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Can we say all natural numbers are whole numbers?___________

•Is the vice versa true even?_____________

Can we say all whole numbers are natural numbers? _________.

•Is the vice versa true even?_______

Can we say all integers are rational numbers? _________.

•Is the vice versa true even?_______

Give five examples of rational numbers. And write respective values of p and q.

 Properties of rational numbers:

1) Closure Property: For two rational numbers say a and b the results of addition,
subtraction and multiplication operations give a rational number. We can say that
rational numbers are closed under addition, subtraction and multiplication. For example:

 (2/5)+(1/3) = 11/15
 (4/6) – (1/3) = 2/6= 1/3
 (7/3). (5/2) = 35/6
The division is not under closure property because division by zero is not defined.

2) Commutative Property:
For rational numbers, addition and multiplication are commutative.

Commutative law of addition: a+b = b+a

Commutative law of multiplication: a×b = b×a.
3
3
3
3
Eg: 2 × = 6 ; → × 2 = 6 ; → 2 × = × 2
11 5 55 5 11 55 11 5 5 11

3 −5
Take a= = , check if rational numbers follow commutative property under
4 3
subtraction and division.
3) Associative Property:
Rational numbers follow the associative property for addition and multiplication.

Suppose a, b and c are rational then