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# Is 3/4 a Rational Number?

TopStart with defining the term real number and its parts and try to understand the term rational, irrational numbers. Rational numbers are those numbers in which an Integer is divided by another integer. Mathematically we can say that if a and b are two integers such that they can be represented in form a/b then a/b is a rational number, where b can never be equal to zero. Irrational numbers are those numbers in which two numbers a and b can never be written in the form a/b. Examples of Irrational Numbers are pi , √2 , √5, etc Now, let us check if ¾ is a rational number. Assume that 3/4 is a rational number. Since every rational number can be expressed as a/b form which do not have any common factor so we can say that a/b = 3/4 Squaring both side we get: a2/b2 = 9/16 a2 = (9/16) b2 Or we can say b2 = a2(16/9) a2 is divided by 9. So we can say that a is divided by 9. It implies that there exist some number c such that a/9 = c a = 9c By squaring both side we get a2 = 81 c2 Put the value of a2 from the equation a2 = (9/16) b2 we get: (9/16)b2 = 81c2 this tends to b2/ 9 = 16 c2 It implies that b2 is divided by 9. So we can say that b is divided by 9. This implies that a and b have a common factor 9. Since a and b have common factor therefore 3/4 is not a irrational number. Hence 3/4 is a rational number.