Question

What should be added to $\dfrac{-5}{7}$ to get $\dfrac{-2}{3}$ ?
(a) $\dfrac{-1}{21}$
(b) $\dfrac{1}{21}$
(c) $\dfrac{125}{8}$
(d) None of these.

Answer 1

Hint: Let the number that is added to $\dfrac{-5}{7}$ to get $\dfrac{-2}{3}$ be x. Represent the statement in the form of a linear equation in terms of x. Now solve the equation using operations like finding LCM and then performing addition or subtraction to get the value of x.

Complete step-by-step answer:
Let us start by letting the number that is added to $\dfrac{-5}{7}$ to get $\dfrac{-2}{3}$ be x.
Now we can interpret the statement given in the question as what should be the value of x such that x added with $\dfrac{-5}{7}$ will give the result as $\dfrac{-2}{3}$ . This can be mathematically represented as:
$\dfrac{-5}{7}+x=\dfrac{-2}{3}$
Now we will take $\dfrac{-5}{7}$ to the other side of the equation. On doing so, we get
$x=\dfrac{-2}{3}+\dfrac{5}{7}$
Now we know that the LCM of 3 and 7 is 21. So, let us take the LCM of the denominator of right-hand side of the equation be 21. On doing so, we get
$x=\dfrac{-2\times 7}{3\times 7}+\dfrac{5\times 3}{7\times 3}$
Now, on multiplication of terms, we get
$\Rightarrow x=\dfrac{-14}{21}+\dfrac{15}{21}$
Since, we have got the denominators as the same, we can represent the terms as
$\Rightarrow x=\dfrac{-14+15}{21}$
$\Rightarrow x=\dfrac{1}{21}$
So, the value of x is $\dfrac{1}{21}$ . Therefore, we can conclude that the number that should be added to $\dfrac{-5}{7}$ to get $\dfrac{-2}{3}$ is equal to $\dfrac{1}{21}$ .
Hence, the answer to the above question is option (b).

Note: Be careful in the calculation part, as the only mistake that can be committed in the above problem is in the calculation part. Also, be careful while reporting the answer, as there are two options with $\dfrac{1}{21}$ as the absolute value, however, one is negative and one is positive.