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State true or false: The rational numbers $− 6 5$ and $− 4 5$ can be added or multiplied in any order.

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True

False

answer is A.

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Detailed Solution

Given a statement, the rational numbers

− 6 5

and

− 4 5

can be added or multiplied in any order.
We need to check whether the given statement is true or false.

− 6 5 + − 4 5 = − 10 5 ... (1) − 4 5 + − 6 5 = − 10 5 ... (2)

From equations (1) and (2), we get,

− 6 5 + − 4 5 = − 4 5 + − 6 5

i.e.,

a + b = b + a

, which means that rational numbers can be added irrespective of their order.

\frac{- 6}{5} \times \frac{- 4}{5} = \frac{24}{25}

(3)

\frac{- 4}{5} \times \frac{- 6}{5} = \frac{24}{25}

(4)
From equations (3) and (4), we get,

− 6 5 × − 4 5 = − 4 5 × − 6 5

i.e.,

a × b = b × a

, which means that rational numbers can be multiplied irrespective of their order.
The general equation

a + b = b + a

and

a × b = b × a

indicates the commutative property of rational numbers, where a and b are rational numbers.
Therefore, the statement is true.
Hence, 1 is the correct option.

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