Class 8, Mathematics - NCERT Guide
RATIONAL NUMBERS
Properties of Closure
Whole
Numbers
>> Whole Numbers are closed under
addition. In general, a + b is a Whole
Numbers for any two Whole Numbers a
and b.
>> Whole Numbers are not closed under
subtraction. 5 - 7 = -2, this is not a Whole Number.
>> Whole Numbers are closed under multiplication. In
general, if a and b are any two Whole Numbers, their
product ab is Whole Number.
>> Whole Numbers are not closed under division..
Integers
>> Integers are closed under addition. In general, a + b is an integer for any two integers
a and b.
>> Integers are closed under subtraction. For any two
integers a and b, a - b is an integer.
>> Integers are closed under multiplication. For any
two integers a and b, a
x b is an integer.
>> Integers e not closed under division.
Rational
Numbers
>> Sum of two rational numbers is again a rational
number. Rational Numbers are closed under addition.
>> The difference of two rational numbers is a rational
number. Rational numbers are closed under subtraction
>> Rational numbers are closed under multiplication.
>> Rational numbers are not closed under division.
Properties of Commutativity
Whole
Numbers
>> Addition is commutative.
>> Subtraction is not commutative.
>> Multiplication is commutative.
>> Division is commutative.
Integers
>> Addition is commutative.
>> Subtraction is not commutative.
>> Multiplication is commutative.
>> Division is commutative.
Rational
Numbers
>> Addition is commutative.
>> Subtraction is not commutative.
>> Multiplication is commutative.
>> Division is not commutative.
Properties of Associativity
Whole
Numbers
>> Addition is
associative.
>> Subtraction
is not associative.
>>
Multiplication is associative.
>> Division is
not associative.
Integers
>> Addition is
associative.
>> Subtraction
is not associative.
>>
Multiplication is associative.
>> Division is
not associative.
Rational
Numbers
>> Addition is
associative.
>> Subtraction
is not associative.
>>
Multiplication is associative.
>> Division is
not associative.
Points to Remember
>> Zero is called the identity for
addition of rational numbers. It is additive identity for integers and whole
numbers.
>> 1 is multiplicative identity for
rational numbers.
>> The additive inverse of the rational
number a / b
is (- a / b) and vice-versa.
>> The
multiplicative or reciprocal inverse of the rational number a / b is c / d
if, a
/ b x c / d = 1
>> Rational
numbers can be represented on a number line.
>> Between any
two rational numbers there are countless rational numbers.
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