#color(brown)("Quotient is the official mathematical name for the answer when you are doing division.")#
#color(green)("In multiply or divide, if the signs are different the answer is negative.")# #color(green)("If they are the same the answer is positive.")#
In this case we have a positive divided by a negative so the answer is negative.
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#color(blue)("Shortcut method")#
Note that the divisor is what you are dividing by.
#color(brown)("Invert (turn upside down) the 'divisor' and multiply")#
#4-:(-2/7) " "->" "-(4xx7/2)#
#-(cancel(4)^2xx7/(cancel(2)^1)) =14#
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#color(blue)("First principles method")#
A fraction is #" "("count")/("size indicator")" "->" "("numerator")/("denominator")#
#color(green)("You can only directly divide the counts if the 'size indicators' are the same.")#
#color(brown)("Making the size indicators the same")#
Multiply by 1 and you do not change the value but 1 comes in many forms.
Multiply the 4 by 1 but in the form of #1=7/7# giving:
#4xx7/7=(4xx7)/7=28/7#
So we can now write:
#-(4-:2/7)" "->" "-(28/7-:2/7)#
#color(brown)("Doing the division")#
As the size indicators (denominators) are the same we can just divide the counts (numerators) giving:
#28-:2=14#
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#color(blue)("Footnote")#
People do not write it this way but you can write #6-:3# as
#6/1-:3/1# As the size indicators are the same you can directly divide the counts: #6/1-:3/1 -> 6-:3=2#
