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Here are some properties of integers and the primary operations:
(1) Integers are closed under addition, subtraction and multiplication. This means that if you add, subtract or multiply two integers the result is an integer.
(2) The integers have the associative property of addition and of multiplication. i.e. for integers a,b,c (a+b)+c=a+(b+c) and (ab)c=a(bc)
(3) The integers have the commutative property of addition and multiplication. i.e. for integers a,b a+b=b+a and ab=ba
(4) The integers have an additive identity, 0. i.e. for any integer a, a+0=0+a=a. The integers have a multiplicative identity,1. i.e. for any integer a a*1=1*a=a
(5) The integers have additive inverses. i.e. for any integer a there is an integer (-a) such that a+(-a)=(-a)+a=0.
Note that the integers do not have a multiplicative inverse.
(6) There is the distributive property of multiplication over addition. For any integers a,b,c a(b+c)=ab+ac
A typical question might ask you to identify the property:
a+(b+c)=(a+b)+c is which property?
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