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Maths...
Fizban140
Registered User, __BANNED USERS regular
Registered User, __BANNED USERS regular
Fffff...
I am going to take a college placement test tomorrow (well sometime this week) and I am going over basic math before I move onto the other stuff. Anyways I have to find what 11 percent of 3000 is, I can do it in my head but that probably won't help me on the test if they have some ridiculous number, I don't want to waste too much time.
Anyways I had to look up how to do long division on paper, I have been using a calculator and doing the rest in my head since about sixth grade when we stopped using that crap. So how the hell do I do this? The practice guide has some bullshit equation where they do this...
Example: 20% of what number is 16?
.2*a=16
(20/100)a=16
1/5a=16/1
5* (1/5)a = (16/1) * 5
a=16*5
a=80
What the bearcock just happened? They explain nothing except that I need to multiply both sides of the equation by five, what a load of shit. Why multiply? Why 5? Why both sides? Why the fuck don't math books ever explain the reasoning behind anything.
Anyways all I need to know is what I do with 11? Five obviously doesn't work so what do I do?
11/100 doesn't reduce all cool like the other one so do I just do times 100 on both sides? This doesn't seem right. Multiply both sides by 100, now I have that same thing had before except with more zeros. So I still have to do 11/3000 so I really got nowhere as far as I can tell.
I am going to take a college placement test tomorrow (well sometime this week) and I am going over basic math before I move onto the other stuff. Anyways I have to find what 11 percent of 3000 is, I can do it in my head but that probably won't help me on the test if they have some ridiculous number, I don't want to waste too much time.
Anyways I had to look up how to do long division on paper, I have been using a calculator and doing the rest in my head since about sixth grade when we stopped using that crap. So how the hell do I do this? The practice guide has some bullshit equation where they do this...
Example: 20% of what number is 16?
.2*a=16
(20/100)a=16
1/5a=16/1
5* (1/5)a = (16/1) * 5
a=16*5
a=80
What the bearcock just happened? They explain nothing except that I need to multiply both sides of the equation by five, what a load of shit. Why multiply? Why 5? Why both sides? Why the fuck don't math books ever explain the reasoning behind anything.
Anyways all I need to know is what I do with 11? Five obviously doesn't work so what do I do?
11/100 doesn't reduce all cool like the other one so do I just do times 100 on both sides? This doesn't seem right. Multiply both sides by 100, now I have that same thing had before except with more zeros. So I still have to do 11/3000 so I really got nowhere as far as I can tell.
Fizban140 on
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Posts
You multiply both sides because it keeps the equation equal. x=y is equivalent to 5x=5y.
The reason you multiply, and the reason you multiply by 5 specifically, is because in order to get the answer you need to go from:
.2*a = 16
to
a = ???
Which you do by converting .2a to 1, which you do by multiplying by 5.
The "trick" to do this is convert it to a fraction (1/5) then turn that fraction upside down (5/1) and multiply by that number.
If all that makes sense, you should have an idea how to do the 11% of 3000 problem. If it doesn't, it's because I haven't had to teach math in aaaaages, so don't blame yourself.
11/100 just ends up turning into 11=3000
What percent of 3000 is 11?
3000x = 11, where x is going to be a percent value
What is 11% of 3000?
(0.11)(3000) = x
3000 is 11% of what number?
0.11x = 3000
11/100 * 3000/1 = 33000/100 = ?
That example problem didn't help at all with the practice problem directly following it.
Erm. That's not even remotely the same. :P
That sounds like a math textbook.
For the first question:
11% is the same as 11/100. So, to find 11% of 3000, multiply 3000 by 11/100.
3000*(11/100) = 330.
For the second question:
20% is the same as 20/100. 20% of the variable a is (20/100)*a. So, to find the number that gives 16 when you take 20% of it, set up this equation:
(20/100)*a = 16.
To solve this equation for a, you need to rewrite the equation so that a is alone by itself on one side of the equation. To do that, you need to get rid of the (20/100) which is currently on the left side of the equation. To get rid of the (20/100), multiply both sides of the equation by the reciprocal (the fraction flipped upside-down).
