Rational Numbers between Two Rational Numbers

 

 

 

 

Natural Numbers: We know that Natural Numbers arecounting numbers. We can represent Natural Numbers indefinitely to the right of 1 on the number line.
Whole Numbers: Whole Numbers are Natural Numbers including zero. We can represent Whole Numbers indefinitely to the right of Zero on the number line.
Integers: Integers are a collection of numbers consisting of all Natural Numbers, their negatives, and zero. We can represent Integers indefinitely on both sides of Zero on the number line
Rational Numbers: Rational number is a number that is expressed in the form , where  and  are Integersand .

In case of a Rational number, the denominator tells us the number of equal parts into which the first unit has been divided, while the numerator tells us ‘how many’ of these parts have been considered.
We can also represent Rational Numbers indefinitely on both sides of Zero on the number line
There are a finite number of Natural Numbers between any two Natural Numbers. Similarly there are a finite number ofWhole numbers between any two Whole Numbers. But there are infinitely many Rational Numbers between any twoRational Numbers. The idea of mean helps us to find Rational Numbers between two Rational Numbers. 

 

 

Properties of Rational Number

 

• Numbers that can be expressed in the form  ,where p and q are integers and q≠0, are known as rational numbers.  The collection ofrational numbers is denoted by Q. Theserational numbers satisfies various laws or properties that are listed below:

• Rational numbers are closed under addition, subtraction and multiplication. If a, b are any two rational numbers, then and the sum, difference and product of these rational numbers is also a rational number, then we say that rational numbers satisfy the closure law.

• Rational numbers are commutative under addition and multiplication. If a, b are rational numbers, then:Commutative law under addition: a+b = b+aCommutative law under multiplication: axb = bxa

• Rational numbers are associative under addition and multiplication. If a, b, c are rational numbers, then:Associative law under addition: a+(b+c) = (a+b)+cAssociative law under multiplication: a(bc) = (ab)c

• 0 is the additive identity for rational numbers.

• 1 is the multiplicative identity for rational numbers.

• The additive inverse of a  is , and the additive inverse of .

• If  , then  is the reciprocal or multiplicative inverse of , and vice versa.

• For all rational numbers, p, q and r,   and , is known as thedistributive property.