Question

What is `143296-:931`?

Answer 1

`143296-:931` gives `153` as quotient and `853` as remainder or
`143296-:931=153 853/931`

Explanation:

We can write `143296` as `143200+90+6`

Hence `143296-:931=(931xx100)+143200-93100+90+6`

= `(931xx100)+50100+90+6=(931xx100)+50190+6`

= `(931xx100)+(931xx50)+50190-931xx50+6`

= `(931xx100)+(931xx50)+50190-46550+6`

= `(931xx100)+(931xx50)+3640+6=(931xx100)+(931xx50)+3646`

= `(931xx100)+(931xx50)+(931xx3)+3646-2793`

= `(931xx100)+(931xx50)+(931xx3)+853=931xx153+853`

Hence, `143296-:931` gives `153` as quotient and `853` as remainder or `143296-:931=153 853/931`

Answer 2

`153color(white)(.) 853/931`

Explanation:

color(white)(..)
`" "143296`
`color(magenta)(100)xx931 ->" "ul(color(white)(.) 93100) larr" Subtract"`
`" "color(white)(..)color(green)(50196)`
`color(magenta)(50)xx931 ->" "color(white)(..)ul(46550) larr" Subtract"`
`" "color(white)(..)3646`
`color(magenta)(3)xx931 ->" "ul(color(white)(..)2793) larr" Subtract"`
`" "color(white)(..)color(magenta)(853 larr" Remainder")`

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(magenta)(100+50+3+853/931)`

`153color(white)(.) 853/931`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Tip about method")`

Suppose you did not know that the maximum number of 10's you could multiply by was 5 giving `color(magenta)(50)`

`" "color(white)(..)bar(color(green)(50196))`
`color(magenta)(20)xx931 ->ul(color(white)(..)18620) larr" Subtract"`
`" "32576`
`color(magenta)(20)xx931 ->ul(color(white)(..)18620) larr" Subtract"`
`" "24956`
`color(magenta)(10)xx931 ->ul(color(white)( ....)9310) larr" Subtract"`
`" "5646 larr " Now the digit count has reduced by 1"`
So there is no more 10's to divide by. Thus the total count of tens is

`color(magenta)(20+20+10 = 50)`