#color(red)("This is much faster if you have memorised that "5xx7=35")#
#color(blue)("Dealing with the negative and positive")#
When multiplying or dividing, if the signs are the same then the answer is positive. If they the signs are not the same then the answer is negative.
We have #(+35) -:(-7)#
The signs are not the same so the answer is negative.
So now we have #" "-(35-:7)#
Write as #" "-(35-:7) ->(-35/7)#
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#color(blue)("Shortcut method")#
#color(red)("If you can do it this is the most efficient way."#
#color(red)("You jump steps by pulling this from memory")#
Known #5xx7=35#
#" "color(brown)(ul(bar(|color(white)(2/2)35-:(-7)=-5" "|)))#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~ #color(purple)("Now we do it the hard way! ")#~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Observe that #" "35->3.5=1/2xx7#
If the above condition is true then the factors of 35 are 5 and 7
#color(blue)("Dealing with the numbers")#
7 is a factor of both 7 and 35 so divide top and bottom by 7
#-35/7" "=" "- (35-:7)/(7-:7) " "=" "-5/1 = -5#
#" "color(brown)(ul(bar(|color(white)(2/2)35-:(-7)=-5" "|)))#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Footnote interesting fact for comparison")#
#3xx5=15" "->" "1/2xx3=1.5 larr" same digits"#
#4xx5=20" "->" "1/2xx4=2 larr" same digit but with 0"#
#5xx5=25" "->" "1/2xx5=2.5 larr" same digits" #
#6xx5=30" "->" "1/2xx6=3 larr" same digit but with 0"#
and so on
