04 - Commutation

 1. The commutative law is the same as the associative law. They are different names for the same thing.



 2. The Commutative law states that: A + A = A



 3. Which of the following are expressions of the Commutative law?
A + B = B + A
A B = B A
A + BC = BC + AB
A + BC = ABC

  The first one

  Only the last two

  The first two

  All of them

 4. According to the Commutative law, A + B is equal to B + A and A + B can also be equal to AB



 5. Fill in the blanks in the following diagram illustrating commutation

  B+A = A+B

  A.B = B.A

  A.B = A

  A.B =B.B

 6. Decide if the following statement is true or false.
a + b = b + a. 

The operation is associative because 
the order of the elements does not affect 
the result of the operation. 

The commutative property,concerns the grouping 
of elements in an operation and is 
always identical to association



 7. Simply put, the commutative property states that the factors in an equation can be rearranged freely without affecting the outcome of the equation



 8. The commutative property can be expressed through the equations a + b = b + a and a x b = b x a. No matter the order of the values in these equations, the _____ will always be the same.





 9. We can tell the difference between the associative and the commutative property by asking the question, “Are we changing the order of the elements, or are we changing the grouping of the elements?
If the elements are being reordered, 
then the commutative property applies. 

If the elements are only being regrouped, 
then the associative property applies.



 10. Decide whether the following statement is true or false.
However, note that the presence of parentheses 
alone does not necessarily mean that the 
property applies. For instance:

(2 + 3) + 4 = 4 + (2 + 3)

This equation is an example of the 
commutative property
of addition of real numbers