Taking percentages Taking a percentage of a number.
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- Let's get started with some problems.
- Let's see.
- First problem: what is fifteen percent of forty?
- The way I do percent problems is I just convert the
- percentage to a decimal and then I multiply it times the
- number that I'm trying to get the percentage of.
- So 15% as a decimal is 0.15.
- You learned that from the percent to decimal conversion
- video, hopefully.
- And we just multiply this times forty.
- So let's say 40 times 0.15.
- five times zero is zero.
- five times four is twenty.
- Put a zero there.
- And then one times zero is zero.
- one times four is four.
- And you get six zero zero.
- Then you count the decimal spots.
- one, two.
- No decimals up there, so you go one, two and you
- put the decimal there.
- So 15% of 40 is equal to 0.15 times 40, which equals 6.00.
- Well, that's just the same thing as six.
- Let's do another problem.
- Hopefully, that didn't confuse you too much.
- And I'm going to try to confuse you this time just
- in case you weren't properly confused the last time.
- What is 0.2% of-- let me think of a number-- of 7.
- So a lot of people's inclinations would just
- say, oh, 0.2%, that's the same thing as 0.2.
- And if that was your inclination you would be wrong.
- Because remember, this isn't 0.2.
- This is 0.2%.
- So there's two ways of thinking about this.
- You could say that this is 0.2/100, which is, if you
- multiply the numerator and denominator by ten, is the
- same thing as two / one thousand.
- Or you can just do the technique where you
- move the decimal space over two to the left.
- In which case, if you're starting with 0.2 and you
- move the decimal space two to the left, you go bam.
- Bam, bam.
- That's where the decimal goes.
- So it's 0.002.
- This is key.
- 0.2% is the same thing as 0.002.
- This can always trip you up and I've made this careless mistake
- all the time, so don't feel bad if you ever do it.
- But just always pay careful attention if you see a
- decimal and a percentage at the same time.
- So now that we've figured out how to write this percentage
- as a decimal we just have to multiply it times the number
- that we want to take the percentage of.
- So we say 0.002 times 7.
- Well, this is pretty straightforward.
- seven times two is fourteen.
- And how many total numbers do we have or how many total
- digits do we have behind the decimal point?
- Let's see.
- It's one, two, three.
- So we need one, two, three digits behind the decimal point.
- So 0.2% of 7 is equal to 0.014.
- And you're probably thinking, boy, that's a really,
- really small number.
- And it makes sense because 0.2%, if you want to
- think about it, that's smaller than even one percent.
- So that's even smaller than one / one hundred.
- And actually, if you think about it, 0.2% is 1/500.
- And if you do the math, one / five hundred of seven will turn
- out to be this number.
- And that's an important thing to do.
- It's always good to do a reality check because when
- you're doing these decimal and these percent problems, it's
- very easy to kind of lose a factor of ten here or there.
- Or gain a factor of ten.
- So always do a reality check to see if your answer makes sense.
- So now I'm going to confuse you even further.
- What if I were to ask you four is twenty percent of what number?
- So a lot of people's reflex might just be,
- oh, let me take twenty percent.
- It becomes 0.20.
- And multiply it times four.
- And in that case, again, you may be wrong.
- Because think about it.
- I'm not saying what is twenty percent of four?
- I'm saying that twenty percent of some number is four.
- So now we're going to be doing a little bit of algebra.
- I bet you didn't expect that in the percent module.
- So let x equal the number.
- And this problem says that twenty percent of x is equal to four.
- I think now it's in a form that you might recognize.
- So how do we write twenty percent as a decimal?
- Well, that's just 0.20 or 0.2.
- And we just multiply it by x to get four.
- So 20%, that's the same thing as 0.2.
- It's the same thing as 0.20, but that last trailing
- zero doesn't mean much.
- 0.2 times x is equal to 4.
- And now we have a level one linear equation.
- I bet you didn't expect to see that.
- So what do we do?
- Well there's two ways to view it.
- You can just divide both sides of this equation
- by the coefficient on x.
- So if you divide 0.2 here and you divide by 0.2 here.
- So you get x is equal to 4 divided by 0.2.
- So let's figure out what 4 divided by 0.2 is.
- I hope I have enough space.
- 0.2 goes into 4-- I'm going to put a decimal point here.
- And the way we do these problems, we move the
- decimal point here one over to the right.
- So we just get a two and then we can move the decimal point
- here one over to the right.
- So this 0.2 goes into 4 the same number of times
- that two goes into forty.
- And this is easy.
- two goes into forty how many times?
- Well, two goes into four two times and then two goes
- into zero, zero times.
- You could've done that in your head.
- two into forty is twenty times.
- So 4 divided by 0.2 is 20.
- So the answer is four is twenty percent of twenty.
- And does that make sense?
- Well, there's a couple of ways to think about it.
- twenty percent is exactly one / five.
- And four times five is twenty.
- That makes sense.
- If you're still not sure we can check the problem.
- Let's take twenty percent of twenty.
- So 20% of 20 is equal to 0.2 times 20.
- And if you do the math that also will equal four.
- So you made sure you got the right answer.
- Let's do another one like that.
- I'm picking numbers randomly.
- Let's say three is nine percent of what?
- Once again, let's let x equal the number that three is nine percent of.
- You didn't have to write all that.
- Well, in that case we know that 0.09x-- 0.09, that's the same
- thing as nine percent of x-- is equal to three.
- Or that x is equal to 3 divided by 0.09.
- Well, if we do the decimal division, 0.09 goes into 3.
- Let's put a decimal point here.
- I don't know how many zero's I'm going to need.
- So if I move this decimal over to the right twice, then I'll
- move this decimal over to the right twice.
- So 0.09 goes into 3 the same number of times
- that nine goes into three hundred.
- So nine goes into thirty three times.
- three times nine is twenty-seven.
- I think I see a pattern here already.
- thirty, three, three times nine is twenty-seven.
- You're going to keep getting thirty-three-- the three's are just
- going to go on forever.
- So it turns out that three is nine percent of-- you can either write it as
- 33.3 repeating or we all know that 0.3 forever is the
- same thing as one / three.
- So three is nine percent of thirty-three and one / three.
- Either one of those would be an acceptable answer.
- And a lot of times when you're doing percentages you're
- actually just trying to get a ballpark.
- The precision might not always be the most important thing,
- but in this case we will be precise.
- And obviously, on tests and things you need to
- be precise as well.
- Hopefully, I didn't go too fast and you have a good
- sense of percentage.
- The important thing for these type of problems is pay
- attention to how the problem is written.
- If it says find ten percent of one hundred.
- That's easy.
- You just convert ten percent to a decimal and multiply it by one hundred.
- But if I were to ask you one hundred is ten percent of what?
- You have to remember that that's a different problem.
- In which case, one hundred is ten percent of-- and if you did the math,
- it would be one thousand.
- I think I spoke very quickly on this problem on this module, so
- I hope you didn't get too confused.
- But I will record more.
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