Properties of Multiplication | Student Worksheet

Math Rules That Always Work!

Multiplication has special rules called properties. These help us solve problems faster and check our answers!

You can multiply in any order!

a × b = b × a

Example: 4 × 6 = 24 AND 6 × 4 = 24

Both = 24!

Break a number apart, multiply each part, then add!

a × (b + c) = (a × b) + (a × c)

Example: 6 × 14 is hard. Let's break apart the 14!
6 × 14 = 6 × (10 + 4) = (6 × 10) + (6 × 4) = 60 + 24 = 84

When multiplying 3 numbers, you can group any two first!

(a × b) × c = a × (b × c)

Example: 5 × 2 × 4 = ?
(5 × 2) × 4 = 10 × 4 = 40 OR 5 × (2 × 4) = 5 × 8 = 40 Same answer!

Any number × 1 = that number

a × 1 = a

7 × 1 = 7
1 × 25 = 25

Any number × 0 = 0

a × 0 = 0

8 × 0 = 0
0 × 100 = 0

1. Use the Commutative Property. If 7 × 3 = 21, then 3 × 7 = _______

2. Use the Distributive Property to solve 5 × 12.

5 × 12 = 5 × (10 + 2) = (5 × ____) + (5 × ____) = ____ + ____ = _______

3. Use the Associative Property. Solve 4 × 5 × 2 two different ways.

(4 × 5) × 2 = ____ × 2 = _______

4 × (5 × 2) = 4 × ____ = _______

4. What property is shown? 9 × 1 = 9

Property:

5. Use the Distributive Property to solve 7 × 13.

7 × 13 = 7 × (10 + 3) = _____________ = _______