Question

Arrange the rational number -3/7, 7/-10, -5/6 in ascending order​

Answer 1

Answer:

-3/7 < 7/-10 < -5/6

Step-by-step explanation:

-3/7 , 7/-10 , -5/6

= -3/7 , -7/10 , -5/6

 LCM of 7, 10 & 6 = 420

 -3/7× 60/60= -180/420

 -7/10× 42/42= -294/420

 -5/6× 70/70= -350/420

 -180/420 < -294/420 < -350/420

therefore, -3/7 < 7/-10 < -5/6

Answer 2

Given:

$\circ \: \: \sf Arrange \: the \:rational \: number \: \dfrac{ - 3}{7} , \: \dfrac{7}{ - 10} , \: \dfrac{ - 5}{6} \: \: in \: ascending \: order$

Solution:

First we have to find the L.C.M of the denominators 7, 10 and 6.

$\tt{\begin{lgathered} \begin{array}{c | c} \underline 2& \underline{7,10,6} \\ & 7,5,3 \end{array}\end{lgathered} }\\ \\ \\ \sf \therefore \: \: \: \: L.C.M \: = 2 \times 7 \times 5 \times 3 = 210$

Now,

$\\ \circ \: \: \: \tt \dfrac{ - 3}{7} = \frac{ - 3 \times 30}{7 \times 30} = \frac{ - 90}{210} \\ \\ \\ \: \circ \: \: \: \tt \dfrac{7}{ - 10} \: = \frac{7 \times ( - 21)}{( - 10) \times ( - 21)} = \frac{ - 147}{210} \\ \\ \\ \circ \: \: \: \tt \dfrac{ - 5}{6} = \frac{ - 5 \times 35}{6 \times 35} = \frac{ - 175}{210} \\ \\ \:$

$\\ \tt \: \: \therefore \: \: \frac{ - 175}{210} \: < \: \frac{ - 147} {210} \: < \: \frac{ - 90}{210} \:$

$\sf \: \: \: Hence \tt \: \: \dfrac{ - 5}{6} \: < \: \dfrac{7}{ - 10} \: < \: \dfrac{ - 3}{7} \:$