(100/20)*(20/100)*a = (100/20)*16.
(100/20)*(20/100) is just 1. So the equation above simplifies to
1*a = (100/20)*16.
a = (100/20)*16.
a = 80.
In your textbook, they multiplied both sides of the equation by 5. That works too, because 5 is equal to 100/20. 5 was chosen because it is equal to 100/20, the reciprocal of 20/100.
Heres another equample: 88 is 11% of what number?
11% is the same as 11/100.
(11/100)*a = 88.
Get rid of the (11/100) on the left side of the equation by multiplying both sides of the equation by the reciprocal, (100/11).
(100/11)*(11/100)*a = (100/11)*88.
1*a = (100/11)*88.
a = (100/11)*88.
a = 800.
That's, uh, the point. I think the reason he can't get from the example problem to the one being asked is because this isn't clear. They're different problems, and you have to look at the phrasing to see why.
Why is it that every math book is set up perfectly for you to hate it just a little bit more every single time you use it? It really is incredible.
I gotcha.
11% of 3000?
11/100 = x/3000
notice how I put the equation in terms of
part/whole = part/whole
20% of what number is 16?
20/100 = 16/x
solve for x.
Try and relate them that way, it might make more sense.
I mean take all steps from end to start .. got it???
First, we know that non-reduced fractions are the same as their reduced versions, right?
So
1/2 = 2/4 = 4/8 = 100/200 and so forth.
To cross multiply, simply take the numerator (top number) of one fraction and multiply it by the denominator (bottom number) of the other fraction. In equal fractions, the multiplied answers will be the same.
For example:
Cross multiplying you get:
1x4 = 4
2x2 = 4
To figure out a percentage of a number, you can use cross multiplication to easily get your answer.
Let's try with something simple first.
"What is 50% of 10?"
100 * x = 50 * 10
100x = 500
x = 5
Let's try it the other way.
"10 is 50% of what number?"
50 * x = 10 *100
50x = 1000
x = 20
Now let's try something more difficult.
"What is 34% of 207400?"
100 * x = 34 * 207400
100x = 7051600
x = 70516
Hope this helps.
11/100 * 3000 = x.
20% of what number is 16.
20/100 * x = 16.
"What number" means x. "Percent of" means "/100 *".
You then divide both sides by the same number, or multiply both sides by the same number, until you get X by itself.
The first problem would go like this:
20% of what number is 16
Use the direction I gave above to translate this into an equation
20/100 * x = 16.
We want to move things to the right and leave x on its own side of the equation.
Multiply both sides by 100 to get rid of the "/100" on the left side.
20 * x = 16 * 100
Halfway there, we need to move the "20*" on the left over to the right side.
Divide both sides by 20.
x = 16 * 100 / 20.
Now it's straightforward multiplication and divison. In this case there is a shortcut of noticing that 100/20 = 5, so you can just do 16*5.
Since these questions pretty much have to use these words it's pretty simple to do the substitution. After that the cross multiplication seems to be covered (I hope I haven't read all of these posts thoroughly)
66% of something is roughly two-thirds, 2/3
50% of something is a half, 1/2
25% of something is a quarter, 1/4
20% of something is a fifth, 1/5
10% of something is a tenth, 1/10
If a problem asks you what is X% of SomeNumber, you should be able to immediately ballpark an answer.
27% of 8300? I dunno exactly, but 27% is pretty close to a fourth, and a fourth of 8000 is 2000, so the answer should be around 200.
Write it down, use it to sanity check the real answer you get. (And if you're really in a time pinch, use it to guess the right answer :P)
To get the real answer, just shift some decimals and multiply.
27% of 8321 in equation form is .27*8300
Whenever I see equations where I have decimals, I like to shift it so the equation lacks decimals. 27*83 is the same as .27*8300, but it's much more palatable to mental math.
Doing 27*83 gets 2241. That's in line with our eyeball answer, 2000, so all is good.
