Question

How do you solve \[\dfrac{3}{4} + x = \dfrac{5}{4}\] ?

Answer 1

Hint:
To solve the equation we have to shift both the fractions in one side and $x$ to another side. Then, subtract both the fractions by making their denominators similar. We can easily solve them by multiplying a number in both numerator and denominator.

Complete step by step solution:
We have been given the equation, \[\dfrac{3}{4} + x = \dfrac{5}{4}\] , we have to find the value of $x$ in the given equation. So, by using the transposition method we will shift both the fraction part in the question in one side and $x$ to another side.
We know that, in the transposition method, with the changing of side the operation also changes. Like, in this question, we will shift the fraction $\dfrac{3}{4}$ to another side of the equation then, it will become negative. Mathematically, it can be expressed as –
$ \Rightarrow x = \dfrac{5}{4} - \dfrac{3}{4}$
For the addition or subtraction of the fractions, the denominators of the fractions should be equal, so that we can easily do our required operations.
But in the above equation both the fractions have similar denominators, therefore, there is no need to multiply any number with numerator and denominator, we can directly solve them –
Taking $\dfrac{1}{4}$ common in the above equation, we get –
$ \Rightarrow x = \dfrac{1}{4}\left( {5 - 3} \right)$
Now, further solving, we get –
$ \Rightarrow x = \dfrac{2}{4}$
Therefore, the value of $x$ is $\dfrac{2}{4}$, but $\dfrac{2}{4}$ can also be further simplified.
Therefore, finding the common factor for 2 and 4. We get the answer as 2.
Hence, the fraction can be simplified as –
$
   \Rightarrow \dfrac{{2 \div 2}}{{4 \div 2}} \\
   \Rightarrow \dfrac{1}{2} \\
 $

Hence, the required value of $x$ is $\dfrac{1}{2}$.

Note:
We can also add or subtract the fractions by taking LCM of their denominators. Then, dividing it with their denominators and multiplying its result with numerators.
It is not necessary to convert the fraction into its simplest form, but doing this makes that fraction small and simpler to solve.