Convert \[4\dfrac{3}{4}\] to an improper fraction.

Hint: An improper fraction is a type of fraction whose numerator is greater than or equal to the denominator. Concepts of addition and multiplication need to be applied for the conversion.

Complete step by step solution:
The given fraction \[4\dfrac{3}{4}\] is a mixed fraction, which is to be converted into an improper fraction.
First multiply the denominator of the fractional part with the whole number of the mixed fraction:
Here whole number \[ = \] \[4\]
Fractional part \[ = \] \[\dfrac{3}{4}\]
\[\therefore \] \[4 \times 4\] \[ = \] \[16\]… (1)
Add the numerator of the fractional part to (1):
\[16 + 3 = 19\]… (2)
The required improper fraction has the numerator \[19\], as obtained above and the denominator equal to the denominator of the fractional part of the mixed fraction.
\[\therefore \] Required mixed fraction:
\[\dfrac{{19}}{4}\]

\[ \Rightarrow \] \[4\dfrac{3}{4}\] \[ = \] \[\dfrac{{19}}{4}\].

Additional information:
An improper fraction is one whose denominator is less than or equal to the numerator.
Example: \[\dfrac{3}{2}\]
A proper fraction is one whose denominator is greater than or equal to the numerator.
Example: \[\dfrac{1}{2}\]
A mixed fraction is a combination of a whole number and a fractional part.
Example: \[2\dfrac{1}{2}\]

Note: Only improper fractions can be converted to mixed fractions and mixed fractions can be converted to only improper fractions. While doing the conversions note that the multiplication occurs first and then the addition. Moreover, check the calculations properly while calculating the numerator.