RATIONALNUMBERS

The numbers of the form p/q (q=0) is called a RATIONAL NUMBER.Examples: 5/7 6/8 -6/9 etc.

RATIONAL NUMBERS.

PROPERTIES OF RATIONAL NUMBERS.

CLOSURE PROPERTYRATIONAL NO. ARE CLOSED UNDER ADDITION , SUBTRACTION & MULTIPLICATION.THEY ARE NOT CLOSED UNDER DIVISION.

CUMMUTATIVE PROPERTYRATIONAL NUMBERS ARE COMMUTATIVE UNDER ADDITION AND MULTIPLICATION.THEY ARE NOT COMMUTATIVE UNDER SUBTRACTION & DIVISION.

ASSOCIATIVE PROPERTYRATIONAL NUMBERS ARE ASSOCIATIVE WITH ADDITION & MULTIPLICATION.THEY ARE NOT ASSOCIATIVE UNDER SUBTRACTION & DIVISION

THE ROLE OF ZEROZERO IS CALLED THE IDENTITY FOR THE ADDITION OF RATIONAL NUMBERS.

IT IS THE ADDITIVE IDENTITY FOR INTEGERS AND FOR WHOLE NUMBERS AS WELL.

EXAMPLE: -5/7+0= - 5/7

THE ROLE OF ONEONE IS THE MULTIPLICATIVE IDENTITY FOR RATIONAL NUMBERS.

EXAMPLE : -3/5 X 1 = - 3/5

ADDITIVE INVERSE -a/b is the additive inverse of a/b & a/b is the additive

inverse of - a/b . a/b + (- a/b ) = 0

ReciprocalReciprocal of a/b is 1/a/b =b/a

Distributivity of multiplication over addition and subtraction .

FOR ALL RATIONAL NUMBERS A,B & C :

Representation of rational no. s on the number line.

Represent 1/5 & 3/5 on the number line.

Represent -5/6 & -2/6 on the number line.

-6/6 -5/6 -4/6 -3/6 -2/6 -1/6 0

A ( b + c )= a x b + a x c

A ( b - c )= a x b - a x c

0 1/5 2/5 3/5 4/5 5/5 6/5

Some points to remember

1. Zero has no reciprocal . 2. The numbers 1 & -1 are there own reciprocal.

3. The product of two rational numbers is always a rational number.

4. The reciprocal of a positive rational number is always positive.5. The rational number 0 is the additive identity for rational

numbers. 6. The rational number 1 is the multiplicative identity for

rational numbers . 7. Between two rational numbers there are countless rational

numbers. The idea of mean helps us to find rational numbers between two rational numbers.