Closure Property of Rational Numbers

posted on: 12 Jan, 2012 | updated on: 16 Aug, 2012

Rational numbers shows one of the important property called as closure property. According to closure property, two Rational Numbers say Q and Z are said to be closed if we perform some operation on these numbers and the answer is also a rational number. Rational numbers are closed under addition, subtraction, multiplication and division by a nonzero rational number.

Ex. Consider two different rational numbers a/b and c/d.

Now we’ll see how rational numbers are closed under different operations.

Addition: a/b + c/d = (ad + cb)/bd,

Subtraction: a/b – c/d = (ad –cb)/bd,

Multiplication: a/b × c/d = ac/bd,

Division: a/b÷ c/d = ad/bc.

Find the addition of given Rational Number using closure property, where rational numbers are 3/4 and 4/4?

According to Closure property of Rational Numbers we can add two Positive Rational Numbers easily. In the given problem both the numbers are positive so simply do addition of both the rational numbers. On adding both the rational number we get:

= (+3/4) + (+4/4),

=3/4 + 4/4 = 7/4.

From the above example, we observe that the sum of rational numbers is a rational number.

Thus,we can say that rational numbers are always closed under addition.