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Composite Mathematics class 8th :-
by S.K. Gupta and Anubhuti Gangal
Chapter 1 Rational Numbers Key Facts :-
1. Closure property : If x and y are any two rational numbers, then
(a) a/b + c/d is a rational number, e.g. 1/2 + 3/4 = 5/4 , is a rational number.
(b) a/b - c/d is a rational number, e.g. 1/2 - 3/4 = -1/4 is a rational number.
2. 0 is the additive inverse of itself. It may be noted that 0 is the only rational number which is its own additive inverse.
3. 1f a/b and c/d are two rational numbers, then a/b -c/d = a/b + (additive inverse of c/d ) = a/b + (- c/d)
4. Property of zero: The sum of any rational number and 0, is the rational number itself, i.e, if a/b is any rational number, then a/b +0 = 0+ a/b = a/b .
5. 1f a/b and c/d are two rational numbers, then (a/b x c/d) = ((a x c)/(b x d))
6. (Property of 1). If a/b is a rational number, then a/b x 1 = 1 x a/b = a/b
7. 1 is called the multiplicative identity for rational numbers.
8. (Multiplication by 0). Every rational number multiplied with 0 gives 0. Thus, if a/b is any rational number, then a/b x 0 = 0 = 0 x a/b
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