Question

What number should be subtracted from $\dfrac{{ - 2}}{3}$to get $\dfrac{{ - 1}}{6}$?

Answer 1

Hint: We will first convert the given word problem to an algebraic equation with an unknown variable.
Solving that algebraic equation for an unknown variable will give us the required value.
After converting with the unknown variable, the equation terms into the linear equation as it contains the degree one. and we will solve to find the unknown variable.

Complete step by step answer:
We aim to find the number which on subtract to the number $\dfrac{{ - 2}}{3}$ will give us $\dfrac{{ - 1}}{6}$
Let us first convert this statement into an algebraic equation. Let \[x\] be the required number thus the given statement can be written as \[\dfrac{{ - 2}}{3} - x = - \dfrac{1}{6}\]
Convert the equation in variables on one side and constant on the other side, thus we get \[ - x = - \dfrac{1}{6} + \dfrac{2}{3}\]
Now solve with the help of the LCM method, we get \[ - x = - \dfrac{1}{6} + \dfrac{4}{6}\]
Where LCM of \[
  3\left| \!{\underline {\,
  {3,6} \,}} \right. \\
  2\left| \!{\underline {\,
  {1,2} \,}} \right. \\
  1\left| \!{\underline {\,
  {1,1} \,}} \right. \\
 \]
and we multiplied the second fraction with the number $2$ to get the common divisor as $6$
From this we get, \[ - x = - \dfrac{1}{6} + \dfrac{4}{6} \Rightarrow \dfrac{{ - 1 + 4}}{6} = \dfrac{3}{6}\]
Multiplying the negative sign in both the sides we get \[x = \dfrac{{ - 3}}{6} \Rightarrow x = \dfrac{{ - 1}}{2}\](by division operation)
Hence, we get the variable value as \[x = \dfrac{{ - 1}}{2}\]
Therefore, the required number is \[\dfrac{{ - 1}}{2}\]

Note: We are also able to check whether the value \[x = \dfrac{{ - 1}}{2}\]is correct or wrong.
Apply the value of the \[x = \dfrac{{ - 1}}{2}\]in the starting equation, then we get \[\dfrac{{ - 2}}{3} - x = - \dfrac{1}{6} \Rightarrow \dfrac{{ - 2}}{3} - (\dfrac{{ - 1}}{2}) = - \dfrac{1}{6} \Rightarrow - \dfrac{1}{6} = - \dfrac{1}{6}\]and hence \[\dfrac{{ - 1}}{2}\]is the correct value.
LCM is the least common multiple which is the simplest method to find out the smallest common multiples between two or more than two numbers.
Similarly, there are two other concepts which are GCD and HCF, where GCD is the greatest common divisor and HCF is the highest common factor.