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State True/False.

The rational numbers are always commutative under division.

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True

False

answer is B.

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Detailed Solution

For example we are taking two rational numbers

a b

and

c d

.
Now, according to the question we need to verify,

a b ÷ c d = c d ÷ a b

Solving L.H.S. first,
Convert the

÷

(division sign) to

×

(multiplication sign) and invert the number to the right of the sign inside the bracket.

a b × d c

a d b c

-------------(1)
Now, solving R.H.S.,
Convert the

÷

(division sign) to

×

(multiplication sign) and invert the number to the right of the sign inside the bracket.

c d × b a

b c a d

-------------(2)
Now, by comparing equations (1) and (2),

a d b c ≠ b c a d

Therefore, the rational numbers are not always commutative under division.
Thus, the given statement is false.
Hence, option (2) is correct.

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