Question

How do you solve $\dfrac{10}{k}=\dfrac{8}{4}$ ?

Answer 1

Hint: Problems on solving this type of simple equation can be done simply by multiplying both sides of the equation with $k$ first. After that we simplify the terms by cancelling the k on the left-hand side of the equation. The final result can be obtained by dividing both the sides of the equation by $2$ .

Complete step-by-step solution:
The given equation we have is
$\dfrac{10}{k}=\dfrac{8}{4}$
Now we multiply both the sides of the given equation with the term $k$ and we get
$\Rightarrow \dfrac{10k}{k}=\dfrac{8k}{4}$
We further simplify the above equation by cancelling the common factor $k$ on the left hand side of the above equation as shown below
$\Rightarrow 10=\dfrac{8k}{4}$
Further simplifying the above equation, we get
$\Rightarrow 2k=10$
Now dividing both the left hand side and right hand side of the above equation by $2$ , we get
$\Rightarrow \dfrac{2k}{2}=\dfrac{10}{2}$
We further simplify the above equation by cancelling the common factor $2$ on the left-hand side of the equation as shown below
$\Rightarrow k=\dfrac{10}{2}$
Further simplifying the above equation, we get
$\Rightarrow k=5$
Hence, following the above steps we conclude the solution of the equation $\dfrac{10}{ k}=\dfrac{8}{4}$ as $\Rightarrow k=5$.

Note: In this type of calculations and simplifications we must be very careful while dividing or multiplying something with the equation, as it can get even more complicated if not done correctly. Also, we must keep our mind that the number that we are multiplying or dividing must be done on both the sides of the equation. Otherwise, inequality will make the equation invalid.