Question

What should be subtracted from $\dfrac{-2}{3}$ to obtain the nearest integer?

Answer 1

Hint: First of all find the nearest integer to the fraction $\dfrac{-2}{3}$ by converting it into the decimal. If the decimal obtained is less than -0.5 then the nearest integer will be -1 and if the decimal obtained will be greater than -5 then the nearest integer will be 0. Assume that the number that should be subtracted is x. Now, multiply both the sides with 3 and form a linear equation in x, solve for its value to get the answer.

Complete step-by-step answer:
Here we have been asked to find the number that must be subtracted from $\dfrac{-2}{3}$ to get the nearest integer. First we need to find the nearest integer.
Now, converting $\dfrac{-2}{3}$ into the decimal form we will get -0.67. Further if we will subtract something from -0.67 then we will further get a number smaller than -0.67, so the resultant nearest integer will be -1. Let us assume that the number that should be subtracted is x. So mathematically we have,
$\Rightarrow \dfrac{-2}{3}-x=-1$
Multiplying both the sides with 3 we get,
$\Rightarrow -2-3x=-3$
Clearly this is a linear equation in x so we need to solve for the value of x. Leaving x in the L.H.S and taking all other terms to the R.H.S we get,
$\begin{align}
  & \Rightarrow -3x=-3+2 \\
 & \Rightarrow -3x=-1 \\
\end{align}$
Dividing both sides with -3 we get,
$\therefore x=\dfrac{1}{3}$
Hence, the required number that must be subtracted is $\dfrac{1}{3}$.

Note: You must know the concepts of rounding off of the numbers because they are used in scientific calculations in Physics and Chemistry. There are certain rules regarding the rounding off of the given numbers that must be remembered. You can directly add or subtract the fractions if you know how to calculate them by taking the L.C.M of their denominators.