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Additive identity = 0Multiplicative identity = 1.

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

For addition, 0 and for multiplication, 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.


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.


Do positive rational numbers form group?

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


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].

Related questions

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

For addition, 0 and for multiplication, 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.


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

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


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.


Do positive rational numbers form group?

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


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].


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

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


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.


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.


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.