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Is the difference of two rational numbers always a rational number?
Wiki User
∙ 12y ago
Yes.
Since they are rational numbers, let's call the first one a/b and the second one c/d where a,b,c, and d are integers.
Now we can subtract by finding a common denominator. Let's use bd.
So we have ad/bd-cb/bc= (ad-bc)/CD which is rational since we know ad and bc are integers being the product of integers and CD is also an integers.
Call ad-bd=P and call CD=Q where P and Q are integers. We now see the difference is of two rationals is rational.
Wiki User
∙ 12y ago
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The difference of two rational numbers is always a rational number?
Yes, that's true.
Is the difference of rational numbers a rational number?
Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction. All natural numbers are rational.
What would be difference of 2 rational numbers?
Another rational number.
List of rational and irrational numbers?
-- There's an infinite number of rational numbers. -- There's an infinite number of irrational numbers. -- There are more irrational numbers than rational numbers. -- The difference between the number of irrational numbers and the number of rational numbers is infinite.
The sum of two rational numbers is always a rational number?
Yes.
The difference of two rational numbers is always a rational number?
Yes, that's true.
Is it true that The difference of two rational numbers always a rational number?
Yes. The rational numbers are a closed set with respect to subtraction.
Is The difference of two real numbers always an irrational number?
No. 5 and 2 are real numbers. Their difference, 3, is a rational number.
Why is the difference of two rational numbers always a whole number?
The question cannot be answered because it is nonsensical. The difference between two rational numbers is very very rarely a whole number.
Is the difference of two rational numbers always rational?
Yes. This is the same as asking for one rational number to be subtracted from another; to do this each rational number is made into an equivalent rational number so that the two rational numbers have the same denominator, and then the numerators are subtracted which gives a rational number which may possibly be simplified.
Is the product of two rational numbers irrational?
The product of two rational numbers is always a rational number.
What s happens when rational numbers are multplied?
The product of two rational numbers is always a rational number.
Would the difference of a rational number and a rational number be rational?
The difference of two rational numbers is rational. Let the two rational numbers be a/b and c/d, where a, b, c, and d are integers. Any rational number can be represented this way. Their difference is a/b-c/d = ad/bd-cb/bd = (ad-cb)/bd. Products and differences of integers are always integers. This means that ad-cb is an integer, and so is bd. Thus, (ad-cb)/bd is a rational number (since it is the ratio of two integers). This is equivalent to the difference of the original two rational numbers.
Does there exist an irrational number such that its square root is rational?
No, and I can prove it: -- The product of two rational numbers is always a rational number. -- If the two numbers happen to be the same number, then it's the square root of their product. -- Remember ... the product of two rational numbers is always a rational number. -- So the square of a rational number is always a rational number. -- So the square root of an irrational number can't be a rational number (because its square would be rational etc.).
Is the difference of rational numbers a rational number?
Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction. All natural numbers are rational.
Is the difference of two rational numbers a rational number?
Yes.
What would be difference of 2 rational numbers?
Another rational number.
