Properties of multiplication

key notes :

Commutative property:
You can multiply numbers in any order and get the same product.

3 × 9 = 9 × 3

Associative property:
You can group the factors in any way without changing the result.

7 × (8 × 6) = (7 × 8) × 6

Zero property:
Multiplying by 0 always gives 0.

3 × 0 = 0

Identity property:
Multiplying by 1 does not change a number.

2 = 1 × 2

Distributive property:
You can multiply a sum by multiplying each addend separately.

5 × (7 + 2) = (5 × 7) + (5 × 2)

The distributive property works with subtraction, too.

5 × (7 − 2) = (5 × 7) − (5 × 2)

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!