Discussion
Association means 'getting together' -- when you go to a party, you associate
with people. Addition and multiplication are binary processes by nature,
that is, you can only add or multiply (and by extension, subtract and divide)
two numbers at a time. So if you have more than two numbers to add, or more
than two numbers to multiply, you have to start by selecting two to
"associate." The Associative Property says it doesn't matter which pair of
numbers you choose.
Associative Property of Addition:
. In words: you can add a to b first and then add the
result to c, or you can add b to c first, and then add that result to a.
Either way, you get the same answer no matter what the numbers are.
Associative Property of Multiplication:
. In words: you can multiply a and b first and then multiply
the result by c, or you can multiply b and c first, and then multiply that result by a.
Either way, you get the same answer no matter what the numbers
are.
You don't need separate properties for subtraction or division because
subtraction is simply adding the negative of a number and division is
multiplication by the reciprocal.
Commute means to travel back and forth. Mathematically, it relates to the
order in which you add or multiply two numbers. The commutative property
says it doesn't matter which number comes first:
Commutative Property of Addition:
.
Commutative Property of Multiplication:
.
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