Question

Find the value of the expression $\dfrac{2}{5} \times \left( { - \dfrac{3}{7}} \right) - \dfrac{1}{6} \times \dfrac{3}{2} + \dfrac{1}{{14}} \times \dfrac{2}{5}$.

Answer 1

Hint: In this particular question use the concept of BODMAS rule that is bracket of division, multiplication, addition and subtraction, to start with the simplification process of the given expression. First simplify the bracket part, and then the multiplication terms, so use these concepts to reach the solution of the question.

Complete step-by-step answer:
Given expression:
$\dfrac{2}{5} \times \left( { - \dfrac{3}{7}} \right) - \dfrac{1}{6} \times \dfrac{3}{2} + \dfrac{1}{{14}} \times \dfrac{2}{5}$
By BODMAS rule (i.e. bracket of division, multiplication, addition and subtraction).
So we have to first simplify the bracket in the given expression.
$ \Rightarrow - \dfrac{2}{5} \times \dfrac{3}{7} - \dfrac{1}{6} \times \dfrac{3}{2} + \dfrac{1}{{14}} \times \dfrac{2}{5}$ (As anything multiplied by negative is negative)
Now simplify multiplication according to the BODMAS rule.
$ \Rightarrow - \dfrac{{2 \times 3}}{{5 \times 7}} - \dfrac{{1 \times 3}}{{6 \times 2}} + \dfrac{{1 \times 2}}{{14 \times 5}}$
$ \Rightarrow - \dfrac{6}{{35}} - \dfrac{1}{4} + \dfrac{1}{{35}}$
Now rearrange the terms we have,
$ \Rightarrow - \dfrac{1}{4} - \dfrac{6}{{35}} + \dfrac{1}{{35}}$
Now as we see that the last two terms has the same denominator so simplify that we have,
$ \Rightarrow - \dfrac{1}{4} + \dfrac{{ - 6 + 1}}{{35}}$
$ \Rightarrow - \dfrac{1}{4} + \dfrac{{ - 5}}{{35}}$
$ \Rightarrow - \dfrac{1}{4} - \dfrac{1}{7}$
Now there are just two terms remaining so simplify this by taking L.C.M so we have,
$ \Rightarrow \dfrac{{ - 7 - 4}}{{4 \times 7}} = \dfrac{{ - 11}}{{28}}$
So this is the required answer.

Note: Whenever we face such types of questions the key concept we have to remember is the simplification according to BODMAS rule, simplification is the basis to solve these types of problems, so always follow the steps as above followed to solve and once all the steps completed we will get the required answer as above, one mistake in any step lead us to a wrong answer.