color(blue)("Introduction to the idea behind the method")Introduction to the idea behind the method
Using actual number to prove my point:
Suppose we had 1/212. This is the same as 5/10510
Which is the same as 1/10xx5110×5
Which is the same as 1/10(3+2) 110(3+2)
This is called 'distributive' property in that the 'multiply by 1/10110' is distributed over both the 3 and the 2. So we have:
(1/10xx3)+(1/10xx2)(110×3)+(110×2)
Which is the same as (0.3+0.2)=0.5=1/2(0.3+0.2)=0.5=12
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color(blue)("Answering the question")Answering the question
Given:" "4(0.2m-0.3n)-6(0.7m-0.5n) 4(0.2m−0.3n)−6(0.7m−0.5n)
Don't like decimals so lets get rid of them
Write as:color(white)(2/2.)4/10(2m-3n)-6/10(7m-5n)larr" distributive"22.410(2m−3n)−610(7m−5n)← distributive
Same as 1/10[color(white)(2/2) 4(2m-3n)-6(7m-5n)color(white)(2/2)]110[224(2m−3n)−6(7m−5n)22]
" "1/10[color(white)(2/2)8m-12n-42m-35ncolor(white)(2/2)] 110[228m−12n−42m−35n22]
" "1/10[color(white)(2/2)-34m-47ncolor(white)(2/2)] 110[22−34m−47n22]
" "3.4m-4.7n 3.4m−4.7n
