Question

How do you simplify `4(0.2m-0.3n)-6(0.7m-0.5n)`?

Answer 1

I have elected to solve this way to try and get you thinking about numbers differently.

`3.4m-4.7n`

Explanation:

`color(blue)("Introduction to the idea behind the method")`

Using actual number to prove my point:

Suppose we had `1/2`. This is the same as `5/10`

Which is the same as `1/10xx5`

Which is the same as `1/10(3+2)`
This is called 'distributive' property in that the 'multiply by `1/10`' is distributed over both the 3 and the 2. So we have:
`(1/10xx3)+(1/10xx2)`

Which is the same as `(0.3+0.2)=0.5=1/2`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Answering the question")`

Given:`" "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"`

Same as `1/10[color(white)(2/2) 4(2m-3n)-6(7m-5n)color(white)(2/2)]`

`" "1/10[color(white)(2/2)8m-12n-42m-35ncolor(white)(2/2)]`

`" "1/10[color(white)(2/2)-34m-47ncolor(white)(2/2)]`

`" "3.4m-4.7n`