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

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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
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# Is the set of whole numbers closed under subtraction?

It depends on your definition of whole numbers. The classic definition of whole numbers is the set of counting numbers and zero. In this case, the set of whole numbers is not closed under subtraction, because 3-6 = -3, and -3 is not a member of this set. However, if you use whole numbers as the set (MORE)

# Are odd numbers closed under addition?

3. 5. 7. 9. 11. 13. 15. 17. 19....the sum total of these numbers is100..make it a group of 5-5..so that each group has its sum totAL OF 50.

# Is Natural numbers are closed under multiplication?

Yes.natural numbers are closed under multiplication.It means when the operation is done with natural numbers in multiplication the sum of two numbers is always the natural number.

# Are prime numbers closed under addition?

no, not all prime numbers are closed under addition. why? because, when you add 2 prime numbers you will not always get a prime number. example: 5+3= 8 5 and 3 are prime numbers but their sum is 8 which is a composite number..

# Are even numbers closed under addition?

Yes, when you add any two even numbers, the result is always an even number.

# What set of numbers is closed under division?

Integers are closed under division I think o.o. It's either counting numbers, integers or whole numbers . I cant remember :/

# Are irrational numbers closed under division?

No. 4 root 2 and 2 root 2 are both irrational. Divide the first by the second you get 2. Which is not a member of the set of irrational numbers.

# Which set of numbers is closed under subtraction?

A set of r eal numbers is closed under subtraction . when you take two real numbers and subtract , the answer is always a real number .

# Are natural numbers closed under division?

No. Closed means that you could do the operation (division) on any two natural numbers and you would get a result in the natural numbers. Take 7/3 for example, this is obviously not a natural number.

# Is the set of irrational numbers closed under subtraction?

No; here's a counterexample to show that the set of irrational numbers is NOT closed under subtraction: pi - pi = 0. pi is an irrational number. If you subtract it from itself, you get zero, which is a rational number. Closure would require that the difference(answer) be an irrational number a (MORE)

# The natural numbers are closed under division?

No, the natural numbers are not closed under division. For example, 2 and 3 are natural numbers, but 2/3 is not.

# 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 irrational numbers closed under multiplication?

No. To say a set is closed under multiplication means that if you multiply any two numbers in the set, the result is always a member of the set. If, say, the 2 numbers are radical 2 and radical 2 we have (1.4142...)(1.4142...) which by definition equals 2. The result is not an irrational numbe (MORE)

# Is irrational numbers closed under division?

Nope. Quick example: e (2.71828) is irrational. Therefore 2*e is irrational making both of them elements of the set of irrational numbers. However, dividing the two, e/(2*e), gives you 1/2, which is a rational number.

# Are odd numbers closed under subtraction?

No, nor under addition, either. The sum or difference of two odd numbers is NOT an odd number. No, nor under addition, either. The sum or difference of two odd numbers is NOT an odd number. No, nor under addition, either. The sum or difference of two odd numbers is NOT an odd number. No, nor unde (MORE)

# Is the set of odd numbers is closed under multiplication but is not under addition?

Let + (addition) be a binary operation on the set of odd numbers S. The set S is closed under + if for all a, b Ïµ S, we also have a + b Ïµ S. Let 3, 5 Ïµ the set of odd numbers 3 + 5 = 8 (8 is not an odd number) Since 3 + 5 = 8 is not an element of the set of the odd numbers, the set (MORE)

# What is closed under subtraction?

The set of all integers; the set of all rational numbers; the set of all real numbers; the set of all complex numbers. Also their multiples - for example the set of all multiples of 2; the set of all multiples of 2.5; the set of all multiples of sqrt(17); the set of all multiples of (MORE)

# Which sets of numbers are closed under subtraction?

To be closed under an operation, when that operation is applied totwo member of a set then the result must also be a member of theset. Thus the sets â (Complex numbers), â (Real Numbers), â (RationalNumbers) and â¤ (integers) are closed under subtraction. â¤+ (the positive i (MORE)

# Give ten examples of natural number are closed under subtraction and division?

You can give hundreds of examples, but a single counterexample shows that natural numbers are NOT closed under subtraction or division. For example, 1 - 2 is NOT a natural number, and 1 / 2 is NOT a natural number.

# Why subtraction and division operations are not closed under the set of natural numbers?

2 - 8 = -6 -6 is not a natural number. 2/8 = 1/4 1/4 is not a natural number.

# Why are odd integers closed under multiplication but not under addition?

The numbers are not closed under addition because whole numbers, even integers, and natural numbers are closed.

# Are natural numbers closed under addition?

Yes, because naturals are counting numbers, {1,2,3...} and any natural number added by another natural number has to be a natural. Think of a number line, and your adding the natural numbers. The sum has to be natural, so yes it is closed.

# Are real numbers closed under addition and subtraction?

Real numbers are closed under addition and subtraction. To get a number outside the real number system you would have to use square root.

