahlen' meaning numbers)

1.2 Types of Integers

Integers can be classified into three main categories:

1.3 Integer Examples

Here are some examples to help you identify integers:

• Integers: –100, –25, –7, 0, 4, 15, 99, 1000
• NOT Integers: ½, 0.5, 3.14, –2.7, ¾ (these are fractions or decimals)

2. Difference Between Integers and Whole Numbers

Understanding the difference between integers and whole numbers is crucial for Class 6 students. This is one of the most commonly asked questions in CBSE exams.

Note: Every whole number is an integer, but not every integer is a whole number. For example, –5 is an integer but NOT a whole number.

3. Representing Integers on a Number Line

A number line is a visual representation that helps us understand the position and relationship between integers. It extends infinitely in both directions.

3.1 How to Draw a Number Line for Integers

1. Draw a horizontal line with arrows on both ends (indicating it extends infinitely)
2. Mark equal intervals (points) along the line
3. Place zero (0) at the center point
4. Write positive integers (+1, +2, +3, ...) to the RIGHT of zero
5. Write negative integers (–1, –2, –3, ...) to the LEFT of zero

Number Line Representation

←───┼───┼───┼───┼───┼───┼───┼───┼───┼───┼───┼───┼───→
 –6 –5 –4 –3 –2 –1 0 +1 +2 +3 +4 +5 +6

3.2 Key Points About Number Line

• Moving RIGHT: Numbers increase in value
• Moving LEFT: Numbers decrease in value
• Any number to the RIGHT is GREATER than the number to its left
• All negative integers are less than zero
• All positive integers are greater than zero

4. Operations on Integers – Rules and Methods

4.1 Rules for Adding Integers

Addition of integers follows specific rules based on the signs of the numbers involved:

Addition on Number Line

To add integers on a number line:

1. Start at zero
2. Move to the first number
3. For adding positive: Move RIGHT
4. For adding negative: Move LEFT

Example: 2 + 4 = ? → Start at 0, move 2 right to reach 2, then move 4 more right to reach 6. Answer: 6

4.2 Rules for Subtracting Integers

Subtraction of integers can be converted to addition using the additive inverse:

Rule: a – b = a + (–b)

To subtract an integer, add its additive inverse (change the sign and add)

Examples of Subtraction:

1. 7 – 2 = 7 + (–2) = 5
2. –10 – (–5) = –10 + 5 = –5
3. 5 – (–3) = 5 + 3 = 8

4.3 Rules for Multiplying Integers

Memory Trick: Same signs = Positive result | Different signs = Negative result

4.4 Rules for Dividing Integers

Division of integers follows the same sign rules as multiplication:

1. (+) ÷ (+) = Positive: (+12) ÷ (+3) = +4
2. (–) ÷ (–) = Positive: (–12) ÷ (–3) = +4
3. (+) ÷ (–) = Negative: (+12) ÷ (–3) = –4
4. (–) ÷ (+) = Negative: (–12) ÷ (+3) = –4

5. Properties of Integers

Understanding the properties of integers helps solve problems more efficiently:

5.1 Additive Inverse

The additive inverse of an integer is the number that when added to it gives zero.

• Additive inverse of +5 is –5 (because +5 + (–5) = 0)
• Additive inverse of –7 is +7 (because –7 + 7 = 0)
• Additive inverse of 0 is 0 (because 0 + 0 = 0)

6. Real-World Applications of Integers

Integers are used extensively in daily life. Here are some practical examples:

7. Formulas and Quick Reference Table

8. Word Problems on Integers with Solutions

Problem 1: Temperature Change

Question: Today's temperature is 2°C, which is 5°C greater than yesterday. What was yesterday's temperature?

Solution: Yesterday's temperature = Today's temperature – 5°C = 2°C – 5°C = –3°C

Problem 2: Remainder Problem

Question: A whole number n, when divided by 5, gives a remainder of 3. What will be the remainder when 2n is divided by 5?

Solution: If n = 5p + 3, then 2n = 10p + 6. When 10p + 6 is divided by 5, 10p gives a remainder of 0, and 6 gives a remainder of 1. So the answer is 1.

Problem 3: Sum of Integers

Question: Find the sum of (–10), 82, (–39), and 68.

Solution: Group same signs: (–10) + (–39) + 82 + 68 = –49 + 150 = 101

9. Important MCQs with Answers

Q1. An integer which is neither positive nor negative is:

(a) 0

(b) 1

(c) –1

(d) None of these

Answer: (a) 0

Q2. The sum (–7) + (–9) + 14 + 6 is equal to:

(a) –4

(b) 24

(c) –6

(d) 4

Answer: (d) 4 [Solution: –7 – 9 + 20 = –16 + 20 = 4]

Q3. Which number will we reach if we move 4 numbers to the right of –2 on number line?

(a) 2

(b) 3

(c) 4

(d) 5

Answer: (a) 2 [Solution: –2 + 4 = 2]

Q4. –51 × 9 + 15 × 9 is equal to:

(a) 224

(b) –324

(c) 324

(d) –224

Answer: (b) –324 [Solution: 9 × (–51 + 15) = 9 × (–36) = –324]

Q5. 888 ÷ 3 ÷ 37 = ?

(a) 8

(b) 3

(c) 37

(d) 296

Answer: (a) 8 [Solution: 888 ÷ 3 = 296, 296 ÷ 37 = 8]

10. Common Mistakes and How to Avoid Them

1. Confusing subtraction with addition of negative → Fix: Remember: 5 – (–3) = 5 + 3 = 8, NOT 5 – 3
2. Wrong sign in multiplication → Fix: Use the rule: Same signs = +, Different signs = –
3. Moving wrong direction on number line →  Fix: Positive = RIGHT, Negative = LEFT (always!)
4. Thinking –5 > –3 → Fix: The number closer to zero is greater. –3 > –5
5. Forgetting that all negative integers < 0 → Fix: Zero is always greater than any negative integer

11. Tips to Score Full Marks in Integers Chapter

1. Master the Number Line: Practice drawing and using number lines for all operations
2. Memorise Sign Rules: Create flashcards for multiplication and division sign rules
3. Practice Word Problems: Convert real-world scenarios to integer operations
4. Use Additive Inverse: Convert all subtractions to additions for easier calculations
5. Check Your Signs: Always double-check the sign of your final answer
6. Group Similar Terms: Group positive and negative integers separately before calculating