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

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

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Division by any non-zero number is the same as multiplication by its reciprocal.

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

It is a division word. The quotient is the result you get when you divide a number (dividend) by another number (divisor).

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.

the whole reason is this: multiplication is adding to that number in groups and division is subtracting from a number in groups.

Related questions

Division by any non-zero number is the same as multiplication by its reciprocal.

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

It is a division word. The quotient is the result you get when you divide a number (dividend) by another number (divisor).

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.

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

Division is the inverse operation to multiplication. Division by a number (other than zero) is the same as multiplication by its reciprocal.

Division by a number is the inverse operation to multiplication by the number (and vice versa).

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

Multiplication and division are related because they are inverse operations of each other. When you multiply a number by another number, you are essentially adding the first number repeatedly, while division is the process of splitting a number into equal parts. By using multiplication and division, you can solve various mathematical problems and find the relationship between quantities.

the whole reason is this: multiplication is adding to that number in groups and division is subtracting from a number in groups.

You are working with numbers. One is a whole number and the other is a fraction of a whole number (with a decimal point, etc). You apply the same principles of subtracting one number from another or a fraction of one number from a fraction of another. Numbers is numbers!