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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 $14-4\times {\color{blue}3}$, which is ${\color{red}2}$.

Here are some problems for you to try.

Using a calculator we find that $22\div 4=5.5$ or $5\frac12$. This means that $4$ goes into $22$ $5$ times with something left over. The quotient is $5$.
We know that $22=4\times 5+\text{remainder}$. Therefore the remainder is $22-4\times 5=2$.

Using a calculator we find that $1236\div 33=37.454545\dots$ or $37\frac{5}{11}$. This means that $33$ goes into $1236$ $37$ times with something left over. The quotient is $37$.
The remainder is $1236-33\times 37=15$.

$3$ goes into $12$ $4$ times and there is nothing left over. That is $12=3\times 4+0$. So the quotient is $4$ and the remainder is $0$.

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