RATIONAL NUMBERS RATIONAL NUMBERS 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.

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Presentation transcript:

RATIONAL NUMBERS RATIONAL NUMBERS

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

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

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.