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Is it possible to divide one rational number by another to obtain an irrational number as the quotient?
Wiki User
∙ 15y ago
It is not possible to divide one rational number by another to obtain an irrational number. A rational number is of the form a/b where a and b are both integers, whereas an irrational is a number which is impossible to express in the previously mentioned way.
Let A=(a/b) and B=(c/d) where A and B are both rational numbers. Consider the quotient A/B, this is the same as A(1/B). Rewrite this as (a/b)x(d/c). Assuming we all know basic arithmetic with fractions we can clearly see that the dividend is axd and the divisor is bxc, and the new expression is (axd)/(bxc). Since a, b, c, and d are all integers and the integers are closed under multiplication (two integers multiplied by each other produce another integer) our new expression as a single fraction is one integer over another and it is therefore a rational number.
Wiki User
∙ 15y ago
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Why can't numbers be both rational and irrational?
By definition, an irrational number is a number that is not rational, or in other words a number that cannot be expressed as an integer divided by another integer. A number cannot be both "rational" and "not rational."
Are irrational numbers always integers?
No. An irrational number is one that is not a rational number. A rational number is once that equals one integer divided by another. So an irrational number cannot be represented by one integer divided by another integer, so it cannot be an integer!
What is anouther name for rational and irrational numbers?
Another name for 'rational' is "numbers that are equal to the ratio of two whole numbers". Another name for 'irrational' is "numbers that are not equal to the ratio of any two whole numbers".
How do you determine if eleven out of twenty is a rational or irrational number?
All whole numbers are rational. Any rational number divided by another (non-zero) rational number is a rational number.
Is negative zero point two a rational or irrational number?
-0.2 is another way of saying -1/5. It's rational.
Is it possible to divide one rational number by another to obtain an irrational number as a quotient?
No. Rational numbers are defined as fractions of whole numbers. Suppose we have two rational numbers A = m/n and B = p/q. Then their quotient is defined as A/B = (m*q) / (n*p). Since m,n,p and q are whole, the products m*q and n*p are whole as well, making A/B a rational number.
Why the product of nonzero rational number and a rational number is an irrational?
Actually the product of a nonzero rational number and another rational number will always be rational.The product of a nonzero rational number and an IRrational number will always be irrational. (You have to include the "nonzero" caveat because zero times an irrational number is zero, which is rational)
How do you turn an irrational number in to a rational number?
Some irrational numbers can be multiplied by another irrational number to yield a rational number - for example the square root of 2 is irrational but if you multiply it by itself, you get 2 - which is rational. Irrational roots of numbers can yield rational numbers if they are raised to the appropriate power
Is negative 2pi a rational number?
No. The number pi is irrational, and if you multiply an irrational number by a non-zero rational number (in this case, -2), you will get another irrational number.As a general guideline, most calculations that involve irrational numbers will again give you an irrational number.
Which irrational number is closest to 6?
Irrational numbers are infinitely dense. That is to say, between any two irrational (or rational) numbers there is an infinite number of irrational numbers. So, for any irrational number close to 6 it is always possible to find another that is closer; and then another that is even closer; and then another that is even closer that that, ...
Is 37 squared a rational or irrational number?
372 = 1,369 is an integer; therefore, it is a rational number. In fact, the square of any integer is always an integer; this is because the sum or product of any two integers is an integer. And every integer is a rational number; this is because a rational number is defined as the quotient obtained by dividing one integer into another; and because every integer is the quotient obtained by dividing that integer by the integer 1.
Why can't numbers be both rational and irrational?
By definition, an irrational number is a number that is not rational, or in other words a number that cannot be expressed as an integer divided by another integer. A number cannot be both "rational" and "not rational."
Irrational number when multiplied by 0.4?
If you multiply an irrational number by ANY non-zero rational number, the result will be irrational.
Why does a rational number plus an irrational number equal an irrational number?
from another wikianswers page: say that 'a' is rational, and that 'b' is irrational. assume that a + b equals a rational number, called c. so a + b = c subtract a from both sides. you get b = c - a. but c - a is a rational number subtracted from a rational number, which should equal another rational number. However, b is an irrational number in our equation, so our assumption that a + b equals a rational number must be wrong.
Can you add two irrational numbers and get a rational number?
Yes - if I had an irrational number x, and I added that to the number (7-x), I would end up with 7.If the number is irrational, it can be subtracted from a rational/integer to make another irrational.
Are irrational numbers always integers?
No. An irrational number is one that is not a rational number. A rational number is once that equals one integer divided by another. So an irrational number cannot be represented by one integer divided by another integer, so it cannot be an integer!
Can you subtract two rational numbers and get an irrational number?
Do you mean can we subtract one rational number from another rational number and get an irrational number as the difference? I'm not a mathematician, but I suspect strongly the answer is no. Wouldn't this imply that we can sometimes add a rational number to an irrational one, and get a rational number as a sum? That doesn't seem possible.Ans 2.It isn't possible. Proof :-Given two rational numbers, multiply the two denominators.Express each rational in terms of the common multiple.Algebraically add the numerators of the new rational numbers.Put this over the common multiple; there's the result expressed as a ratio.
