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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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Q: What are 5 properties of addition that apply to rational numbers?
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Related questions

Does the Commutative Property apply to addition of fractions?

Yes, it applies to even multiplication of fractions and rational and irrational numbers.


Which operation of rational numbers lets you add all the numerators then copy the denominator?

Operations on rational numbers refer to the mathematical operations carrying out on two or more rational numbers. A rational number is a number that is of the form p/q, where: p and q are integers, q ≠ 0. Some examples of rational numbers are: 1/2, −3/4, 0.3 (or) 3/10, −0.7 (or) −7/10, etc. We know about fractions and how different operators can be used on different fractions. All the rules and principles that apply to fractions can also be applied to rational numbers. The one thing that we need to remember is that rational numbers also include negatives. So, while 1/5 is a rational number, it is true that −1/5 is also a rational number. There are four basic arithmetic operations with rational numbers: addition, subtraction, multiplication, and division.


How are the properties of multiplication and addition similar?

Mainly that in both cases, the numbers can be changed, in any order. This is related to the commucative property, as well as the associative property, which apply to both. - Also, in both cases there is a neutral element (0 for addition, 1 for multiplication).


Is a rational number a real number?

Yes, a rational number is a real number. A rational number is a number that can be written as the quotient of two integers, a/b, where b does not equal 0. Integers are real numbers. The quotient of two real numbers is always a real number. The terms "rational" and "irrational" apply to the real numbers. There is no corresponding concept for any other types of numbers.


What is the 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.


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.


Is 55 an odd number?

The concepts "even" and "odd" apply to whole numbers. They don't make sense for other classes of numbers, such as rational numbers, real numbers, complex numbers, etc.


What is the distributive property for 79.45?

The distributive property is applicably to the operation of multiplication over either addition or subtraction of numbers. It does not apply to single 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.


Can a number be irrational and rational at the same time?

No they cant because that would be contradicting each other ( The numbers wont end and don't have a pattern but rational is the complete opposite)


Does the commutative property of addition apply when you add to negative integers?

Yes. The commutative property of addition (as well as the commutative property of multiplication) applies to all real numbers, and even to complex numbers. As an example (for integers): 5 + (-3) = (-3) + 5


What makes a number not prime or composite?

0 and 1 (and -1) are the only integers which are not prime nor composite. All non-integral numbers are also non-prime and non-composite. This is because the property is not defined for such numbers.