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For addition, 0 and for multiplication, 1.

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Q: What are the identity elements for the addition and multiplication of rational numbers?
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Related questions

What are the identity elements for the addition and multiplication of rational number?

Additive identity = 0Multiplicative identity = 1.


In the set of rational numbers what is the identity element for multiplication?

1 is the identity for multiplication. 1*x = x = x*1 for all rational x.


Is a rational number closed for addition and for multiplication?

A rational number is not. But the set of ALL rational numbers is.


Are rational numbers closed under division multiplication addition or subtraction?

Rational numbers are closed under addition, subtraction, multiplication. They are not closed under division, since you can't divide by zero. However, rational numbers excluding the zero are closed under division.


Can you add two rational numbers and get an irrational number?

No. The set of rational numbers is closed under addition (and multiplication).


Do positive rational numbers form group?

Yes, with respect to multiplication but not with respect to addition.


Is the sum of rational numbers always rational?

Yes. In general, the set of rational numbers is closed under addition, subtraction, and multiplication; and the set of rational numbers without zero is closed under division.


Are rational numbers are closed under addition subtraction division or multiplication?

The set of rational numbers is closed under all 4 basic operations.


Why does a rational number plus a rational number or a rational number multiplied by a rational number equal to rational number?

The way in which the binary functions, addition and multiplication, are defined on the set of rational numbers ensures that the set is closed under these two operations.


How are the rules for adding integers applied to operations with rational numbers?

You need the rules of multiplication as well as of addition. But multiplication of integers can be viewed as repeated addition. Thus, if p/q and r/s are two rational numbers then their sum is(p*s + q*r)/(q*s)


Does the Commutative Property apply to addition of fractions?

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


What are the different properties of a rational number?

The set of rational numbers is a mathematical field. This requires that if x, y and z are any rational numbers then their properties are as follows:x + y is rational : [closure of addition];(x + y) + z = x + (y + z) : [addition is associative];there is a rational number, denoted by 0, such that x + 0 = x = 0 + x : [existence of additive identity];there is a rational number denoted by -x, such that x + (-x) = 0 = (-x) + x : [existence of additive inverse];x + y = y + x : [addition is commutative];x * y is rational : [closure of multiplication];(x * y) * z = x * (y * z) : [multiplication is associative];there is a rational number, denoted by 1, such that x * 1 = x = 1 * x : [existence of multiplicative identity];for every non-zero x, there is a rational number denoted by 1/x, such that x * (1/x) = 1 = (1/x) * x : [existence of multiplicative inverse];x * y = y * x : [multiplication is commutative];x * (y + z) = x * y + x * z : [multiplication is distributive over addition].


What are the numbers in division mutliplication addition subtraction?

You can have counting number in multiplication and addition. All integers are in multiplication, addition and subtraction. All rational numbers are in all four. Real numbers, complex numbers and other larger sets are consistent with the four operations.


What are 5 properties of addition that apply to rational numbers?

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)


How are multiplying and addition different?

In some respects they are the same in others they are not. At a simple level, multiplication is simply repeated addition so that the two operations are the same. However, an inverse operation can be defined on the set of rational or real numbers for addition (it is called subtraction) but not in its entirety for multiplication (division by zero is not defined).


Is 8 over 9 an irrational number?

Any addition, subtraction, multiplication, or division of rational numbers gives you a rational result. You can consider 8 over 9 as the division of 8 by 9, so the result is rational.


What is closing a rational number under addition And can you close them under subtraction multiplication and division?

Rational numbers are numbers that can be expressed as a fraction a/b where a and b are both integers and b is not equal to zero. All integers n are rational numbers because they can be expressed as the fraction n/1. Rational numbers are closed under addition, subtraction, multiplication and division by a non-zero rational. To be closed under addition, subtraction, multiplication and division by a non-zero rational means that if you have two rational numbers, when you add, subtract, multiple or divide them, you will get another rational number. For example, take the rationals 1/3 and 4/3. When you add them together, you get another rational number, 5/3. Same with the other operations. 1/3 - 4/3 = -1 (remember integers are rational, too) (1/3) * (4/3) = 4/9 (1/3) / (4/3) = 1/4


How do multiplication and division of rational number relate to one another?

Division by a non-zero rational number is equivalent to multiplication by its reciprocal.


Select any irrational number and turn it into a rational number by using addition subtraction multiplication division or exponentiation?

Other than multiplication by 0 or by its own reciprocal, it if often not possible. Try it with pi, if you think otherwise.


Are rational numbers closed under multiplication?

Rational numbers are closed under multiplication, because if you multiply any rational number you will get a pattern. Rational numbers also have a pattern or terminatge, which is good to keep in mind.


Are rational numbers closed under subtraction?

Yes. They are closed under addition, subtraction, multiplication. The rational numbers WITHOUT ZERO are closed under division.


What is the product of a number and its inverse is 1?

That is the identity property of multiplication for all rational numbers, or all real numbers or all complex numbers except (in each case) for 0.


Are rational numbers are closed under addition subtraction multiplication and division?

They are closed under all except that division by zero is not defined.


Which rational number is the multiplicative identity for rational number?

1


What is the combination of rational numbers and irrational?

It the combination is multiplication and the rational number is 0, then the result is rational. Otherwise it is irrational.