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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.

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).

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

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

Division is the inverse operation to multiplication (except by 0). Multiplication by a number is equivalent to division by its reciprocal.

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

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.

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).

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.

There is no real difference between the two operations. Division by a scalar (a number) is the same as multiplication by its reciprocal. Thus, division by 14 is the same as multiplication by (1/14).

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.

It the combination is multiplication and the rational number is 0, then the result is rational. Otherwise it is irrational.

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,

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

Converting a rational number to a decimal using long division. For example if you have a rational number of 2/5 you would set up the equation as 2 divided by 5 which requires long division. The answer to this would then be the decimal number 0.4.

by using multiplication backwards Division is the opposite of multiplication. It is the equivalent of when you diminish a number by multiplying it by a fraction or a decimal.

No. Zero is a rational number, but division by zero is not defined.

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

Yes. Any number which can be expressed as a division of two integers is called a rational number. 12 = 12/1 is clearly rational.

Zero times anything is zero.

Another rational number

multiplication/division: least number of significant figures addition/subtraction: least number of numbers to the right of decimal point