Commutative Property of Real Numbers

The commutative property states that changing the order of numbers in addition or multiplication does not change the value of an expression.

Imagine you run a warehouse where three trucks deliver shipments every day. Truck A brings 110 boxes, Truck B brings 200 boxes, and Truck C brings 90 boxes.

One day, the trucks arrive in the order A, B, and C. Another day, they arrive in the order A, C, and B. On both days, your manager records the shipments in the order they arrive.

Even though the order changes, the total number of boxes stays the same. This shows the commutative property of addition.

Now, imagine you have 6 stacks in the warehouse, each with 10 boxes. This gives 6 times 10, or 60 boxes.

Before shipping, workers repack the same boxes into 10 stacks of 6 boxes each. You can also write this as 10 times 6.

The arrangement changes, but the total number of boxes stays the same. This shows the commutative property of multiplication.

The same idea works with algebraic expressions. We can rearrange terms and factors to place like terms together and simplify.