#color(blue)("Solving by the shortcut method")#
Write as: #9/5-:63/10#
With fractions the general shortcut rule is:
#color(brown)("Invert the divisor and then multiply")#
So we have: #" "color(brown)(9/5xx10/63)#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
As an example: #2xx3" is exactly the same in value as " 3xx2#
Applying this principle:
#9/5xx10/63" " =" " 9/63xx10/5#
#3/21xx2" "=" "6/21#
#color(blue)("~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~")#
#color(blue)("Solving from first principles")#
consider:#" "9/5-:63/10" "# for a moment
The top number is a count (Numerator)
The bottom number is an indicator of the 'size' of what you are counting (Denominator).
Make the sizes the same and all we have to do then is divide the counts.
Multiply #9/5" by 1 but in the form of "2/2#
#" "(9/5xx2/2)-:63/10#
#" " 18/10-:63/10" " ->" "#the sizes are now the same (denominator)
By the law of ratios the answer to #18/10-:63/10#
gives 'exactly' the same answer as just dividing the 'counts' #18/63#
So# 18/10-:63/10 = 18/63 " "#This is the bit that translates into the shortcut!
#color(white)("xxxxxxxxx")#
Divide 'top' and 'bottom' by 3
#" "(18-:3)/(63-:3) = 6/21#
