color(red)("Shortcut approach")Shortcut approach
1 is the same as 100%. So 1/212 is the same as 50% and 3 is the same as 300%
so 3+1/2 -= 300%+50% = 350%3+12≡300%+50%=350%
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
color(red)("First principle method - takes longer to explain than to do.")First principle method - takes longer to explain than to do.
color(blue)("First convert to an improper fraction")First convert to an improper fraction
write as 3+1/23+12
Multiply by 1 and you do not change the value but 1 comes in many forms. So you can change the way a number looks without changing what it is 'worth'.
write as " "color(green)([3color(red)(xx1)]+1/2 [3×1]+12
" "color(green)([3color(red)(xx2/2)]+1/2 [3×22]+12
" "6/2" "+1/2" " =" " 7/2 62 +12 = 72
.................................................................................................
color(blue)("Converting to percentage")Converting to percentage
We need " "("some number")/100 some number100
("some number")/100 -=7/2some number100≡72
Change the 2 into 100. For multiply or divide what we do to the bottom we also do to the top.
Not that -=≡ means 'equivalent to'
("some number")/100 -=7/2 -=(7xx50)/(2xx50) =350/100some number100≡72≡7×502×50=350100
.....................................................................................................
Note that % is a unit of measurement and is worth 1/1001100
So we have:
" "color(blue)(bar(ul(|color(white)((2^2)/(2^2))3 1/2 =350/100-= 350%" "|)))
