Properties of Rational Number

Chapter 1 Class 8 Rational Numbers
Concept wise

Let’s check closure for rational numbers

 Operation Commutative Closed or not Addition 2/5 + 4/5 = 6/5 6/5 is a rational number Also, (−3)/5 + 0 = (−3)/5 (−3)/5 is a rational number So, rational numbers are closed under addition So, if we add any two numbers, we get a rational number So, it is closed Subtraction 2/5 – 4/5 = (2 − 4)/5 = (−2)/5 (−2)/5 is a rational number Also, (−3)/5 – 0 = (−3)/5 (−3)/5 is a rational number So, rational numbers are closed under subtraction So, if we subtract any two numbers, we get a rational number So, it is closed Multiplication 2/5 × 4/5 = (2 × 4)/(5 × 5) = 8/25 8/25 is a rational number Also, (−3)/5 × 0 = 0 0 is a rational number So, rational numbers are closed under multiplication So, if we multiply any two numbers, we get a rational number So, it is closed Division 2/5 ÷ 4/5 = 2/5  × 5/4 = 2/4 = 1/2 1/2 is a rational number Also, (−3)/5 ÷  0 = (−3)/5 × 1/0  1/0 is not defined ∴ (−3)/5 × 1/0 is also not defined So, it is not a rational number So, rational numbers are not closed under division So, if we divide any two numbers, we do not get a rational number So, it is not closed

To summarize

 Numbers Closed under Addition Subtraction Multiplication Division Natural numbers Yes No Yes No Whole numbers Yes No Yes No Integers Yes Yes Yes No Rational Numbers Yes Yes Yes No