Question

How do you simplify the term \[\dfrac{{3\pi }}{2} + \dfrac{\pi }{4}\]?

Answer 1

Hint: For getting the value of equation in this kind of fraction form, you just need to simplify the fraction, if simplification is possible with the fraction term then first simplify it and then put the value of the pie, and after that with some sort of simplification the final result can be obtained.

Complete step by step solution: The given question is to simplify the term \[\dfrac{{3\pi }}{2} +
\dfrac{\pi }{4}\]
And to find the value of we have to first put the value of pie then after further simplification we can have our result.
\[
\Rightarrow \dfrac{{3\pi }}{2} + \dfrac{\pi }{4} \\
\Rightarrow \dfrac{{3 \times 3.14}}{2} + \dfrac{{3.14}}{4} \\
\Rightarrow \dfrac{{9.42}}{2} + 0.785 \\
\Rightarrow 4.71 + 0.785 \\
\Rightarrow 5.495 \\
\]
This is our final solution for the question.
Method :2
Here we will first simplify the fraction terms and then after simplification we will put the value of pie and then solve the fraction for the final solution, on solving we get:
\[
\Rightarrow \dfrac{{3\pi }}{2} + \dfrac{\pi }{4} \\
\Rightarrow \dfrac{{2 \times (3\pi ) + \pi }}{4} = \dfrac{{6\pi + \pi }}{4} = \dfrac{{7\pi }}{4} =
\dfrac{{7 \times 3.14}}{4} = 5.495 \\
\]
The results are the same.
Additional Information:The above question can also be solved by taking the common denominator term and then finally after solving the fraction term together then we will obtain a single fraction in which we have to put the value of pie and then after solving we will get our answer.

Note:Here we can also solve by taking the lowest common factor then solve with the pie term then finally we can put the value of pie and get the answer, but in that case also we will have the same answer as we got here. No changes can be seen with that solution also.