Question

What should be added to $\dfrac{7}{{12}}$ to get $\dfrac{{ - 4}}{{15}}$?
A. $\dfrac{{17}}{{20}}$
B. $ - \dfrac{{17}}{{20}}$
C. $\dfrac{7}{{20}}$
D. $ - \dfrac{7}{{20}}$

Answer 1

Hint: We will first assume the number we add to be ‘x’. Then, we will just proceed with the given data and then do the required modifications to get the required answer.

Complete step-by-step solution:
Let us assume that we add ‘x’ to $\dfrac{7}{{12}}$ to get $\dfrac{{ - 4}}{{15}}$.
Now, as per the given data, we will then get:-
$ \Rightarrow \dfrac{7}{{12}} + x = \dfrac{{ - 4}}{{15}}$
Now, we will take the $\dfrac{7}{{12}}$ from addition in the left hand side to subtraction in the right hand side to obtain the following expression:-
$ \Rightarrow x = \dfrac{{ - 4}}{{15}} - \dfrac{7}{{12}}$
Now, we can take out the negative sign common from the right hand side to obtain the following expression:-
$ \Rightarrow x = - \left( {\dfrac{4}{{15}} + \dfrac{7}{{12}}} \right)$
Now, we will take the Least common multiple of the denominators of both the fractions in the right hand side and then eventually calculate the sum of the two fractions on the right hand side only to obtain the following:-
$ \Rightarrow x = - \left( {\dfrac{{16 + 35}}{{60}}} \right)$
Simplifying the calculations in the numerator of the right hand side to obtain the following result:-
$ \Rightarrow x = - \left( {\dfrac{{51}}{{60}}} \right)$
Taking 3 out from both the numerator and denominator on the fraction in right hand side and cancelling them out to obtain the following result:-
$ \Rightarrow x = - \left( {\dfrac{{17}}{{20}}} \right)$

Hence, the correct required answer is option (B).

Note: The students must note that they may directly just find the difference without assuming the number to be ‘x’ or anything else. But assuming the number to be some alphabet basically helps us to imagine the situation and thus evaluate the assumed alphabet. This will help us easily evaluate the situation as we did above and if there are more than 2 numbers involved, it will be easier in that situation as well.
The students must also note that addition of fraction involves taking the least common multiples if the denominators of both the fractions are not equal. If they are equal, we can just directly add the numerator and get the required answer.