Question

What is `87.92\div 6.28`?

Answer 1

`87.92 div 6.28 = 14`

Explanation:

The problem is the division by the decimal. It is better to have the divisor as a whole number.

`87.92/6.28 xx 100/100 = 8792/628`

`rarr`normal long division is painful, but if this calculation is done on a calculator, there is no point to the adjustment in the first place!

`color(white)(xxxxx..x)14`
`color(white)(xxx)628)bar8792" "larr879div628 = 1`
`color(white)(xxxxxx)ul628 " "larr1xx628 = 628.` Subtract
`color(white)(xxxxxx)2512larr" bring down" 2." " 2515div628=4"`
`color(white)(xxxxxx)ul2512" "larr4xx628 = 2512" "` subtract
`color(white)(xxxxxxx..)0`

Answer 2

A very different approach
You can use the same approach for algebraic division.

`87.92-:6.28 =14`

Explanation:

I don't like division by decimals so I get rid of them as soon as I can.

`color(brown)("This is another way of writing the numbers so that they give the")` `color(brown)("same answer.")`

`[(87.92)/(6.28)color(magenta)(xx1)] -> [(87.92)/(6.28)color(magenta)(xx10/10)] -> 8792/628`

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`color(brown)("Alignment is very important - make the left line up.")`

`"start point "->8792`
`color(magenta)(1)xx628 ->" "color(white)(..)ul(628) larr" subtract "color(magenta)("(maximum number of 10's)")`
`color(white)(xxxxxxxxxx.)2512`
`color(magenta)(4)xx628->" "color(white)(..) ul(2512) larr" subtract "color(magenta)("(max number of units)")`
`color(white)(.........................)0000`

So `87.92-:6.28 = color(magenta)(14)`

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Slightly better explained!")`

`"start point "->8792`
`color(magenta)(10)xx6280 ->""color(white)(..)ul(6280) larr" subtract "color(magenta)(20 xx" is too big")`
`color(white)(xxxxxxxxxx.)2512`
`color(magenta)(4)xx628->" "color(white)(..) ul(2512) larr" subtract "color(magenta)("(max number of units)")`
`color(white)(.........................)0000 larrcolor(magenta)(" as these are 0 we have finished")`

So `87.92-:6.28 = color(magenta)(10+4=14)`