# Why are fractions closed under addition?

For a set to be closed under any operation, the result of the operation must also be a member of the set. The result of adding fractions is another fraction, thus it is closed under addition. Remember that 8 / 3 , 8 / 4 , 4 / 4 , 2 / 1 are all fractions - they have a numerator and denomin (MORE)

# Which set of numbers is closed under addition?

Natural (â), integer (â¤), rational (â), real (â) and complex (â) numbers are all closed under addition.

# What is closed and not-closed under addition?

The set of even numbers is closed under addition, the set of odd numbers is not.

# Is the set of even integers closed under subtraction and division?

Subtraction: Yes. Division: No. 2/4 = is not an integer, let alone an even integer.

# Are real numbers closed under addition?

yes because real numbers are any number ever made and they can beclosed under addition

# Are composite numbers closed under addition?

No, they are not. You can add two composite numbers, 15 and 14 for example, and get a sum, 29, that is prime.

# What sets of numbers are closed under addition?

I know that whole numbers, integers, negative numbers, positive numbers, and even numbers are. Anyone feel free to correct me.

# Are odd numbered sets closed under addition and multiplication?

No. 1 + 3 = 4, which is not odd. In fact, no pair of odds sums to an odd. So the set is not closed under addition.

# Why is the set of positive whole numbers closed under subtraction?

The set of positive whole numbers is not closed under subtraction! In order for a set of numbers to be closed under some operation would mean that if you take any two elements of that set and use the operation the resulting "answer" would also be in the original set. 26 is a positive whole numb (MORE)

# Why are rational numbers closed in subtraction?

Because when one rational number is subtracted from another rational number the result is a rational number. Don't forget that integers (â¤) are a subset of rational numbers (â).

# What is the smallest set of numbers closed under subtraction?

Any one of the sets of the form: {kz : where k is any fixed integer and z belongs to the set of all integers} Thus, k = 1 gives the set of all integers, k = 2 is the set of all even integers, k = 3 is the set of all multiples of 3, and so on. You might think that as k gets larger the sets become (MORE)

# Why are whole numbers closed under multiplication?

Because if X and Y are any two whole number, then X*Y is also a whole number. Always.

# Is the set of natural numbers closed under addition?

Yes, when you add any group of natural numbers, the sum will also be a natural number.

# Are irrational addition numbers closed under the closure property?

No. For example, the square root of two plus (minus the square root of two) = 0, which is not an irrational number.

# Is whole numbers are closed under division?

No, whole numbers are not closed under division. It is possible to divide one whole number by another whole number and get a result which is not a whole number, for example, 1/2. One divided by two is a half.

# Is natural numbers a closed set under subtraction?

No. A set is closed under subtraction if when you subtract any two numbers in the set, the answer is always a member of the set. The natural numbers are 1,2,3,4, ... If you subtract 5 from 3 the answer is -2 which is not a natural number.

# What is a counterexample to the set of negative numbers is closed under subtraction?

- 2 - ( - 5) = - 2 + + 5 = + 3. ( + 3 is not in the set of negativenumbers.)

# Are the whole numbers closed under addition if so explain?

Yes because being closed under an operation means that when the operation is performed on members of a set the result is also a member of the set, and when any two [members of the set of] whole numbers are added together the result of the addition is also a whole number which is, unsurprisingly, a m (MORE)

# Why are even whole and natural numbers closed under addition?

For a set to be closed under an operation, doing the operations on any two members of the set must result in another member of the set. The set of even natural numbers is {2, 4, 6, ...}. When two even numbers are added, the result is also an even number. Adding two positive numbers results (MORE)

# 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.

# What does this mean Which set of these numbers is closed under subtraction?

It means whatever members of the set you subtract, the answer will still be a member of the set. For example, the set of positive integers is not closed under subtraction, since 3 - 8 = -5

# Is the set of real numbers closed under addition?

Yes. The set of real numbers is closed under addition, subtraction, multiplication. The set of real numbers without zero is closed under division.

# Which sets of numbers are closed under multiplication?

There are infinitely many sets of this type. Some of the common sets include natural numbers, integers, rational numbers, real numbers, complex numbers. Also, as an example, all sets of multiples of some whole number, for instance: { ... -6, -4, -2, 0, 2, 4, 6, ...} {... -9, -6, -3, 0, 3, 6, 9, ...} (MORE)

# Is the whole number closed under subtraction?

If you interpret "whole numbers" as "integers", then yes. If you interpret "whole numbers" as "non-negative integers", then no.

# How do i solve the set of odd numbers is closed under addition?

You can't. Adding any two odd numbers always gives an even number,which is not a member of the set of odd numbers.

# Are Irrational Numbers Closed Under Addition counter example?

No. Here is a counter-example: x = 1 + sqrt(2) y = 2 - sqrt(2) x and y are irrational. x + y = 3 is rational.

# What does it mean for a polynomial to be closed under addition subtraction and multiplication?

If you perform any of those operations on a polynomial, the resultwill be a polynomial.