# More Help

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.

Find the quotient when $22$ is divided by $4$. Find the remainder when $22$ is divided by $4$.
How many times does $33$ go into $1236$ and what is the remainder?
How many times does $3$ go into $12$ and what is left over?