Question

Using appropriate properties find the value of $ - \dfrac{2}{3} \times \dfrac{3}{5} + \dfrac{5}{2} - \dfrac{3}{5} \times \dfrac{1}{6}$.

Answer 1

Hint: Use the rule of BODMAS to calculate the value of the expression. First solve multiplication and division simultaneously by cancelling out the common factors and then solve addition and multiplication by taking LCM. Simplify the final expression to get the answer.

Complete step-by-step solution:
According to the question, we have to calculate the value of the given mathematical expression. The expression is $ - \dfrac{2}{3} \times \dfrac{3}{5} + \dfrac{5}{2} - \dfrac{3}{5} \times \dfrac{1}{6}$.
We will apply the rule of BODMAS to solve the expression and determine its value.
First let the value of expression be denoted as $x$. So we have:
$ \Rightarrow x = - \dfrac{2}{3} \times \dfrac{3}{5} + \dfrac{5}{2} - \dfrac{3}{5} \times \dfrac{1}{6}$
As discussed earlier, we will use BODMAS. According to this, first we’ll solve division and multiplication by cancelling out common factors. But before that, we can represent the expression in a different way to make it look easier.
We can take the expression as consisting of 3 terms separated by addition and subtraction. This is shown below:
$ \Rightarrow x = \left( { - \dfrac{2}{3} \times \dfrac{3}{5}} \right) + \left( {\dfrac{5}{2}} \right) - \left( {\dfrac{3}{5} \times \dfrac{1}{6}} \right)$
Now in the first term, 3 will be cancelled out from numerator and denominator. And in the last term, 3 in numerator will be cancelled out by 6 in denominator leaving 2 in denominator. This will give us:
$ \Rightarrow x = \left( { - \dfrac{2}{1} \times \dfrac{1}{5}} \right) + \left( {\dfrac{5}{2}} \right) - \left( {\dfrac{1}{5} \times \dfrac{1}{2}} \right)$
Multiplying numbers in first and last terms, we have:
$ \Rightarrow x = \left( { - \dfrac{2}{5}} \right) + \left( {\dfrac{5}{2}} \right) - \left( {\dfrac{1}{{10}}} \right)$
Now, we can take 10 as LCM for the entire expression. Doing so and simplifying it, we’ll get:
$
   \Rightarrow x = \dfrac{{ - 4 + 25 - 1}}{{10}} = \dfrac{{20}}{{10}} \\
   \Rightarrow x = 2
 $

Thus the value of the given mathematical expression is 2.

Note: The rule of BODMAS can be used to find the value of such complex mathematical expressions easily. According to this rule, first we have to solve all the brackets in the expression. In the next step, we have to solve all the orders. Then in the next step we need to solve divisions and multiplications. In the final step we solve additions and subtractions.