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Negative fractions are Rational number?
They are rational, if the numerator and denominator are integers. For example, -2 / 3 would be a rational number.They are rational, if the numerator and denominator are integers. For example, -2 / 3 would be a rational number.They are rational, if the numerator and denominator are integers. For example, -2 / 3 would be a rational number.They are rational, if the numerator and denominator are integers. For example, -2 / 3 would be a rational number.
If a is rational and b is rational is a to the b power is rational?
No. For example, 20.5 is irrational; indeed it was one of the first irrational numbers to be discovered.
Can you add two irrational numbers to get a rational number?
Yes Yes, the sum of two irrational numbers can be rational. A simple example is adding sqrt{2} and -sqrt{2}, both of which are irrational and sum to give the rational number 0. In fact, any rational number can be written as the sum of two irrational numbers in an infinite number of ways. Another example would be the sum of the following irrational quantities [2 + sqrt(2)] and [2 - sqrt(2)]. Both quantities are positive and irrational and yield a rational sum. (Four in this case.) The statement that there are an infinite number of ways of writing any rational number as the sum of two irrational numbers is true. The reason is as follows: If two numbers sum to a rational number then either both numbers are rational or both numbers are irrational. (The proof of this by contradiction is trivial.) Thus, given a rational number, r, then for ANY irrational number, i, the irrational pair (i, r-i) sum to r. So, the statement can actually be strengthened to say that there are an infinite number of ways of writing a rational number as the sum of two irrational numbers.
Are all real numbers rational numbers?
No. For example, pi is a real number, but it is irrational (it cannot be converted into an exact fraction).The reverse is true, however: all rational numbers are also real numbers.
What are numbers that can be written in the quotient of two integers?
These are called "rational numbers" (ratio -> rational), and can be represented by the set Q (integers are Z, natural numbers are N, real numbers are R, complex numbers are C). Any number that can be expressed as a fraction is a rational number. For example, 0.01 is a rational number, because it can be expressed as 1/100. Irrational numbers are often square roots of non-perfect squares (such as the square root of 2 or 7, but not 4 or 9).
