Question

How do you solve $0.12$ of $\dfrac{\left( 0.0104-0.002 \right)+0.366\times 0.002}{0.12\times 0.12}$ ?

Answer 1

Hint: These types of problems require the implementation of the BODMAS rule. We start with the numerator of the fraction, apply BODMAS there, then proceed to the denominator. Finally, having solved the fraction, we now multiply $0.12$ to the fraction and get our final answer.

Complete step-by-step answer:
The given expression is
$\dfrac{\left( 0.0104-0.002 \right)+0.366\times 0.002}{0.12\times 0.12}$
As this is a huge expression, we solve it part by part. Let us first simplify and solve the numerator. The numerator is
$\left( 0.0104-0.002 \right)+0.366\times 0.002$
We solve it by applying the BODMAS rule which states that a given expression must be simplified in the following sequence
Bracket, Of, Division, Multiplication, Addition and Subtraction.
Therefore, we first work on the bracket and simplify it as
$\Rightarrow \left( 0.0084 \right)+0.366\times 0.002$
Which gives,
$\Rightarrow 0.0084+0.366\times 0.002$
We then perform the multiplication of the two terms $0.366$ and $0.002$ . Thus, the numerator becomes,
$\Rightarrow 0.0084+0.000732$
We now perform addition of the two terms $0.0084$ and $0.000732$ . The numerator thus becomes,
$\Rightarrow 0.009132$
The numerator is thus solved to $0.009132$ .
Having solved the numerator, we now solve the denominator. The denominator is
$0.12\times 0.12$
The denominator contains only the multiplication of the two terms $0.12$ and itself. We perform the multiplication and thus the denominator becomes,
$\Rightarrow 0.0144$
Having solved both the numerator and the denominator, we now solve the corresponding fraction, which is
$\Rightarrow \dfrac{0.009132}{0.0144}$
Which, upon simplification by division gives
$\Rightarrow 0.634167$
The above result has been rounded to six decimal places.
The expression remaining is thus,
$0.12$ of $0.634167$
“Of” means nothing but multiplication of the two concerned terms. So, here we need to simply multiply
$0.12$ and $0.634167$ . The expression thus becomes,
$\Rightarrow 0.12\times 0.634167$
Which gives $0.07610004$ that can be rounded off to five decimal places as $0.0761$ .
Therefore, we can conclude that the given expression can be solved to $0.0761$ .

Note: These types of problems are not very difficult; they just seem to be very complicated owing to so many decimals and operations. We should keep in mind the BODMAS rule and sequentially solve the expression. The multiplication part is where most of the students commit mistakes. So, we should be more careful over there.