How do you simplify (2n)/5 + (-n/6)?

Sep 11, 2016

$\frac{7 n}{30}$

Explanation:

Consider $+ \left(- \frac{n}{6}\right)$

This is like $\left(+ 1\right) \times \left(- 1\right) \times \frac{n}{6}$

Multiply plus and minus and the answer is minus

So $\left(+ 1\right) \times \left(- 1\right) \times \frac{n}{6} = - \frac{n}{6}$

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Giving:$\text{ } \frac{2 n}{5} - \frac{n}{6}$

To be able to directly add or subtract the top numbers of fraction (count) the bottom numbers (size indicators) must be the same.

$\left(\text{top number")/("bottom number")->("count")/("size indicator")->("numerator")/("denominator}\right)$

So we need to make the bottom numbers the same. I chose 30

$\textcolor{b r o w n}{\text{Write as: }} \left(\frac{2 n}{5} \times 1\right) - \left(\frac{n}{6} \times 1\right)$

$\textcolor{b r o w n}{\text{But 1 comes in many forms}}$

$\left(\frac{2 n}{5} \times \frac{6}{6}\right) - \left(\frac{n}{6} \times \frac{5}{5}\right)$

$\frac{2 n \times 6}{5 \times 6} - \frac{n \times 5}{6 \times 5}$

$\frac{12 n}{30} - \frac{5 n}{30} \textcolor{b r o w n}{\leftarrow \text{ Now we can directly subtract the counts}}$

$\textcolor{b r o w n}{\text{but }} 12 n - 5 n = 7 n$

$\implies \frac{12 n}{30} - \frac{5 n}{30} = \frac{7 n}{30}$