Question

How do you simplify `(2/5+1/5)-3/10`?

Answer 1

`3/10`

Explanation:

`color(blue)("Important fact 1")`

Multiply by 1 and you do not change the value. However 1 comes in many forms. So you can change a the way a fraction looks without changing its actual value.

`color(blue)("Important fact 2")`
A fraction consists of `("count")/("size indicator") -> ("numerator")/("denominator")`

You can not directly add or subtract the counts unless the size indicators are the same

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`" "color(green)(=[2/5color(red)(xx1)] color(white)(.)" "+" "[1/5color(red)(xx1)]" "-" "3/10`

`color(white)(..)color(green)(=[2/5color(red)(xx2/2)]" " +" "[1/5color(red)(xx2/2)]" "-" "3/10`

`color(white)(.)" "=[4/10 ]color(white)(...)" "+" "color(white)(...)[2/10]" "-" "3/10`

`" "=6/10" "-" "3/10`

`" " =(6-3)/10`

`" " = 3/10`

color(white)(.)