What is #87.92\div 6.28#?

2 Answers
Oct 4, 2016

#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#

Oct 5, 2016

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)#