Question

What should be subtracted from \[ - \dfrac{5}{3}\] to get \[\dfrac{5}{6}\] ?

Answer 1

Hint: We are given with two fractions with a relation such that something subtracted from the first will give the second fraction. So we will consider that something as x. then we will form an equation from the given data. On solving we will get the value of x. and that is our answer.

Complete step-by-step answer:
Given that x should be subtracted from \[ - \dfrac{5}{3}\] so we can write,
\[ - \dfrac{5}{3} - x\]
The answer we get is \[\dfrac{5}{6}\]
Thus the equation as a whole becomes,
\[ - \dfrac{5}{3} - x = \dfrac{5}{6}\]
Now transpose x on other side,
\[ - \dfrac{5}{3} - \dfrac{5}{6} = x\]
Now we will take LCM on LHS by cross multiplication method,
\[ \Rightarrow \dfrac{{ - 5 \times 6 - 5 \times 3}}{{3 \times 6}} = x\]
On multiplying we get,
\[ \Rightarrow \dfrac{{ - 30 - 15}}{{18}} = x\]
On adding the numbers we get,
\[ \Rightarrow \dfrac{{ - 45}}{{18}} = x\]
To simplify the fraction, we have to divide them by their HCF. The GCF of 45 and 18 is 9. Thus we get,
\[ \Rightarrow \dfrac{{ - 5}}{2} = x\]
Thus this the value that is to be subtracted from the given fraction to get the answer.
So, the correct answer is “$\dfrac{{ - 5}}{2}$”.

Note: Note that, the words used in the question are far more important. That is either the variable is getting subtracted from a number or a number is subtracted from the variable. Thus always read the question carefully. Because a single wrongly placed term will collapse the full problem.
Also note that two negative terms when added are summed up but the sign is minus only.