Question #bc8d3

The shortcut method is based on what follows:

I will highlight in red the bit that the shortcut method uses.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("First principle method")#

Using ratios in fractional format.

Lookin at the units to decide how we write this. We are told
'mass per metre' so this is written as:

#("mass")/("metres")->(Kg)/m -> 15/3.25#

The word 'per' means for each of 1. So 'per metre' is for each of 1 metre

Thus we need to change the #3.25# metres to 1 metre
Note that #3.25xx1/3.25 = 1#

So we multiply top and bottom of #15/3.25# by #1/3.25#

#(color(red)(15xx1/3.25))/(3.25xx1/3.25)" "=(color(red)(15xx1/3.25))/1#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Shortcut method")#

To determine the mass for one metre apply #color(red)(15-:3.25)#

Now you see where the shortcut approach comes from

This produces a decimal solution which I am choosing to be rounded, so not precise.

#15-:3.25 = 4.61538..... = 4.6# rounded to 2 decimal places

Or you can write: #15/3.25xx 4/4=60/13# which is an exact value