Mathematics

craner

Beast of Burden
Can anybody send me or help me with or point me to info on working out percentages and ratios?

I can't do ratios at all*; but I can do basic percentage sums, but I can't do trickier stuff, so I feel like I must be missing the point of my sums.

* I mean, I can read and apply them, obviously, but I can't calculate them.
 
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don_quixote

Trent End
ok the main issue with ratios and percentages is that they are multiplicative relationships rather than additive relationships.

do you use skype or something? pm me your username. i'm on half term at the moment so have a load of time (and am a maths teacher)
 

IdleRich

IdleRich
What do you wanna know Craner? Should be able to explain it easily enough if you are more specific in your question.
 

craner

Beast of Burden
Tomorrow, chaps, when I have some time I'll post/email some of the questions that flummoxed me -- it's got something to do with my latest attempt to find employment. I'm off to a "how to market yourself" workshop now, which ought to be funny, at least.
 

Mr. Tea

Shub-Niggurath, Please
Staff member
I'm imagining Craner in tottery heels, hanging around on a street corner...

I don't have any formal teacher training like d_q (ooh, that looks like a little face, doesn't it?), but I did do a fair amount of one-to-one tuition a few years ago, which sounds like it might be relevant here. So I'll toss my hat into the ring too: ollie dot harris at gmail dot com.

I remember a lot of my kids having difficulty with fractions and ratio, actually, so I got a lot of practice at teaching this subject.
 

craner

Beast of Burden
I'm imagining Craner in tottery heels, hanging around on a street corner...
I'm trying to get a job in a high street bank branch, so that's quite close to the mark, T-Boz.

You're all great by the way -- I'll get some example of the sums bugging me later this afternoon, hang fire...
 

baboon2004

Darned cockwombles.
Good luck with the job app.

Percentages are in essence ratios multiplied by 100 (never tried to explain it actually, so I'll be rubbush compared to the maths teachers here).

2/5 is equiv. to 2 divided by 5 times 100 = 40 per cent , but I guess you'll be looking at more complicated stuff than that.

And for quickly calculating rough percentages in your head, work out 1 per cent of the amount by moving the decomal point over twice, and then multiply by the number you need
eg 5 per cent of 792 = 5 x 7.92 = roughly 40
 
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craner

Beast of Burden
Huh??

Age Group ""Average number of daily commuters ""Rail""Car""Subway""Bus""Others

Under 35"""""425,600""""""""""""""""""""""""""""""""""""""""43%""9%"""27%"""12% """9%

35 and over""638,400""""""""""""""""""""""""""""""""""""""""42%""12%""25%"""14%""""7%



Question 1:

If the number of bus passengers who are under 35 decreased by 0.8% next year and 11% this age group travelled by bus, approximately how many commuters are under 35?

Question 2:

Within under 35 'others' group, if 65% walk and the remainder cycle, what is the approximate ratio of walkers to cyclists?
 
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baboon2004

Darned cockwombles.
Age Group ""Average number of daily commuters ""Rail""Car""Subway""Bus""Others

Under 35"""""425,600""""""""""""""""""""""""""""""""""""""""43%""9%"""27%"""12% """9%

35 and over""638,400""""""""""""""""""""""""""""""""""""""""42%""12%""25%"""14%""""7%

Question 1:
If the number of bus passengers who are under 35 decreased by 0.8% next year and 11% this age group travelled by bus, approximately how many commuters are under 35?

Question 2:
Within under 35 'others' group, if 65% walk and the remainder cycle, what is the approximate ratio of walkers to cyclists?
Q1: Firstly, for this year, 0.12 x 425,600 = 51,072 under-35s travelling by bus this year.
This number decreases by 0.8% next year (this is a bit amiguous actually - do they mean the relative percentage goes down by 0.8%, or the number of under 35 passengers? - I take it as the latter).
So number of bus passengers next year = 99.2 per cent of this year = 50,663 roughly.
This number represents 11 per cent of total under 35s next year, so total number of under 35s = 100/1 x 50,663 = 460,573.

hmm, this seems complicated - maybe I've made a mistake.

Q2: Er, 13:7?
 

craner

Beast of Burden
Aye -- I can follow what you're doing in Q1, I think. I don't know if it's right though -- it looks right. I think. As for Q2 -- still none the wiser.
 

vimothy

yurp
Craner, think of this: If you had a hundred people, and 65 of them were walkers, and the remainder cyclists, how would you express this as 1, a percentage, and 2, a ratio?

When you're doing ratios keep in mind the fact that the ratio just tells you that every however many people or things (add the two numbers in the ratio, e.g. 65+35=100) so many will be one and so many the other (e.g. for every hundred people 65 walk and 35 cycle). This means that the numbers themselves are irrelevant, it's just their relative proportions, which are given for each number by dividing it by the sum of both numbers. So 65:35 is the same as 130:70 is the same as 1300:700 is the same as 13:7 is the same as 0.4095:0.2205 because each and every time their relative proportions are the same and therefore 65/(65+35)=0.65=65% and 130/200=0.65=65% and 13/20=0.65=65% and 0.4095/0.63=0.65=65%. Per cent literally means "every one-hundred"--as in, "every 100 people" 65 walk--and so a percentage is already a ratio, just one that's so standard you use and understand it without ever thinking or worrying about it.

When you get stuck with anything in maths, try to make the problem as simple as possible and lay out what you already know for certain. Like in Q2, you know that 65% of your group are walkers so that every hundred people in the sample 65 walk. You can multiply those numbers up however you like--multiply both by any number (the same number!) and their proportions stay the same. 65% of 1000 and 65% of 100 is still 65% even though 0.65*1000=650 and 0.65*100=65. There are as many ways of expressing this ratio (65:35=13:7, etc) as there are real numbers but the ratio between the two numbers is always the same.
 
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vimothy

yurp
They're both naff questions. First one seems to be saying that you have one group, call it BP, which is 12% of under 35s. BP declines by 0.8%. Now BP makes up 11% of under 35s. So how many under 35 are there?
 

vimothy

yurp
Here's an excellent maths resource:

http://www.khanacademy.org/

Khan Academy is beyond awesome. Plenty of tutorials on ratios, as well as almost everything else you could possibly want. Kinda like if somebody did video tutorials for Stroud's two classic Maths for Engineers textbooks. Craner, you should be able to find everything you need here.

If you prefer it on paper, though, Stroud's textbook is the one :http://www.amazon.co.uk/Engineering...=sr_1_1?s=books&ie=UTF8&qid=1287931192&sr=1-1

Don't be put off by the word "engineering". It's covers the basic foundations needed for any vaguely technical degree. And you can usually get an old edition for next to nothing.
 
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