Properties of multiplication

key notes :

1. Commutative Property

Definition: The order of the numbers does not change the product.

Example:

  • 6×4=24
  • 4×6=24
  • ✅ Both are equal.

2. Associative Property

Definition: When multiplying three or more numbers, the grouping does not change the product.

Example:

  • (2×3)×4=6×4=24
  • 2×(3×4)=2×12=24
  • ✅ Both are equal.

3. Identity Property

Definition: Any number multiplied by 1 remains the same.

Example:

  • 9×1=9
  • 1×9=9

4. Zero Property

Definition: Any number multiplied by 0 is always 0.

Example:

  • 45×0=0
  • 0×99=0

5. Distributive Property

Definition: Multiplication can be distributed over addition or subtraction.

Example:

  • 5×(3+2)=(5×3)+(5×2)
  • 5×5=15+10=25

✅ Summary

Multiply over addition/subtraction → Break and multiply (Distributive)

Changing order → Same answer (Commutative)

Changing grouping → Same answer (Associative)

Multiply by 1 → Same number (Identity)

Multiply by 0 → Always 0 (Zero)

Learn with an example

🎯 Which equation shows the commutative property of multiplication?

  • 7 × 8 + 7 × 5 = 7 × (8 + 5)
  • 6 × 1 = 1 × 6
  • 5 + 5 + 5 + 5 = 5 × 4
  • 0 × 3 = 0
  • 6 × 1 = 1 × 6
  • This equation shows the commutative property. The order of the factors is changed.

🎯 Which equation shows the zero property of multiplication?

  • 8 × (1 × 7) = (8 × 1) × 7
  • 0 = 0 × 6
  • (2 × 6) × 1 = 2 × (6 × 1)
  • 5 × 1 = 5
  • 0 = 0 × 6
  • This equation shows the zero property. 0 times any number is always 0.

🎯 Which property of multiplication is shown?

🎯 9 × 5 = 5 × 9

  • associative
  • commutative
  • distributive
  • zero
  • 9 × 5 = 5 × 9
  • This equation shows the commutative property. The order of the factors is changed.

Let’s practice!