# Why does your math work

## Basic arithmetic: this is how division works

### Examples of division

Here are a few Examples for the Division of numbers. At the beginning even smaller numbers up to 10, in the last examples the numbers go beyond 10.

\$6 \; : \; 3 \; = \; 2\;\$

Let's imagine the task.

We have exactly 6 apples bought from the supermarket. We want this with our two friends shareso each of us three has the same number of apples. So we calculate them 6 apples through 3. So it is checked how often the 3 fits into the 6. It's exactly 2 times. So everyone gets exactly 2 apples. We do the same with the other tasks. But it can also happen that you have a rest receive. We then write that as follows:

\$ 7 \; : \; 2 \; = \; 3 \; Remainder \; \$ 1

Here the \$ 2 \$ fits exactly \$ 3 \$ times into the \$ 7 \$, but there is still a \$ 1 \$ over, so the \$ remainder \ remains; \$ 1.

Further Examplesthedivision are:

\$ 5 \; : \; 3 \; = \; 1\; Remainder \; \$ 2

\$9 \; : \; 3 \; = \; 3\;\$

\$21 \; : \; 7 \; = \; 3\;\$

\$ 15 \; : \; 2 \; = \; 7 \; Remainder \; \$ 1

\$45 \; : \; 5 \; = \; 9\;\$

### Written division

There is at the division also the possibility to divide in writing. The two numbers that are to be divided are written next to each other as always, but one calculates one below the other gradually. This is a very good method of finding the right one quickly, especially with large numbers solution get.

Let's take a look at those written division using an example:

Written division example: \$ 112: \$ 4

In the figure we can see that the two numbers are written down first one after the other. The next step is to think about how many times the divisor is in that firstnumber fits. Since this is a \$ 1 \$, it doesn't even fit in. Thus we consider how often the divisor is in the first two numbers fits.

We find out that the number \$ 4 \$ fits exactly 2 times into the number 11, so it is one rest from \$ 3 \$ there. We enter this one line lower, here marked in \$ \ textcolor {blue} {blue} \$, and write the next number next to it, so here the \$ \ textcolor {blue} {2} \$. Now let's see how often that divisor fits into the number. It turns out exactly \$ 8 times. So the answer to dividing \$ 112 is \; : \; \$ 4 exactly \$ 28. There is no rest. This is how the writtendivision.

To find out more about this topic, have a look at the Exercises!