All whole numbers (integers) are rational because they can be written as the number over 1.
1 = 1/1 so it can be written as a fraction so is rational.
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The number in the question is rational. It is not at clear how a rational number can be rationalised!
All factors are whole numbers and all whole numbers are rational numbers (a rational number is one which can be expressed as one integer over another integer, and whole numbers can be expressed as themselves over 1), thus all factors are rational numbers and so all greatest common factors are rational numbers. The set of whole numbers is a [proper] subset of the set of rational numbers: ℤ ⊂ ℚ
Real numbers are composed of rational and irrational numbers. Integers are part of the group (set) of rational numbers. And the integers are composed of the counting numbers (1, 2, 3, ...) and their negative counterparts (-1, -2, -3, ...). Oh, almost forgot. There is one more integer that is neither positive or negative. It's the number zero. Zero is an integer (neither positive or negative). The smallest real number ever is zero.
To prove a number ab is rational, you have to find two integers t and n such that t/n = ab.Since we know that a, and b are rational, they can be expressed as follows:a = p1/q1b = p2/q2then ab = p1p2/q1q2Since p1, p2, q1, and q2 are all integers, p1p2 is an integer, and q1q2 is an integer. This gives us the t, and n we are looking for. t = p1p2 and n = q1q2, and ab = t/n, so ab is rational.
It is 332/15.