# Commutative property of multiplication

The commutative property of multiplication says that changing the order in which the factors are multiplied does not change the product. Generally:

a × b = b × a

Examples

1. 8 × 5 = 40

5 × 8 = 40

2. 1.3 × 4 = 5.2

4 × 1.3 = 5.2

In either case, changing the order of the factors does not change the result. If we add more factors, the same still holds true. Regardless of how many factors they are, or in what order we multiply them, the result will be the same.

3. 4 × 6 × 7 × 2 = 336

7 × 6 × 4 × 2 = 336

There are more combinations than those two listed above, but their result will still be 336.

To visualize how the commutative property works, use the figure below.

The orange lines in the figure show how the groups are separated. Multiplying 4 × 2 is the same as adding 2 groups of 4. On the other hand, multiplying 2 × 4 is the same as adding 4 groups of 2. Although we are grouping both differently, we can clearly see that the result is the same.