2. RATIONAL NUMBERS RATIONAL NUMBERS

3. 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 PROPERTY RATIONAL NO. ARE CLOSED UNDER ADDITION, SUBTRACTION & MULTIPLICATION. THEY ARE NOT CLOSED UNDER DIVISION. CUMMUTATIVE PROPERTY RATIONAL NUMBERS ARE COMMUTATIVE UNDER ADDITION AND MULTIPLICATION. THEY ARE NOT COMMUTATIVE UNDER SUBTRACTION & DIVISION. ASSOCIATIVE PROPERTY RATIONAL NUMBERS ARE ASSOCIATIVE WITH ADDITION & MULTIPLICATION. THEY ARE NOT ASSOCIATIVE UNDER SUBTRACTION & DIVISION

4. THE ROLE OF ZERO ZERO 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 ONE ONE 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 Reciprocal Reciprocal of a/b is 1/a/b =b/a

5. 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

6. 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.