Question

Verify the following :
$(\dfrac{1}{5} + \dfrac{{( - 2)}}{5}) + \dfrac{3}{{10}} = \dfrac{1}{5} + ( - \dfrac{2}{3} + \dfrac{3}{{10}})$

Answer 1

Hint: Compute the left hand side and the right hand side of this algebraic equation separately to check if the result of both the sides are equal. For calculating both the sides, follow the BODMAS rule. Evaluate the terms of the bracket first and then do the rest.

Complete step-by-step answer:
We will equate the left hand side(LHS) and the right hand side(RHS) of the equation separately to show that they are equal.
For both the sides, we will use the BODMAS rule. So will start by evaluating the bracket and then proceed with the other arithmetic operations.
For the LHS, we have:
$
  (\dfrac{1}{5} + \dfrac{{( - 2)}}{5}) + \dfrac{3}{{10}} \\
   = (\dfrac{1}{5} - \dfrac{2}{5}) + \dfrac{3}{{10}} \\
   = - \dfrac{1}{5} + \dfrac{3}{{10}} \\
   = \dfrac{{\{ 2 \times ( - 1)\} + 3}}{{10}} \\
   = \dfrac{{ - 2 + 3}}{{10}} \\
   = \dfrac{1}{{10}} \\
 $
So the value of LHS is $\dfrac{1}{{10}}$ . We will now evaluate the value of the RHS to see if they are equal.
For the RHS, we have,
$
  \dfrac{1}{5} + ( - \dfrac{2}{3} + \dfrac{3}{{10}}) \\
   = \dfrac{1}{5} + [\dfrac{{( - 2 \times 10) + (3 \times 3)}}{{30}}] \\
   = \dfrac{1}{5} + [\dfrac{{ - 20 + 9}}{{30}}] \\
   = \dfrac{1}{5} + [\dfrac{{ - 11}}{{30}}] \\
   = \dfrac{1}{5} - \dfrac{{11}}{{30}} \\
   = \dfrac{{(1 \times 6) - 11}}{{30}} \\
   = \dfrac{{6 - 11}}{{30}} \\
   = \dfrac{{ - 5}}{{30}} \\
   = \dfrac{{ - 1}}{6} \\
 $
The RHS is $\dfrac{{ - 1}}{6}$ . Therefore, since the LHS$ \ne $ RHS, the given equation is wrong.

Note: To solve such questions, always evaluate the LHS and the RHS separately and then check if both give the same answer. In this question the answers come out to be different. That’s because the one of the three fractions on the RHS ($\dfrac{2}{3}$ ) is different from its LHS counterpart($\dfrac{2}{5}$ ).The values would have been the same if they were equal.