What is \[1\dfrac{2}{3}\] as an improper fraction?

Hint: From the given question we have been asked to find the improper fraction for \[1\dfrac{2}{3}\]. For this mixed fraction to convert into an improper fraction we have a process which is as follows. First for a mixed fraction of form \[a\dfrac{b}{c}\] we have to add the \[a\] to the fraction \[\dfrac{b}{c}\] then we have to solve that with the help of basic operation in mathematics which is addition. After adding we will get the required improper fraction to the given question. So, the solution will be as follows.

Complete step-by-step solution:
First as said in the above we have to compare the given mixed fraction in the question with \[a\dfrac{b}{c}\].
So, after comparing we got the values as follows.
\[a=1,\dfrac{b}{c}=\dfrac{2}{3}\].
So, we will add the \[a\] to the fraction \[\dfrac{b}{c}\]. So, we get the expression reduced as follows.
\[\Rightarrow 1+\dfrac{2}{3}\]
Here we will make the denominators the same for both the terms which we are adding as it makes the solution easier. So, we get the expression as follows.
\[\Rightarrow \dfrac{3}{3}+\dfrac{2}{3}\]
Now we will add the numerators as the denominators are the same. So, we get the expression reduced to as follows.
\[\Rightarrow \dfrac{3+2}{3}\]
\[\Rightarrow \dfrac{5}{3}\]
Therefore the answer is \[ \dfrac{5}{3}\].

Note: Students must be very careful in doing the calculations, they must not make any mistakes. We can also solve this in another way which is as follows.
\[\Rightarrow 1\dfrac{2}{3}\]
Here we will multiply the one with the denominator three and then we add it to the numerator term.
\[\Rightarrow \dfrac{3\times 1+2}{3}\]
\[\Rightarrow \dfrac{5}{3}\]