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State true or false: $− 27 45$ and $− 3 5$ and represent equivalent rational numbers.

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True

False

answer is A.

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Detailed Solution

As per the given statement,

− 27 45

and

− 3 5

are equivalent rational numbers and we have to state if it’s true or not.
Equivalent rational numbers are those rational numbers whose standard forms are equal.
So, we can observe that

− 3 5

is already in standard form, but

− 27 45

can be reduced.
So,

− 27 45 = − (3 × 3 × 3) 3 × 3 × 5 = − 3 5

So, the standard form of

− 27 45

− 3 5

, which is also the second fraction as per the statement.
Therefore, we conclude that

− 27 45

and

− 3 5

have their standard forms equal as

− 3 5 = − 3 5

, and so by definition, they are equivalent fractions.
Hence, the statement is true.
Hence, the correct option is (1).

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