8.2 Communicative Law  
What is the sum if you add the following two numbers? Use your calculator if you are unsure.

A) 3 + 7 = ?

B) 7 + 3 = ?

Hopefully you have figured out that the answer becomes the same, 10.
We can therefore write: 3 + 7 = 7 + 3
Addition

Because if works no matter which number you choose, we can write a rule:

Multiplication

We can try to see what applies when multiplying. What does the product become if you multiply:

A) 3 · 7 = ?
B) 7 · 3 = ?

Hopefully, you noted that you received the same product, 21.

We can therefore write: 3 · 7 = 7 · 3

Even this expression should apply for all numbers. We can therefore write it with variables instead:
If you haven’t done calculations with variables earlier, you might think that it looks odd to calculate with letters. You can learn more about this in the section Algebra.

Have you ever thought that it might be easier sometimes to multiply two factors if you change their place?

Which of the following calculations is the easiest?

7 · 8 = 56 or 8 · 7 = 56?

It is different depending on how you think. If you are practicing your multiplication tables, you can cross out have the table because the communicative law applies.

Practice and check that you know your multiplication tables – you will have greater use of this.
Here, you have learned that the communicative law applies concerning addition and multiplication. Does this work even with subtraction and division?  We will show you with an example:

Subtraction

A. 5 - 2 = 3

B. 2 - 5 is not 3, and it cannot be expressed with natural numbers.

Division

A. 36 ÷ 9 = 4

B. 9 ÷ 36 is not 4 and it cannot be expressed with natural numbers.