Question

Write the following rational numbers in ascending order:
$\dfrac{{ - 3}}{7},\dfrac{{ - 3}}{2},\dfrac{{ - 3}}{4}$

Answer 1

Hint: Here we will arrange the rational numbers in ascending order by using the concept of LCM and by making the denominator the same for each rational number.

Complete step-by-step answer:

The L.C.M of 7, 2, and 4 is 28.So, convert the denominator to 28, in all rational numbers
$
   \Rightarrow \dfrac{{ - 3}}{7} = \dfrac{{ - 3 \times 4}}{{7 \times 4}} = \dfrac{{ - 12}}{{28}} \\
   \Rightarrow \dfrac{{ - 3}}{2} = \dfrac{{ - 3 \times 14}}{{2 \times 14}} = \dfrac{{ - 42}}{{28}} \\
   \Rightarrow \dfrac{{ - 3}}{4} = \dfrac{{ - 3 \times 7}}{{4 \times 7}} = \dfrac{{ - 21}}{{28}} \\
 $
Now it is clear that
$\dfrac{{ - 42}}{{28}} < \dfrac{{ - 21}}{{28}} < \dfrac{{ - 12}}{{28}} \Rightarrow \dfrac{{ - 3}}{2} < \dfrac{{ - 3}}{4} < \dfrac{{ - 3}}{7}$
So this is your required ascending order.

Note: In this type of questions always take the L.C.M of the denominator, then make all the rational numbers denominator same to the L.C.M value, by appropriate multiplication in numerator and denominator.