Question

How do you solve \[\dfrac{3}{8}=r+\dfrac{2}{3}\]?

Answer 1

Hint: From the question given we have been asked to solve \[\dfrac{3}{8}=r+\dfrac{2}{3}\]. We can solve the above given equation from the question by using some simple transformations. By using the simple transformations, we can get the solution for the above given equation very easily.

Complete step by step answer:
From the question given, we have been given that \[\dfrac{3}{8}=r+\dfrac{2}{3}\]
Now, we have to do some transformation to the given equation to make it simplify easier.
Here, the transformation we have to do is shift \[\dfrac{2}{3}\] from the left hand side of the given equation to the right hand side of the given equation.
By shifting \[\dfrac{2}{3}\] from left hand side of the given equation to the right hand side of the given equation, we get the below equation \[\Rightarrow \dfrac{3}{8}-\dfrac{2}{3}=r\]
Now, rearrange the equation, such that \[r\] should be in the left hand side of the equation.
By rearranging the equation, we get \[\Rightarrow r=\dfrac{3}{8}-\dfrac{2}{3}\]
Now, simplify the above equation furthermore to get the equation more simplified.
By simplifying the above equation furthermore, we get the equation as \[\Rightarrow r=\dfrac{9-16}{24}\]
On furthermore simplifying the above equation, we get \[\Rightarrow r=-\dfrac{7}{24}\]
Hence, the given equation is solved by using the simple transformation to the equation.

Note: We should do the calculation very carefully after applying the transformation to the given equation. Also, we should be well known about what transformation should be made to the given equation to get it simplified. Also, we should be very careful while applying the transformation. We should have more practice on this type of problem. Similarly we can solve \[\dfrac{6}{8}=x+\dfrac{4}{5}\Rightarrow x=\dfrac{6}{8}-\dfrac{4}{5}\Rightarrow x=\dfrac{30-32}{40}\Rightarrow x=\dfrac{-2}{40}\Rightarrow x=\dfrac{-1}{20}\] .