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

Nov 25, 2016

$\frac{3}{10}$

#### Explanation:

$\textcolor{b l u e}{\text{Important fact 1}}$

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.

$\textcolor{b l u e}{\text{Important fact 2}}$
A fraction consists of $\left(\text{count")/("size indicator") -> ("numerator")/("denominator}\right)$

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

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$\text{ "color(green)(=[2/5color(red)(xx1)] color(white)(.)" "+" "[1/5color(red)(xx1)]" "-" } \frac{3}{10}$

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

$\textcolor{w h i t e}{.} \text{ "=[4/10 ]color(white)(...)" "+" "color(white)(...)[2/10]" "-" } \frac{3}{10}$

$\text{ "=6/10" "-" } \frac{3}{10}$

$\text{ } = \frac{6 - 3}{10}$

$\text{ } = \frac{3}{10}$

color(white)(.)