# Commutative Swap

The `Commutative Property` of numbers says that we can re-order two `addition` or `multiplication` terms so that one occurs before the other in the expression, without changing the value of the expression.

The formulation of this property is the same for addition and multiplication:

• Addition `a + b = b + a`
• Multiplication `a * b = b * a`

The commutative property is used for re-arranging the order of parts of an expression, and is as such very important for working with mathematical expressions.

### Transformations¶

Given a common parent node, this rule switches the order of the children of that node. It can only be applied to addition or multiplication nodes.

`a + b = b + a`

``````        +                  +
/ \                / \
/   \     ->       /   \
/     \            /     \
a       b          b       a
``````

#### Multiplication¶

`a * b = b * a`

``````        *                  *
/ \                / \
/   \     ->       /   \
/     \            /     \
a       b          b       a
``````