# How do you solve 5/2 + 9 divided by 3 - 2/6?

Feb 5, 2016

$4 \frac{5}{16}$

#### Explanation:

Given: $\text{ } \left(\frac{5}{2} + 9\right) \div \left(3 - \frac{2}{6}\right)$

But $9 \text{ is the same as } \frac{18}{2}$

And $3 \text{ is the same as } \frac{18}{6}$

Substituting gives:

$\left(\frac{5}{2} + \frac{18}{2}\right) \div \left(\frac{18}{6} - \frac{2}{6}\right)$

$\left(\frac{23}{2}\right) \div \left(\frac{16}{6}\right)$

$\frac{23}{2} \div \frac{16}{6}$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Using the shortcut method:

Invert the divisor (turn $\frac{16}{6}$ upside down) and multiply

$\frac{23}{2} \times \frac{6}{16}$

This is the same as:

$\frac{23}{16} \times \frac{6}{2}$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Doing the arithmetic

But $6 \div 2 = 3$ giving:

$\textcolor{b r o w n}{\frac{23}{16} \times 3}$

$\textcolor{b l u e}{\frac{23 \times 3}{16}} \text{ if this bit confuses you think of } \textcolor{b r o w n}{\frac{23}{16} \times \frac{3}{1}} \textcolor{b l u e}{= \frac{23 \times 3}{16 \times 1}}$

$\frac{69}{16}$

$4 \frac{5}{16}$