Question

What minimum should be added to $-\dfrac{7}{12}$ to get to the number $\dfrac{5}{9}$.

Answer 1

Hint: Here we use the variable. We assume a variable which is added to $-\dfrac{7}{12}$ to get $\dfrac{5}{9}$. We find the linear equation of the problem. We solve the equation by using binary operation to get the variable and the solution.

Complete step-by-step answer:
We need to find the minimum number that’s to be added to $-\dfrac{7}{12}$ to get to the number $\dfrac{5}{9}$.
Let’s assume the number is x.
When we add x to $-\dfrac{7}{12}$, we get $\dfrac{5}{9}$. We express the notion in the form of a linear equation of x.
So, $x+\left( -\dfrac{7}{12} \right)=\dfrac{5}{9}$. We got a linear equation of x.
Now we solve the equation to get the value of x.
The equation becomes $x-\dfrac{7}{12}=\dfrac{5}{9}$.
Solving we get
$\begin{align}
  & x-\dfrac{7}{12}=\dfrac{5}{9} \\
 & \Rightarrow x=\dfrac{5}{9}+\dfrac{7}{12} \\
\end{align}$
Now we need to get the L.C.M of 9 and 12 to solve for the value of x.
The L.C.M of 9 and 12 is $3\times 3\times 4=36$. Now we solve the equation.
$\begin{align}
  & x=\dfrac{4\times 5+3\times 7}{36}=\dfrac{20+21}{36} \\
 & \Rightarrow x=\dfrac{41}{36} \\
\end{align}$
So, we add $\dfrac{41}{36}$ to the number $-\dfrac{7}{12}$ to get to the number $\dfrac{5}{9}$.

Note: We can also directly use the addition of the two given numbers to find the solution. The variable part will not be required to find the solution. The word minimum is not required to change the solution. There can’t be any range of solution, as it is a single solution.