Question

How do you divide `2248\div 18`?

Answer 1

Solution in 2 parts: This is part 1

`124 17/18`

Explanation:

Sometimes division can seem quite daunting and the traditional long division very confusing. However, If you can get your head round the traditional method (algorithm) you will find it quite efficient.

You do not have to use it. There are other ways. I am going to show you one of them.
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As an `ul("estimate")` of the starting point consider this.
18 is nearly 20 `->2248/(2xx10)=1124/10~~112`

The `~~` means approximately equal to..

So lets see where this takes us: `112=100+10+2`

`color(green)(100)xx18->1800`
`color(green)(color(white)(0)10)xx18->color(white)(1)180`
`color(green)(color(white)(10)2)xx18->ul(color(white)(18)36) larr" add"`
`" "color(white)(.)2016`

But we need `2248` so we are left with `2249-2016=233`

`" "233`
`color(green)(10)xx18->ul(180) larr" subtract"`
`" " 53`
`color(magenta)(3xx18color(white)(..)->54 larr" Too much"`

`" "53`
`color(green)(2)xx18color(white)(..)->ul(36) larr" subtract"`
`" "17larr" REMAINDER"`

`2248-:18=color(green)(100+10+10+2+2+17/18)`

`124 17/18`
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Answer 2

Solution in 2 parts: This is part 2
Dealing with the fraction to decimal, if needed.

So `124 17/18 = 124.944` to 3 decimal places

Explanation:

`124 17/18`

So we need the decimal equivalent of `17-:18`

I am 'going for' 3 decimal places
Not that 17 is the same as `17000xx1/1000`

`color(magenta)("We will multiply by the "1/1000" at the end")`

`" "17000`
`900xx18->ul(16200)larr" subtract"`
`" "800`

`color(brown)(10xx18=180" so")`
`color(brown)(20xx18=360" so")`
`color(brown)(40xx18=720" giving:")`
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Starting again:

`" "17000`
`color(green)(900)xx18->ul(16200)larr" subtract"`
`" "800`
`color(white)(9)color(green)(40)xx18->" "ul(720) larr" subtract"`
`" "80`
`color(magenta)(color(white)(.)5xx18->" " 90 larr" too much so not included" )`
`color(white)(.)color(green)(4)xx18->" "ul(72)`
`color(white)(.)80 - 72color(white)(.)=" "8`

We are going to get a ever repeating cycle of `80-72`
so the 4's keep on going for ever.

`color(green)(900+40+4+...) ~~944`

But we have the `944xx1/1000 = 0.944`

So `124 17/18 = 124.944` to 3 decimal places