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Q.

Which of the following rational numbers lies between $\frac{- 4}{5}$ and $\frac{- 7}{5}$ ?

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a

\frac{- 36}{45}

b

\frac{- 35}{45}

c

\frac{- 39}{45}

d

\frac{- 63}{45}

answer is C.

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Detailed Solution

Given range is

\frac{- 4}{5}

to

\frac{- 7}{5}

and the options are

\frac{- 36}{45}

,

\frac{- 35}{45}

,

\frac{- 39}{45}

and

\frac{- 63}{45}

.
The denominators of all the options are 45.
As per the given options, let us multiply both numbers with

\frac{9}{9}

.

∴ \frac{- 4}{5} \times \frac{9}{9} = \frac{- 36}{45}

and

\frac{- 7}{5} \times \frac{9}{9} = \frac{- 63}{45}

∴

Clearly,

\frac{- 39}{45}

lies between

\frac{- 36}{45}

and

\frac{- 63}{45}

Thus,

\frac{- 39}{45}

lies between

\frac{- 4}{5}

and

\frac{- 7}{5}

.
Therefore, option (3) is correct.

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