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This page contains more examples of quotient and remainder calculations. It also contains a section on how to use your calculator to assist with these calculations.
Here is a question about remainders and quotients. It's the same question written in four different ways.
 How many times does $4$ go into $14$ and what is the remainder?
 How many times does $4$ go into $14$ and what is left over?
 What is $14$ divided by$4$ and what is left over?
 What is the quotient and the remainder when $14$ is divided by $4$?
We can picture this by taking $14$ circles
$$\Huge{\circ\hspace{5pt}\circ\hspace{5pt}\circ\hspace{5pt}\circ\hspace{5pt}\circ\hspace{5pt}\circ\hspace{5pt}\circ\hspace{5pt}\circ\hspace{5pt}\circ\hspace{5pt}\circ\hspace{5pt}\circ\hspace{5pt}\circ\hspace{5pt}\circ\hspace{10pt}\circ}$$
and putting them into groups of $4$. How many groups will there be abd how many circles will be left over?
$$\Huge{\color{blue}{\underbrace{\color{black}{\circ\hspace{5pt}\circ\hspace{5pt}\circ\hspace{10pt}\circ}}\quad\underbrace{\color{black}{\circ\hspace{5pt}\circ\hspace{5pt}\circ\hspace{10pt}\circ}}\quad\underbrace{\color{black}{\circ\hspace{5pt}\circ\hspace{5pt}\circ\hspace{10pt}\circ}}}\quad{\color{red}{\circ\hspace{5pt}\circ}}}$$
There are ${\color{blue}3}$ groups of $4$ and ${\color{red}2}$ circles left over. This tells us that $4$ goes into $14$ ${\color{blue}3}$ times (because we have ${\color{blue}3}$ groups) with ${\color{red}2}$ left over. We call ${\color{blue}3}$ the quotient and ${\color{red}2}$ the remainder.
A calculator can be used to find the quotient and remainder. there are several ways of doing this. here is one.
Use your calculator to find $14$ divided by $4$. It is ${\color{blue}3}.5$ or ${\color{blue}3}\frac12$. So the answer is a bit more than ${\color{blue}3}$. That is, the answer is ${\color{blue}3}$ (the quotient) and something left over (the remainder). So we know that $$14=4\times {\color{blue}3} +\text{remainder.}$$
A calculator can then be used to find the remainder. It is $144\times {\color{blue}3}$, which is ${\color{red}2}$.
Here are some problems for you to try.
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