Simplify: \[7\dfrac{5}{6} - 4\dfrac{3}{8} + 2\dfrac{7}{{12}}\]

Hint: It is a simple algebraic expression which contains mixed fractions. We can solve this by converting it into the simplest form that is improper fraction and after that we can take lcm followed by BODMAS rule. The obtained solution can be either in terms of improper fraction or in terms of mixed fraction.

Complete step by step answer:
Given, \[7\dfrac{5}{6} - 4\dfrac{3}{8} + 2\dfrac{7}{{12}}\]
Now, convert the mixed fractions to improper fraction we get
\[ \Rightarrow \dfrac{{47}}{6} - \dfrac{{35}}{8} + \dfrac{{27}}{{12}}\]
Now, by taking the lcm of the denominators that is lcm of 6,8 and 12 is 24 we get,
\[ \Rightarrow \dfrac{{188 - 105 + 62}}{{24}}\]
Now, as per the BODMAS rule first priority should be given for addition so let us add the terms containing plus in numerator so we get
\[ \Rightarrow \dfrac{{250 - 105}}{{24}}\]
Now simplifying the numerator, we get
\[ \Rightarrow \dfrac{{145}}{{24}}\]
Now convert it into mixed fraction, we get
\[\therefore 6\dfrac{1}{{24}}\]

Hence, the required solution for the given problem is \[6\dfrac{1}{{24}}\].

Note:A mixed fraction is a form of a fraction which is defined as the ones having a fraction and a whole number Ex: \[7\dfrac{5}{6}\], to convert it into improper fraction first multiply the denominator with the whole number, in this example multiply \[7 \times 6 = 42\]next add numerator 5 to 42 we get 43 keep it in numerator and denominator keep as it is so we get converted fraction as \[\dfrac{{47}}{6}\].