That helps quite a bit, but I am sure I will fuck up on where to put the x since I don't quite understand how all this works.
Math really isn't my thing.
So 6% of 50 would be
6/100 = 50/x?
20 is what percentage of 50?
50/100 = 20/x?
No, not quite.
6% of 50 would be
6/100 = x/50
say it out loud:
"six out of one-hundred is equal to 'what' out of 50?"
20 is what percentage of 50?
x/100 = 20/50
Kind of like... 50 is what percentage out of 50?
x/100 = 50/50
where x = 100
100/100 = 50/50
1 = 1
So, 50/50 = 100%
Hopefully this helped a bit. Kind of hard to teach this kind of thing over the internet.
1% of 50 is 0.5, so 6% is six times that. 6 times 0.5 is 3.
EDIT: I should mention that this works best for round numbers, like 3000 or 50. Although it will be harder to do something like x% of 43, its not impossible to do so with this method. As with every method in math, your mileage may vary.
Steam: CavilatRest
Fuck I think I need to take a break already, this is so humiliating.
(1/3)*8=8/24
(3/8)*3=9/24
(1/4)*6=6/24
Note that I just multiplied the fractions by the amount it takes to get the denominator to equal 24.
(8+9+6)/24=23/24
So it's d
Steam: CavilatRest
Give it some time to digest. Think about what we are saying and intermittently throughout the day go through it in your head. It will click and you will /facepalm yourself.
Remember it's all about parts of a whole. "PARTS OF A WHOLE".
I worked in a Math Lab for years; you're doing about as well as anyone not "dialed in. . ." to math does. It isn't even close to being "humiliating".
I would suggest checking out Khanacademy.org. He most definitely has a video on percentages (and other algebra subjects). I would say the most important thing you should take from all of this is how to convert a word problem into an equation, and that comes with recognizing what words "mean". "Is" is "=" and "of" is "*" in this case (and generally all cases). The related ratios approach is also useful, but that only works if you both understand and agree that it works. You may not be there yet.
Anyways I have been taking practice tests and I can't get 25 or 30.
http://webs.anokaramsey.edu/bordwell/Accuplacer%20Study%20Material/elementary_algebra_test.pdf
I will use multilevel spoilering here, with a warning before the final (solution) spoiler.
25:
Break the problem down in to parts. You want to know how far the bike goes in a given period of time, and you know how many revolutions it goes in a (different) given period of time. So, calculate how far it goes in one revolution, then calculate how many revolutions it goes in one minute, then multiply the two. Make sure to convert the answer to meters!
FINAL SPOILER
30:
First, the algebraic way:
You want to use some facts about geometry to come up with two equations, then solve for x and y. At that point, you can plug your values for x and y in to the equations given by the problem and see which one is not true.
FINAL SPOILER
Second, the non-algebraic but probably unhelpful way:
Notice that if x = 3x + 10 is true (equation D), then x and 3x + 10 are either both acute, both right, or both obtuse.
FINAL SPOILER
You can go do the traditional long route (more time consuming), or be a little clever (and save time). Easiest way would be breaking down the percentage.
3000 * (10/100 + 1/100) = 3000 * (10/100) + 3000 * (1/100) = 330
In other words 10% of 3000 is 300. 11% of 3000 is 300 plus a tenth of 300 (30).
For example, what is 17% of 3000?
3000 * (10/100 + 7/100) = 3000 (10/100 + 7 * 1/100) = 300 + 7 * 30 = 300 + 210 = 510
At least for me, breaking it down like that makes it a lot easier to do basic mental math. Definitely helped me during the years I was in college when I was studying Chemical Engineering
The measure of an exterior angle of a triangle is equal to the sum of the two remote interior angles; that is, the two interior angles which don't touch the exterior angle. This means that 3x+10=X+90 in that diagram. So it can't be true that x=3x+10.
Just be careful, this ONLY applies to triangles. If they throw an exterior angle of a quadrilateral at you, it won't work.
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