identify such properties
as commutativity, associativity, and distributivity and
use them to compute with whole numbers.
Commutative Property
What it says: This property
states that the order of numbers in an addition
or multiplication expression will not change the sum or product.
In the example below the 5 and the 4 come
first. If you add those two numbers the sum (answer to
an addition expression) will be 9. When you add the 3
the sum will be 12. But would the sum be the same if you changed
the order of those two numbers so that the new expression reads
4 + 5 + 3?
Click on the CHANGE ORDER button on the left
and see what happens to the sum. Will it be the same? Then click
the change order button on the right to change the order again.
Will the sum change?
The sum stays the same no matter what the
order of the numbers. No matter how you order the numbers, the
sum will always be 12. This is the commutative property.
Does it work with multiplication?
Let's see. In the example below, the numbers
2 and 5 come first. If you multiply those two numbers the product
(answer to a multiplication expression) would be 10.
When you multiply by 3 you get a product of 30. Would the product
be the same if you changed the order of the 2 and 5 so that the
new expression read 5 x 2 x 3?
Click on the MOVE PARENTHESIS button below
and see what happens to the product when the parenthesis are moved
to the 4 and 2.
Click on the CHANGE ORDER button on the left
and see what happens to the product. Will it be the same? Then
click the change order button on the right to change the order
again. Will the product change?
The product stays the same no matter what
the order of the numbers. No matter how you order the numbers,
the product will always be 30. This is the commutative
property.
