Q1.ਹੇਠ ਲਿਖਿਆਂ ਵਿੱਚੋਂ ਕਿਹੜਾ ਵਿਅੰਜਕ ਪ੍ਰਮੇਯ ਸੰਖਿਆਵਾਂ ਦੇ
ताठ रे मउिचाउ गृष्ठ हुँ रतमाठिटा ?Which of
the following expressions shows that
rational numbers are associative
under multiplication. निम्नलिखित में से
ऐसे कौन सा व्यंजक यह दर्शाता है कि परिमेय
संख्याओं का गुणन सहचारी है?
Answers
Given :- Which of the following expressions shows that rational numbers are associative under multiplication. ?
(for options refer to image.)
Solution :-
As we know that,
- Rational numbers follow the associative property for addition and multiplication.
Suppose x, y and z are rational numbers , then :-
- for addition :- x + (y + z) = (x + y) + z
- for multiplication :- x(y * z) = (x * y)z .
checking Options one by one now, we get,
Option 1) :- (2/3)(-6/7 * 3/5) = (2/3 * -6/7) * 3/5
as we can see ,
- a * (b * c) = (a * b) * c
Therefore, Option (1) shows associative property under multiplication.
Option 2) :- (2/3)(5/4 + 6/3) = (2/3 * 5/4) + (2/3 * 6/3)
as we can see ,
- a * (b + c) = (a * b) + (a * c)
Therefore, Option (2) shows Distributive Property under multiplication.
Option 3) :- 4/5 * 5/7 = 5/7 * 4/5
as we can see ,
- a * b = b * a
Therefore, Option (3) shows Commutative Property under multiplication.
Option 4) :- 2/4 + (-2/4) = 0
as we can see ,
- a * (-a) = 0
Therefore, Option (4) shows Inverse Property under addition.
Hence, Option (1) shows associative property under multiplication and is correct answer.
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