# Commutative property

Certainly, in commutative property, we see the word commute which means exchange from the latin word commutare.

The word exchange in turn may mean switch. For examples, washing my face and combing my hair is a good example of this property.

Another good example is doing my math homework and then finishing my science reading.

The important thing to notice in the two examples above is that the order we do things can be switched, so it does not matter or will never cause any problems or conflicts.

However, reading a math lesson and then answering the review questions is not commutative.

Here the order does matter because I have to read the lesson before knowing how to answer the review questions.

In mathematics, we know that

2 + 5 = 5 + 2

12 + 4 = 4 + 12

-1 + 8 = 8 + -1

All the above illustrates the commutative property of addition. This means that when adding two numbers, the order in which the two numbers are added does not change the sum

All three examples given above will yield the same answer when the left and right side of the equation are added

For example, 2 + 5 = 7 and 5 + 2 is also equal to 7

The property is still valid if we are doing multiplication

Again, we know that

3 × 4 = 4 × 3

12 × 0 = 0 × 12

9 × 6 = 6 × 9

Again, 3 × 4 = 12 and 4 × 3 = 12

More examples: Take a close look at them and study them carefully

(3 + 2) × 4 = 4 × (3 + 2)

x + y = y + x

x × y = y × x

2 × x = x × 2

(x + z) × (m + n) = (m + n) × (x + z)

4 + y = y + 4

Warning! Although addition is commutative, subtraction is not commutative

Notice that 3 − 2 is not equal to 2 − 3

3 − 2 = 1 , but 2 − 3 = -1

Therefore, switching the order yield different results

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