Simplify $\left( {\dfrac{7}{8}} \right) \div \left( {\dfrac{3}{4}} \right)$

Hint:For converting the mathematical process of division into multiplication in fractions all we have to do is to take the reciprocal of the divisor and then to multiply the reciprocal of the divisor with the dividend. So here also we can use the same procedure and thus simplify the given question by dividing the given fractions.

Complete step by step solution:
Given
$\left( {\dfrac{7}{8}} \right) \div \left( {\dfrac{3}{4}} \right)...............................\left( i \right)$
So we have to simplify (i) by using the process of division.
Now for converting the mathematical process of division into multiplication in fractions all we have to do is to take the reciprocal of the divisor and then to multiply the reciprocal of the divisor with the dividend.
Such that here the divisor is$\left( {\dfrac{3}{4}} \right)$and the dividend is$\left( {\dfrac{7}{8}}
\right)$.
Now taking the reciprocal of the divisor, we get:
\[\left( {\dfrac{3}{4}} \right) \Rightarrow \left( {\dfrac{4}{3}} \right)...........................\left( {ii}
\right)\]
Now the next step is the simple multiplication of the reciprocated divisor with the dividend.
\[ \Rightarrow \left( {\dfrac{7}{8}} \right) \times \left( {\dfrac{4}{3}} \right).........................\left( {iii}
\right)\]
Such that we know that:
For multiplying fractions we have to multiply the numerator and denominator separately, and then represent the final answer as such as we get.
So on applying the above property on (iii) we get:
\[
\Rightarrow \left( {\dfrac{7}{8}} \right) \times \left( {\dfrac{4}{3}} \right) = \dfrac{{7 \times 4}}{{8
\times 3}} \\
\Rightarrow \dfrac{{7 \times 4}}{{8 \times 3}} = \dfrac{{28}}{{24}}......................\left( {iv} \right)
\\
\]
On observing (iv) we can see that it can be further simplified.
Such that on simplifying (iv) we get:

\[
\dfrac{{28}}{{24}} = \dfrac{{7 \times 4}}{{6 \times 4}} \\
= \dfrac{7}{6}.........................\left( v \right) \\
\]
Therefore we can say that $\left( {\dfrac{7}{8}} \right) \div \left( {\dfrac{3}{4}} \right) = \dfrac{7}{6}$

Note: On solving similar questions one should know the basic properties in general which can be applied to simplify a given expression easily. Also if in a fraction there exists a common factor for both the numerator and the denominator we can then cancel it and thus simplify it, and care must be taken while undertaking the mathematical process.