# What are the rules of integers and can you give me an example of a question

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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?