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?

  • 1 × 4 = 4
  • 8 × 2 + 8 × 1 = 8 × (2 + 1)
  • 7 × 2 = 2 + 2 + 2 + 2 + 2 + 2 + 2
  • 3 × 1 = 1 × 3
  • 3 × 1 = 1 × 3
  • This equation shows the commutative property. The order of the factors is changed.

✈️ Which property of multiplication is shown?

✈️ (7 × 3) × 6 = 7 × (3 × 6)

  • associative
  • zero
  • commutative
  • identity
  • (7 × 3) × 6 = 7 × (3 × 6)
  • This equation shows the associative property. The grouping of the factors is changed.

✈️ Which equation shows the associative property of multiplication?

  • 7 × 3 − 0 × 3 = (7 − 0) × 3
  • (5 × 1) × 9 = 5 × (1 × 9)
  • 7 × 9 + 1 = 63 + 1
  • 6 + 6 + 6 = 3 × 6
  • (5 × 1) × 9 = 5 × (1 × 9)
  • This equation shows the associative property. The grouping of the factors is changed.

Let’s practice!🖊️