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Rules of Arithmetic22
- Commutative Property for Addition: for any two numbers a and b,
- Associative Rule for Addition: for any three numbers a, b, and c,
- Existence of Additive Identity (aka Zero): there is a number 0 such that for any number a,
- Existence of Additive Inverse (aka “the negative” and “the opposite): for every number a, there is another number, called the additive inverse or negative of a, and denoted by -a, such that
- Commutative Rule for Multiplication: for any two numbers a and b, we have
- Associative Rule for Multiplication: for any three numbers a, b, and c,
- Existence of Multiplicative Identity (aka One): there is a number 1 such that for any number a,
- Existence of Multiplicative Inverse (aka “the reciprocal”): for every non-zero number a, there is another number, called the multiplicative inverse or reciprocal of a, and written as 1⁄a(or sometimes also as a-1), such that
- Distributive Rule: for any three numbers a, b, and c,
a + b = b + a
(a + b) + c = a + (b + c)
0 + a = a
-a + a = 0
a X b = b X a
(a X b) X c = a X (b X c)
1 X a = a
a X (b + c) = a X b + a X c
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