{Solved} Better way to find % of a number (Y) equal to another number (X) [closed]

I don't understand why the video just doesn't do 150/.25 to get the answer. It makes so much more sense. The way the video does it is SO CONFUSING. I don't even know where four comes from. http://www.khanacademy.org/math/arithmetic/percents/v/identifying-percent-amount-and-base

All you have to do is [number X]/[percent of Y as a decimal] -- that's the formula. I don't understand all this complexity that video is creating. I don't think this video can teach at all. I was SO CONFUSED, and other people in the talk were confused as well.

The goal
~ I don't think at all that this is a good way to solve this problem compared to the formula way I understand
~ Maybe it is a good way and I'm missing something
~ The goal is to understand why it's taught like this so I can find out if it's a good way or not
~ Which in turn leads me to learn something that corrects my assumption
~ I don't think that I'm wrong though

Result
~ I found out I was right all along (for now) -- and voting down just because you don't like what I say doesn't change the truth, or the facts :)

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Um, and your question was? –  Henning Makholm Sep 28 '12 at 19:26
why is the video teaching it like that because it doesnt make any sense to me and it makes it all complicated and confusing -- i feel that the inherent question is clear from what i wrote, just saying –  kittensatplay Sep 28 '12 at 19:27
If you were to write out what you are trying to do and what the video does, I'd be much more inclined to help. –  mixedmath Sep 28 '12 at 19:28
im trying to understand why so i can make sense of this -- and the video is doing i dont know what, and i dont know how to explain it because it doesnt make any sense and i dont feel that it's a good way to learn or solve this kind of problem –  kittensatplay Sep 28 '12 at 19:29
Essentially, it looks like he implicitly used the fact that .25=$\frac{1}{4}$. Then he noticed that it was easier to multiply both sides by 4 instead of dividing by .25. –  chris Sep 28 '12 at 19:30

closed as not a real question by whuber, Thomas, Norbert, Noah Snyder, Nate EldredgeOct 6 '12 at 15:45

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The problem as set up in the video is asking "150 is 25% of what number?" So we want to be able to solve equations that have the form $$\text{percent}\times \text{what number} = \text{the given number}$$ When you're given a percent, you're actually given a fraction. So $25\%=\frac{25}{100}=.25$. There are two ways to go about solving this problem, and they're actually the same, they just look different. I'm going to replace the "what number" in the equation above by the letter $x$. So, now we want to solve the equation $$\frac{25}{100}\times x = 150 \qquad \text{OR} \qquad .25\times x=150$$ These are the same equation. We can solve the equation on the left by multiplying both sides by the inverse of the fraction: $$\frac{100}{25}\times\frac{25}{100}\times x = 150\times\frac{100}{25} \Rightarrow x=600$$ Notice that $\frac{100}{25}=4$, so we're really just multiplying both sides by 4. We can solve the equation on the right by dividing by .25: $$\frac{1}{.25}\times .25\times x = 150\times \frac{1}{.25} \Rightarrow x=600$$ Notice how I wrote the division in the second equation. Division is implicitly multiplication by a fraction. If you notice that $.25=\frac{25}{100}=\frac{1}{4}$, then we can simplify the division by $.25$: $$\frac{1}{.25}=\frac{1}{\frac{1}{4}}=4$$ So it just becomes multiplication by 4, exactly what the first equation uses to solve the equation. So the two methods really are the same, they just look a little different. In practice, use whatever makes sense to you.