Chapter 3 – Integers

1. 🔑 Important Keywords and Definitions

• Integers: The set of numbers that includes positive numbers, negative numbers, and zero.
  Example: …, –3, –2, –1, 0, 1, 2, 3, …

• Positive Integers: Numbers greater than zero (1, 2, 3, …)

• Negative Integers: Numbers less than zero (–1, –2, –3, …)

• Zero (0): Neither positive nor negative.

• Number Line: A horizontal line to represent integers.

• Absolute Value: The distance of a number from zero on the number line, always positive.
  Example: |–4| = 4 and |3| = 3

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2. 🧠 Key Concepts and Explanations

• Integers are used to show gains and losses, elevations above or below sea level, temperatures, etc.

• Comparing Integers:

  • A number is greater if it lies to the right on the number line.

  • Negative integers are always less than positive integers.

• Successor of an integer = Integer + 1

• Predecessor of an integer = Integer – 1

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3. 📏 Formulas and Rules

To Represent Integers on a Number Line:

1. Draw a horizontal line.

2. Mark 0 at the center.

3. Mark positive integers to the right and negative integers to the left.

To Add/Subtract Integers Using Number Line:

1. Start at the first number.

2. Move right for addition, left for subtraction.

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5. ✅ Examples with Full Solutions

Example 1: Add (–3) + (–4)
Solution: Both negative → Add and keep minus sign
⇒ (–3) + (–4) = –7

Example 2: Subtract 5 – (–2)
Solution: Two negatives become plus
⇒ 5 – (–2) = 5 + 2 = 7

Example 3: Arrange: –3, 4, –1, 0 in ascending order
Solution: –3 < –1 < 0 < 4

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6. ⚠️ Common Mistakes to Avoid

• Don’t mix up signs in addition/subtraction.

• Remember: (–) – (–) becomes addition.

• Don’t forget to place zero in the middle of the number line.

• Positive numbers don’t have a ‘+’ sign written, but are still positive.

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7. ✍️ Practice Questions

1. Represent the following integers on a number line: –5, 0, +3, –2

2. Add the following: (–6) + 8, (–4) + (–3), 10 + (–9)

3. Subtract the following: 5 – (–2), (–7) – (–5), (–10) – 4

4. Write the successor and predecessor of: –3, 0, 7

5. Arrange in ascending order: –7, –2, 0, 3, –1

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8. 📊 Conceptual Diagrams

• Number line showing integers from –10 to +10

• Movement on number line for positive and negative direction

• Visual representation of addition and subtraction of integers

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9. 💡 Word Problems Section

Q: A submarine is at –300 meters. It rises 150 meters. What is its new depth?
A: –300 + 150 = –150 meters

Q: The temperature was –5°C in the morning. It rose by 7°C. What is the temperature now?
A: –5 + 7 = 2°C

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10. 📝 Important Points / Quick Revision

• Integers include both negative and positive numbers and zero.

• Positive numbers lie to the right of 0, negatives to the left.

• Zero is neutral; it is neither positive nor negative.

• Adding a negative = subtracting the number.

• Subtracting a negative = adding the number.

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11. 🔗 Connections to Other Chapters

• Useful in Algebra (Simple Equations)

• Basis for Data Handling and Graph plotting

• Applied in Geometry (Coordinate Systems)

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12. 🎯 Extra Tips or Tricks

• Use a number line to solve questions in exams for accuracy.

• Always double-check sign rules before final answer.

• Practice daily with real-life examples (temperature, gains/losses).