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📘 Properties of Addition of Integers | Class 6 | CH-4 PART-4
Welcome to FunMathology — Part 4 of our Integers series (CBSE Class 6). In this lesson we cover the key properties of addition for integers: Closure, Commutative, Associative, Additive Identity (0), and Additive Inverse. Each property is shown with number-line visuals and worked examples.

⏱ Timestamps
00:00 Intro
01:00 What is a property?
01:20 Closure property (example)
02:33 Commutative property (example)
04:28 Associative property (example)
06:54 Additive Identity (0)
07:52 Additive Inverse
10:20 Practice exercises (pause & try)

1) Closure Property
Definition: Sum of any two integers is always an integer.
Number-line idea: Add −4 and +3 → land at −1 (still an integer).
Numeric example: (−4) + (+3) = −1 → result is an integer.
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2) Commutative Property
Definition: Changing the order does not change the sum.
Formula: a + b = b + a
Number-line demo: Start at a, move b steps right/left vs start at b, move a steps — land at the same point.
Numeric example (step-by-step):
• Example: (−5) + (+3)
o Interpretation on number line: start at −5, move 3 steps right → land at −2.
o Using commutative order: (+3) + (−5)
 Start at +3, move 5 steps left → land at −2.
o Both give −2, so (−5) + (+3) = (+3) + (−5) = −2.
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3) Associative Property
Definition: Grouping doesn’t change the sum.
Formula: (a + b) + c = a + (b + c)
Numeric example (step-by-step):
• Take a = 2, b = −3, c = 5.
o Left group: (2 + (−3)) + 5
 2 + (−3) = −1 → then (−1) + 5 = 4.
o Right group: 2 + ((−3) + 5)
 (−3) + 5 = 2 → then 2 + 2 = 4.
o Both → 4. (Show the number-line steps for both groupings.)
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4) Additive Identity (0)
Definition: Adding zero does not change a number.
Formula: a + 0 = a (and 0 + a = a)
Example: (+7) + 0 = +7; (−4) + 0 = −4.
Number-line: Starting at a, moving 0 steps stays at a.
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5) Additive Inverse
Definition: For every integer a there exists −a such that a + (−a) = 0.
Example: (+6) + (−6) = 0; (−9) + (+9) = 0.
Number-line: a and −a are same distance from 0 on opposite sides; together they cancel to 0.

📝 Practice Worksheet (PDF): https://drive.google.com/file/d/1n1cr...

▶️ Watch playlist — Integers | Class 6:    • Integers Class 6 CBSE | Chapter 4 | Mathem...  
▶️ Previous Lectures on Integers:
Part1:    • Introduction to Integers | Difference Betw...  

Part2:    • Comparing & Ordering Integers | Opposites ...  

Part3:    • How to Add Integers — Number Line Method &...  

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