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State true or false: The rational numbers $− 8 28$ and $32 − 112$ and are equal.

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True

False

answer is A.

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Detailed Solution

The given statement says that

− 8 28

and

32 − 112

are equal and we have to state if this is true or not.
Now,

28 = 2 × 2 × 7 112 = 2 × 2 × 2 × 2 × 7

The LCM of 28 and 112 is obtained as

2 × 2 × 2 × 2 × 7 = 112

.
So, we can write the given rational numbers as rational numbers with same denominator as follows,

− 8 × 4 28 × 4 = − 32 112 32 − 112 = − 32 112

Now, we can observe that the numerators of both the rational numbers are equal, i.e.,

− 32 = − 32

.
So, we conclude that

− 8 28 = 32 − 112

.
Hence, the statement is true.
Hence, the correct option is (1).

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