identify such properties
as commutativity, associativity, and distributivity and
use them to compute with whole numbers.
Associative Property
What it says: This property
states that the grouping of numbers in an addition or multiplication
expression will not change the sum or product. This is important
when parenthesis are used in the expression.
In the example below the 9 and the 7 are
grouped in the parenthesis. The order of operations states that
you do all operations in parenthesis first. Therefore, you will
add 9 and 7 to get a sum (answer to an addition expression)
of 16 and then add 5 to get a sum of 21. But would the sum be
the same if you moved the parenthesis to the 7 and 5 and then
added them first?
Click on the MOVE PARENTHESIS button below
and see what happens to the sum when the parenthesis are moved
to the 7 and 5.
The sum stays the same no matter how the
numbers are grouped. No matter how you group the numbers, the
sumwill always be 21. This is the associative property.
Does it work with multiplication?
Let's see. In the example below, the parenthesis
are around the numbers 3 and 4. The order of operations states
that we would mulitply these two numbers first. The product
(answer to a multiplication expression) would be 12.
Then we would multiply 12 by 2 to get a product of 24. Would the
product be the same if you moved the parenthesis to the 4 and
2.
Click on the MOVE PARENTHESIS button below
and see what happens to the product when the parenthesis are moved
to the 4 and 2.
The product stays the same no matter how
the numbers are grouped. No matter how you group the numbers,
the product will always be 24. This is the associative
property.
