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

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

How do you use reciprocals to solve a division problem with rational numbers?

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

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.

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

Is quotient a division word or a multiplication word?

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

Is a rational number closed for addition and for multiplication?

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

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.

What is the relationship between multiplication and division?

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

How can knowing that multiplication is repeated addition and division is repeated subtraction help you understand that multiplication and division are related?

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

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.

How do you Relate Division to Multiplication?

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

How is multiplication and division related?

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

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.

What is different between multiplication and division of vector by a number?

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).

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.

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 is an algebraic expresion?

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,

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

How do you change rational number to decimal?

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.

How do you learn division?

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.

Is the set of rational numbers closed under division and Why?

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

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

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

Is twelve a rational number?

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

What is multiplication of a rational number by zero?

Zero times anything is zero.

What is square of a rational number?

Another rational number

When finding significant figures for multiplication and division problems you go by the least number of?

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