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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.

Q: Are rational numbers closed under division multiplication addition or subtraction?

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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.

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

an algebraic expression is an expression built up from constants, variables, and a finite number of algebraic operations (addition, subtraction, multiplication,division and exponentiation to a power that is a rational number). For example,

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

For addition, 0 and for multiplication, 1.

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

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

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

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.

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.

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.

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

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

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).

an algebraic expression is an expression built up from constants, variables, and a finite number of algebraic operations (addition, subtraction, multiplication,division and exponentiation to a power that is a rational number). For example,

From Wikipedia: "In mathematics, an algebraic expression is an expression built up from constants, variables, and the algebraic operations (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number)". So, the answer is yes - since any polynomial can be obtained by applying only a subset of these operations (additions, subtraction, multiplication).

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