Question

Compare the rational number​

Answer 1

First let's find the LCM of denominators

LCM of 5, 10, 7, 11 & 1 turns out to be 770

We will find LCM as only like fractions can be compared

Therefore,

$\frac{3}{5} = \frac{ 3 \times 154}{5 \times 154} = \frac{462}{770} .................... \: (i)$

$\frac{ - 9}{10} = \frac{ - 9 \times 77}{10 \times 77} = \frac{ - 693}{770} .....................(ii)$

$\frac{ - 5}{7} = \frac{ - 5 \times 110}{7 \times 110} = \frac{ - 550}{770} ..................(iii)$

$\frac{7}{11} = \frac{7 \times 70}{11 \times 70} = \frac{490}{770} ...................(iv)$

$\frac{2}{1} = \frac{2 \times 770}{1 \times 770} = \frac{1540}{770} .................(v)$

Now, we can just compare the Numerators.

( - 693) < ( - 550) < ( + 462) < ( + 490) < ( + 1540)

Therefore...

$(ii) < (iii) < (i) < (iv) < (v)$

Therefore,

$\frac{ - 9}{10} < \frac{ - 5}{7} < \frac{3}{5} < \frac{7}{11} < 2$

HoPe iT HeLpS YoU..