How do you write $10\dfrac{5}{{12}}$ as an equivalent improper fraction $?$

Hint: First we know that mixed numbers and improper fractions. For example $4\dfrac{1}{5}$ this is a mixed number. And $\dfrac{{425}}{5}$ this is an improper fraction.
This has been shown using first principles.
The given numbers change into the suitable denominator number. And then we use multiplication and division.
And that finally we add the numerator. It gives the solution.
Finally we get the improper fraction.

Complete step by step answer:The given information is $10\dfrac{5}{{12}}$
This has been shown using first principles.
The First principles with a full explanation.
This can be written as: $10 + \dfrac{5}{{12}}$
Although not normally done, it is perfectly correct to write $10$ as $\dfrac{{10}}{1}$, we get
So we now have: $\dfrac{{10}}{1} + \dfrac{5}{{12}}$
To be able to add the top numbers (numerator) directly the bottom numbers (denominators) need to be the same.
If we multiply a number by $1$ then its value is not changed and it still looks the same.
However, the value of $1$can be presented in many ways. For example $1 = \dfrac{{12}}{{12}}$
Consider the $\dfrac{{10}}{1}$ let us multiply it by $1 = \dfrac{{12}}{{12}}$ so we have,
$\dfrac{{10}}{1} \times \dfrac{{12}}{{12}} = \dfrac{{10 \times 12}}{{1 \times 12}}$
Multiply numerator and denominator, hence we get
$ = \dfrac{{120}}{{12}}$
The $\dfrac{{120}}{{12}}$ is the same value as $\dfrac{{10}}{1}$but it just looks different.
So now we can write,
\[10\dfrac{5}{{12}} = \dfrac{{10}}{1} + \dfrac{5}{{12}}\]
$ = \dfrac{{120 + 5}}{{12}}$
Now you can directly add the top numbers.
$\dfrac{{120}}{{12}} + \dfrac{5}{{12}}$
We just added,
$ = \dfrac{{120 + 5}}{{12}}$
We just added the numerator terms, we get
$ = \dfrac{{125}}{{12}}$
Hence we get improper fraction is,
$10\dfrac{5}{{12}} = \dfrac{{125}}{{12}}$

Note:
We use the alternative method.
The given fraction is $10\dfrac{5}{{12}}$
First we write multiply $12$ by $10$ and its divide by $12$
Hence we get,
$\dfrac{{10 \times 12}}{{12}}$
This term add with $\dfrac{5}{{12}}$, hence we get
$\dfrac{{10 \times 12}}{{12}} + \dfrac{5}{{12}}$
Multiply $12$ by $10$ , hence we get
$\dfrac{{120}}{{12}} + \dfrac{5}{{12}}$
Now add the numerator, hence we get
$\dfrac{{125}}{{12}}$