Question

How do you evaluate `5888 -: 92`?

Answer 1

This is a sort of cheat method. You can conduct the division using approximations which slowly 'whittle down' to the correct value.

`5888-:92=64`

Explanation:

`color(blue)("Initial estimation")`

Note that `6xx90=540` needs to be bigger
`" "60xx90=5400` so our value is between 60 and 70

`color(blue)("Conducting the division")`

`" "5888`
`color(red)(60)xx92 ->ul( 5520) larr" subtract"`
`" "368`
`color(white)(6)color(red)(3)xx92 ->ul(color(white)(1)276) larr" subtract"`
`" "92`
`color(white)(6)color(red)(1)xx92->ul(color(white)(..)92) larr" subtract"`
`" "0`

So `5888-:92 = color(red)(60+3+1)=64`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Comment about method")`

This approach is tagging advantage of something called the 'distributive property of multiplication'.

Writing `92xx64` as `92(64)` where the brackets mean: multiply everything inside the brackets by 92. You get this a lot in algebra.

`92(color(red)(64))->92(color(red)(60+3+1))`

`=92color(red)(xx60)" "+" "92color(red)(xx3)" "+" "92color(red)(xx1)`