#color(red)("Using shortcut method")#
Move #5 2/7# to the other side
#k=color(brown)(2 27/70)color(green)(-5 2/7)#
By reversing the numbers I can subtract the lesser value from the greater. However, I have to multiply the whole by (-1) to maintain the original values.
Write as #k= -1xx(color(green)(4 9/7)color(brown)(-2 (2.7)/7)) = -2 (6.3)/7=-2 63/70 = -2 9/10#
#color(blue)(" "k= -2 9/10)#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(red)("Using first principles method")#
I have elected to show this process in a lot of detail
Given:#" "5 2/7+k=2 27/70#
Subtract #5 2/7# from both sides
#k=2 27/70-5 2/7#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Consider "2 27/70)#
Write as #2+27/70#
Multiply the 2 by 1 but in the form #1=70/70#
#(2/1xx70/70)+27/70" "->" "140/70+27/70 color(blue)(= 167/70)#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Consider "5 2/7)#
Write as #5+2/7#
Multiply 5 by 1 but in the form #1=7/7#
#(5/1xx7/7)+2/7" "->" "35/7+2/7 = 37/7#
Multiply by 1 but in the form #10/10#
#37/7xx10/10color(blue)( = 370/70)#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Putting it all together")#
#color(brown)(" "k=2 27/70-5 2/7" "->" "color(green)(k=167/70-370/70)#
#color(blue)(" "k=-203/70 =-2 9/10)#
