Question

How do you solve the equation \[5\dfrac{2}{7}+k=2\dfrac{27}{70}\] ?

Answer 1

Hint: Now to solve the given equation we will first convert the mixed fraction into regular fraction. Now we will take the LCM of all the denominators and multiply the whole equation by LCM. Now we have a linear equation with its coefficient and constants as integers. Now we will rearrange the terms to find the value of k.

Complete step-by-step solution:
Let us consider the given equation \[5\dfrac{2}{7}+k=2\dfrac{27}{70}\] .
Now first let us convert all the mixed fractions in the equation into regular fraction. We know that the mixed fraction $a\dfrac{p}{q}=\dfrac{aq+p}{q}$ Hence using this we get,
$\Rightarrow \dfrac{5\times 7+2}{7}+k=\dfrac{2\times 70+27}{70}$
$\Rightarrow \dfrac{37}{7}+k=\dfrac{167}{70}$
Now we want to convert the fractions into integers. To do so we will multiply the whole equation by LCM of all the denominators. Here the denominators are 7,1 and 70. Hence the LCM of denominators is 70. Therefore we will multiply the whole equation by 70.
$\Rightarrow \dfrac{37\times 70}{7}+70k=\dfrac{167\times 70}{70}$
Now simplifying the above equation we get,
$\Rightarrow 370+70k=167$
Now let us take the term 370 on RHS. Since we are transposing the term its sign will change Hence, we get
$\begin{align}
  & \Rightarrow 70k=167-370 \\
 & \Rightarrow 70k=-203 \\
\end{align}$
Now dividing the whole equation by 70 we get the value of k.
$\Rightarrow k=\dfrac{-203}{70}$
Hence the solution of the given equation is $k=\dfrac{-203}{70}$.

Note: Note that for converting mixed fraction of the type $a\dfrac{p}{q}$ into regular fractions we have $\dfrac{aq+p}{q}$ and not $a\times \dfrac{p}{q}$ . Also after solving any equation always remember to substitute the obtained value in the given equation and check if the equation holds. For example if we substitute $k=\dfrac{-203}{70}$ in the given equation we will get LHS = RHS.