Prove the following

Question:

$9 / 6$ lies between 1 and $2 .$

Solution:

True.

Express each of the given rational numbers with 6 as the common denominator.

Now,

$1 / 1=[(1 \times 6) /(1 \times 6)]=(6 / 6)$

$2 / 1=[(2 \times 6) /(1 \times 6)]=(12 / 6)$

Then,

$6 / 6<9 / 6<12 / 6$

$1<9 / 6<2$

So, $9 / 6$ is lies between 1 and 2 .

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