The properties of addition are:
* communicative: a + b = b + a
* associative: a + b + c = (a + b) + c = a + (b + c)
* additive identity: a + 0 = a
* additive inverse: a + -a = 0
The properties of multiplication:
* communicative: a × b = b × a
* associative: a × b × c = (a × b) × c = a × (b × c)
* distributive: a × (b + c) = a × b + a × c
* multiplicative identity: a × 1 = a
* multiplicative inverse: a × a^-1 = 1
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The set of integers is closed with respect to multiplication and with respect to addition.
Addition, by itself, does not have a distributive property. Multiplication has a distributive property over addition, according to which: a*(b + c) = a*b + a*c
Addition, by itself, does not have a distributive property. Multiplication has a distributive property over addition, according to which: a*(b + c) = a*b + a*c
addition and multiplication
The distributive property of multiplication over addition.