# Properties of multiplication

Explore the commutative, associative, and identity properties of multiplication.
In this article, we'll learn the three main properties of multiplication. Here's a quick summary of these properties:
Commutative property of multiplication: Changing the order of factors does not change the product. For example, $4 \times 3 = 3 \times 4$.
Associative property of multiplication: Changing the grouping of factors does not change the product. For example, $(2 \times 3) \times 4 = 2 \times (3 \times 4)$.
Identity property of multiplication: The product of $1$ and any number is that number. For example, $7 \times 1 = 7$.

## Commutative property of multiplication

The commutative property of multiplication says that changing the order of factors does not change the product. Here's an example:
$4 \times 3 = 3 \times 4$
Notice how both products are $12$ even though the ordering is reversed.
Here's another example with more factors:
$1 \times 2 \times 3 \times 4 = 4 \times 3 \times 2 \times 1$
Notice that both products are $24$.
Which of these is an example of the commutative property of multiplication?

## Associative property of multiplication

The associative property of multiplication says that changing the grouping of the factors does not change the product. Here's an example:
$\blueD{(2 \times 3) \times 4} = \goldD{2 \times (3 \times 4)}$
Remember that parentheses tell us to do something first. So here's how we evaluate the left-hand side:
$\phantom{=}\blueD{(2 \times 3) \times 4}$
$= 6 \times 4$
$=24$
And here's how we evaluate the right-hand side:
$\phantom{=}\goldD{2 \times (3 \times 4)}$
$= 2 \times12$
$=24$
Notice that both sides equal $24$ even though we multiplied the $2$ and the $3$ first on the left-hand side, and we multiplied the $3$ and the $4$ first on the right-hand side.
Which of these is an example of the associative property of multiplication?
The identity property of multiplication says that the product of $1$ and any number is that number. Here's an example:
$7 \times 1 = 7$
The commutative property of multiplication tells us that it doesn't matter if the $1$ comes before or after the number. Here's an example of the identity property of multiplication with the $1$ before the number:
$1 \times 6 =6$