Give one example each to show that the rational numbers

Solution:

Rational numbers are closed under addition:-

Example:- 5/4 + 1/2

The LCM of the denominators 4 and 2 is 4

∴ (5/4) = [(5×1)/ (4×1)] = (5/4)

and (1/2) = [(1×2)/ (4×2)] = (1/4)

Then,

= 5/4 + ¼

= (5 + 1)/ 4

= 6/4

= 3/2 is a rational number

Rational numbers are closed under subtraction:-

Example:- 5/4 – 1/2

The LCM of the denominators 4 and 2 is 4

∴ (5/4) = [(5×1)/ (4×1)] = (5/4)

and (1/2) = [(1×2)/ (4×2)] = (1/4)

Then,

= 5/4 – ¼

= (5 – 1)/ 4

= 4/4

= 1 is a rational number

Rational numbers are closed under addition:-

Example:- 5/4 × 1/2

= 5/8 is a rational number.

For any rational number x, x ÷ 0 is not defined,

Hence not all rational numbers are closed under division. We can say that except zero, all rational numbers are closed under division.

Example, ¾ ÷ 4/5

= ¾ × 5/4

= 15/16 is a rational number.