Question

If you have 10 dollars how much money can you split between 3 friends?

Answer 1

Each frind would get $3 (technically $3.33 if we're allowed to use coinage)

Explanation:

If there are 10 dollars and three friends to share it with. That means that we'll be dividing three into 10. We could do scary long division, or we can just think through this. We need the closest number we can get to `10`.
`3*1=3`. Too small.
`3*2=6`. We can keep going!
`3*3=9`. Let's try a few more...
`3*4=12` GO BACK! WE"VE GONE TOO FAR.

Okay so `9` is as close as we can get, with `$3` to each friend. If we can go smaller, than we need to deal with the difference between `9` and `10`: `1`. We need to dived that `$1` amongst the three friends. We could do some math or just write a fraction `1/3`. I know the conversionn in my head that `1/3=0.33`. So the total each person would get is `$3.33`. If we want to check we can just multiply that by `3`, which should give us `10` (or something very close).

`color(white)(xx)3.33`
`xx`
`color(white)(3.3)3`
`--`
`color(white)(xx)9.99`

And it is! Good work.

Answer 2

Each person gets `$3 1/3`

Explanation:

starting value`$10`
`color(magenta)(3)xx3->" "ul(color(white)(.)9) larr" subtract"`
`" "1 larr" remainder"`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
remainder in `10^("ths") -> 10`
`color(magenta)3xx3/10->" "ul(color(white)(,) 9) larr" Subtract"`
`" "1 larr" remainder in "10^("ths")`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
And the cycle repeats for ever giving `color(magenta)(3.3)333...`

By recognition: `0.3333...->1/3`

By mathematics
Let x=0.3333...
Let 10x=3.333...

Then `10x-x" "=" "3.333...`
`" "ul(0.333..) larr" Subtract"`
`" "9x" "=" "3.0`

`x=3/9-=1/3`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
So each person gets `$3 1/3`