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Rational numbers include integers, and any number you can write as a fraction (with integers in the numerator and denominator). Most numbers that include roots (square roots, cubic roots, etc.) are irrational - if you take the square root of any integer except a perfect square, for example, you'll get an irrational number. Expressions involving pi and e are also usuallyirrational.

Q: Tell whether each number is rational?

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Each of the two numbers is a rational number.

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.

Not quite. A rational number is a ratio and each rational number is a ratio of specific pairs of integers - not ANY two integers. And, of course, 0 is not allowed on the denominator.

Rational numbers are of the form n/m where n and m<>0 are integers. Since for each integer n and integer 1 we know that n = n/1, each integer is a rational number.

Any natural number, such as 37, will also be in each of the other categories.

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Each of the two numbers is a rational number.

Write each rational number as b. 0.31

I have no idea what "compersion" means or what you are trying to say. A rational number is so called because it can be expressed as ratio of two integers. Each rational number is a ratio and each ratio is a rational number. However, the relationship is not one of equivalence: each rational number can be represented by infinitely many equivalent ratios.

Not necessarily.

It is each one of them.

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.

Let `a` be a rational number and `b` be an irrational number,assume that the sum is rational. 1.a +b =c Where a and c are rational and b is irrational. 2.b=c-a Subtracting the same number a from each side. 3.b is irrational c-a is a rational number we arrived at a contradiction. So the sum is an irrational number.

Not quite. A rational number is a ratio and each rational number is a ratio of specific pairs of integers - not ANY two integers. And, of course, 0 is not allowed on the denominator.

A number is prime if it only has two distinct factors.

101, 173 and 911 are all prime numbers. 173911 is not.

Each and every rational number except 0. Once you leave the domain of integers, all rational numbers (excluding 0) divide into every other rational number with a quotient that is rational. The above can be extended to real numbers.

In theory it is possible but in practice, if a number is a product of two very large primes - each being a hundred digits long, or larger - then it is very difficult to tell whether it is prime or composite. The fact that it is so difficult makes this characteristic particularly useful for data encryption.