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The set of rational number satisfies the following properties with regard to addition: for any three rational numbers x, y and z, · x + y is a rational number (closure under addition) · (x + y) + z = x + (y + z) (associative property of addition) · There is a rational number, 0, such that x + 0 = 0 + x = x (existence of additive identity) · There is a rational number, -x, such that x + (-x) = (-x) + x = 0 (existence of additive inverse) · x + y = y + x (Abelian or commutative property of addition)
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Does the Commutative Property apply to addition of fractions?
Yes, it applies to even multiplication of fractions and rational and irrational numbers.
What is Adding integers and rational number rules?
The set of integers is closed under addition so that if x and y are integers, then x + y is an integer.Addition of integers is commutative, that is x + y = y + xAddition of integers is associative, that is (x + y) + z = x + (y + z) and so, without ambiguity, either can be written as x + y + z.The same three rules apply to addition of rational numbers.
Does the comunitive property of addition apply when you add two negative integers?
Communitive means of, or belonging to, a community. No numbers has this property.
Do all rational numbers apply to the 11 Field axioms?
yes they do. because a rational number is any number that can be made into a fraction there is no field axiom which goes against this. For example the multiplicative identity. 5/6 times 1 equals 5/6 exc....
What is the after to 17 over 1?
As soon as you introduce fractions (even division by 1), the concept of "next" can no longer apply. There are infinitely many rational numbers between any two numbers. So between any number an a potential "next" number, there are infinitely many numbers.
