# Properties ofÂ 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:

Notice how both products are $12$ even though the ordering is reversed.

Here's another example with more factors:

Notice that both products are $24$.

## 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:

Remember that parentheses tell us to do something first. So here's how we evaluate the left-hand side:

And here's how we evaluate the right-hand side:

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.

## Identity property of multiplication

The identity property of multiplication says that the product of $1$ and any number is that number. Here's an example:

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: