Write as #color(brown)((1.638)/(0.35))#

Multiply the given expression by 1 but in the form of #1=1000/1000#

#(1.638)/(0.35)xx1000/1000" " =" " (1.638xx1000)/(0.35xx1000)#

#" "color(brown)(=1638/350)" " #

This looks different to #1.638/0.35# but if you divide them both out you end up with the same answer. So they are 'equivalent'.

'~~~~~~~~~~~~ For reference ~~~~~~~~~~~~

#1xx350=350#

#2xx350=700#

#3xx350=1050#

#4xx350=1400#

#5xx350=1750#

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

#color(blue)("Calculating the division into 1638")#

5 lots of 350 is too big a number so we chose 4

#color(brown)("So the first number of our division is 4")#

We have 4 + the remainder of #1638-1400=238#

So we write #4 + 238/350#

#color(brown)(=> 4 238/350)" "# which simplifies to #color(brown)(" "4 17/25)#

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

This means that

#(1.638 -: 0.35) = 1638-:350 = 4 17/25" "#

As a decimal this is 4.68