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 carefuly
(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