# how to rearrange a division

At 3:55 we have $\tan 34.4^\circ=9.16/b$, and the kind sir says that to calculate $b$ he needs to change the equation to $b = 9.16/\tan 34.4^\circ$.

I've seen this trick used alot before, but I never seem to grasp it. What is the logic behind him changing the order? How do I know what to divide or multiply?

Does the trick have a name? I've tried to search for "rearranging formula" like it said in the video, but it didnt get me far.

I hope I used the right tag.

Thanks!

• $$\rm x=\frac{y}{z}\iff xz=y\iff z=\frac{y}{x}$$ – anon Jul 28 '13 at 0:31
• @anon I understand thats the formula but I don't understand the logic behind it – user1534664 Jul 28 '13 at 0:35
• @anon I understand it now, lol, thanks. – user1534664 Jul 28 '13 at 0:37
• To go from $x=\frac{y}{z}$ to $xz=y$, we multiply by $z$. If we wanted to do that in reverse, we would have dividied $xz=y$ by $z$ to obtain $x=\frac{y}{z}$. What we can do is divide $xz=y$ by $x$ to obtain $z=\frac{y}{x}$ instead. – anon Jul 28 '13 at 0:40
• What do I do when a comment answers my question? Do I leave this open? – user1534664 Jul 28 '13 at 0:45

What he's done is multiply both sides of the equation by $$\frac b{\tan{34.4^\circ}},$$ which is legal because $\tan{34.4^\circ} \neq 0$.