What is $45\%$ of $1\dfrac{2}{3}$?

Hint: To solve this question first we will convert the mixed fraction into improper fraction. Then we will use the concept of percentage that is $x\%\text{ }of\text{ }y=\dfrac{x}{100}\times y$. Substituting the values and simplifying the obtained equation we will get the desired answer.

Complete step by step answer:
We have to find $45\%$ of $1\dfrac{2}{3}$.
Now, let us first convert the fraction $1\dfrac{2}{3}$ in to improper fraction then we will get
\[\Rightarrow 1\dfrac{2}{3}=\dfrac{5}{3}\]
Now, we have to find $45\%$ of \[\dfrac{5}{3}\].
Now, we know that the basic rule of percentage is $x\%\text{ }of\text{ }y=\dfrac{x}{100}\times y$.
To solve the percentage the word ‘of’ represents the multiplication so always replace the word ‘of’ by multiplication and the word ’is’ represents the sign equal “$=$”. So we can write the given expression as
\[\Rightarrow 45\%\times \dfrac{5}{3}\]
Now, we know that one percent is the part of hundred percent. To write a percentage in to decimal form we will divide it by 100. Then simplifying the above obtained equation we will get
\[\Rightarrow \dfrac{45}{100}\times \dfrac{5}{3}\]
Now, simplifying the above obtained equation we will get
\[\begin{align}
  & \Rightarrow \dfrac{15}{20} \\
 & \Rightarrow \dfrac{3}{4} \\
\end{align}\]

Hence we get $45\% $ of $1\dfrac{2}{3}$ is \[\dfrac{3}{4}\].

Note: In this particular question it is necessary to convert the mixed fraction because we cannot solve the mixed fraction directly. Students must know to convert the mixed fraction into proper or improper fraction. Alternatively we can also solve the question by using the concept of proportion. For this we need to compare the quantities by taking the part of the whole.