Question

What should be added to \[\dfrac{2}{5}\] to get \[ - \dfrac{3}{7}\]?

Answer 1

Hint: We will first convert the given word problem to an algebraic equation with an unknown variable.
Solving that algebraic equation for an unknown variable will give us the required value.
This problem will give us a linear equation with one unknown variable and we will solve for that unknown variable.

Complete step by step answer:
We aim to find the number which on adding to the number \[\dfrac{2}{5}\] will give us \[ - \dfrac{3}{7}\]
Let us first convert this statement into an algebraic equation. Let \[x\] be the required number thus the given statement can be written as \[\dfrac{2}{5} + x = - \dfrac{3}{7}\]
Thus, we got a linear equation with one unknown variable.
Consider the equation \[\dfrac{2}{5} + x = - \dfrac{3}{7}\]
We aim to find the value for the variable \[x\] so we need to keep the variable \[x\] alone on one side and other terms on the other side.
\[\dfrac{2}{5} + x = - \dfrac{3}{7} \Rightarrow x = - \dfrac{3}{7} - \dfrac{2}{5}\]
On shifting the term \[\dfrac{2}{5}\] to the other side it has become a negative number.
Let us simplify the above equation to get the value of the variable \[x\].
On the right side, we have a fraction, to add or subtract a fraction we need to have the same denominators. So, to make those denominators the same we need to take the least common multiple for the denominator.
The least common multiple for \[7\& 5\] is \[35\]
Thus, the equation will become \[x = \dfrac{{ - 15 - 14}}{{35}}\]
On simplifying this equation, we get \[x = \dfrac{{ - 29}}{{35}}\].
Integers having the same signs have to be added and the resultant will get the sign of those numbers. Thus, \[ - 15 - 14\] has become \[ - 29\] .
Thus, the value of \[x\] is \[ - \dfrac{{29}}{{35}}\] . Therefore, \[ - \dfrac{{29}}{{35}}\] is the number that has to be added to the number \[\dfrac{2}{5}\]to get \[ - \dfrac{3}{7}\].

Note: We can also check whether the answer we got is correct or not by adding the terms \[\dfrac{2}{5}\] and \[ - \dfrac{{29}}{{35}}\] On adding those terms,
we get \[\dfrac{2}{5} - \dfrac{{29}}{{35}} = - \dfrac{3}{7}\] thus the answer we got from the above calculation is correct. It is always safe to cross-check the answer we got in solving algebraic equations.