WELCOME. 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. PROPERTIES OF RATIONAL NUMBERS. CLOSURE PROPERTY RATIONAL NO. ARE CLOSED UNDER ADDITION , SUBTRACTION & MULTIPLICATION.
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The numbers of the form p/q (q=0) is called a RATIONAL NUMBER.
Examples: 5/7 6/8 -6/9 etc.
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
-a/b is the additive inverse of a/b & a/b is the additive inverse of - a/b . a/b + (- a/b ) = 0
Reciprocal of a/b is 1/a/b =b/a
A ( b - c )= a x b - a x c
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
0 1/5 2/5 3/5 4/5 5/5 6/5
Zero has no reciprocal .
The numbers 1 & -1 are there own reciprocal.
The product of two rational numbers is always a rational number.
The reciprocal of a positive rational number is always positive.
The rational number 0 is the additive identity for rational numbers.
The rational number 1 is the multiplicative identity for rational numbers .
Between two rational numbers there are countless rational numbers. The idea of mean helps us to find rational numbers between two rational numbers.