Question

Fill in the boxes with the correct symbol out of <, > and =
\[\dfrac{1}{{ - 3}}\boxed{}\dfrac{{ - 1}}{4}\]

Answer 1

Hint: In this question remember to use the method of L.C.M to make the denominator of both numbers the same also remember that greater numbers with the negative sign are smaller than the smaller numbers with the negative sign for example – 3 is greater than – 4, use this information to approach the solution.

Complete step-by-step solution:
According to the given information we have numbers $\dfrac{1}{{ - 3}}$ and $\dfrac{{ - 1}}{4}$
Since both the given numbers are negative
Now ignoring the sign, we get
$\dfrac{1}{3}$and $\dfrac{1}{4}$
Now we have to compare the numbers but since the denominator of both the numbers is different so we have to make the same denominator
To find the common denominator for both of the numbers let’s find the L.C.M of 3 and 4

3	3, 4
4	1, 4
	1, 1

So, the L.C.M of 3, 4 = $3 \times 4$
L.C.M of 3, 4 = 12
Now multiplying and dividing R.H.S by 3 and L.H.S by 4 we get
L.H.S = $\dfrac{1}{3} \times \dfrac{4}{4} = \dfrac{4}{{12}}$
R.H.S = $\dfrac{1}{4} \times \dfrac{3}{3} = \dfrac{3}{{12}}$
Multiplying both the numbers by – 1 we get
$\dfrac{4}{{ - 12}}$ and $\dfrac{{ - 3}}{{12}}$
Now comparing the numbers, we can conclude that
$\dfrac{4}{{ - 12}} < \dfrac{{ - 3}}{{12}}$
Here denominator is same so we compare only numerator , on the number line of we go to the negative direction as magnitude increases number becomes small, Hence
It can also be written as $\dfrac{1}{{ - 3}} < \dfrac{{ - 1}}{4}$
Therefore, the symbol which should be filled in the given problem is” <”.

Note: In these types of questions, the denominator and numerator of the equations can be multiplied by various numbers, which needs to be chosen wisely. Then, the symbol can be selected by analysis of the equation so obtained.