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

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โˆ™ 2013-08-30 07:12:56
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Q: Is a rational number closed for addition and for multiplication?
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Related questions

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

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

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.

Is a rational number closed under addition?

No. A number cannot be closed under addition: only a set can be closed. The set of rational numbers is closed under addition.

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.

Is a positive number closed for addition and for multiplication?


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

Additive identity = 0Multiplicative identity = 1.

Which number produces a rational number when added to 0.5?

Since the set of rational numbers is closed under addition, any rational number added to 0.5 will total another rational number.

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.

When is a set of negative irrational numbers closed?

It cannot be closed under the four basic operations (addition, subtraction, multiplication, division) because it is indeed possible to come up with two negative irrational numbers such that their sum/difference/product/quotient is a rational number, indicating that the set is not closed. You will have to think of a different operation.

Addition of rational number with a rational one gives a rational number?

Yes, it does.

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.

Why is the multiplication of rational numbers always result in a rational number?

It follows from the closure of integers under addition and multiplication.Any rational number can be expressed as a ratio of two integers, where the second is not zero. So two rational numbers may be expressed as p/q and r/s.A common multiple of their denominators is qs. So the numbers could also have been expressed as ps/qs and qr/qs.Both these have the same denominator so their sum is (ps + qr)/qs.Now, because the set of integers is closed under multiplication, ps, qr and qs are integers and because the set of integers is closed under addition, ps + qr is an integer.Thus the sum has been expressed as a ratio of two integers, ps + qr, and qs and so it is a rational number.

How is multiplication and addition different?

Multiplication is repeated adding. Addition is a number with another number combined for a total.

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 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.

What do rational and irrational numbers have in common?

Rational and irrational numbers are part of the set of real numbers. There are an infinite number of rational numbers and an infinite number of irrational numbers. But rational numbers are countable infinite, while irrational are uncountable. You can search for these terms for more information. Basically, countable means that you could arrange them in such a way as to count each and every one (though you'd never count them all since there is an infinite number of them). I guess another similarity is: the set of rational numbers is closed for addition and subtraction; the set of irrational numbers is closed for addition and subtraction.

What combines multiplication and addition by multiplying each addend by the number and adding the products?

The distributive property of multiplication over addition.

Why does the sum of rational number and irrational numbers are always irrational?

Let your sum be a + b = c, where "a" is irrational, "b" is rational, and "c" may be either (that's what we want to find out). In this case, c - b = a. If we assume that c is rational, you would have: a rational number minus a rational number is an irrational number, which can't be true (both addition and subtraction are closed in the set of rational numbers). Therefore, we have a contradiction with the assumption that "c" (the sum in the original equation) is rational.

Can half of an irrational number be rational?

No, it cannot. The product of a rational and irrational is always irrational. And half a number is equivalent to multiplication by 0.5

Are set of irrational number closed under addition?

No. 2 + sqrt(5) and 2 - sqrt(2) are both irrational but their sum, 4 is rational.

What property represents a rational number added to a rational number gives a rational number answer?

The relevant property is the closure of the set of rational numbers under the operation of addition.

What is the addition of a rational number and irrational number?

It is an irrational number.

Why is division not closed for rational numbers give an example?

If a set is closed under an operation. then the answer will be a part of that set. If you add, subtract or multiply any two rational numbers you get another national number. But when it comes to division, it is closed except for one number and that is ZERO. eg 3.56 (rational number) ÷ 0 = no answer. Since no answer is not a rational number, that rational numbers are not closed under the operation of division.