Math and Me

MrAl said:

Hi again,

After reading some more posts i think what might also help is looking into approximation techniques such as using differentials. For example, calculating the square root of a number in your head using differentials.

The more general problem however should be approached with the fact that problems can be different so different arrangements will help with different problems.

I am sure you have heard some of these already but i'll mention a few here...

Approximating a 15 percent tip. Well, 15 percent is 10 percent plus 5 percent, or even more simply put it is 10 percent plus half of that ten percent. So here we observe that we must calculate 15 percent and that 10 is very easy to calculate, and then taking half of that is easy too, so if we do it this way we just have to add the two calculations. 10 percent of 21 dollars is 2.10, and half of that is 1.05, and the sum is 2.10+1.05 which equals 3.15 . But another point is that approximation works in many cases because it is just good enough, and so here we would say that 10 percent of 21 dollars is 2.00, and half of that is 1.00, and so the sum is 2.00+1.00=3 dollars and that's good enough.

Approximating the conversion from Celsius to Farenheit uses a similar idea but slightly different.
We know that we have to multiply by 9/5 and then add 32. But 9/5 is just 10 percent less than 2. So we double the number, then subtract 10 percent of that number, then add 32 or just 30 for an approximation.
So 100, doubled, is 200, then subtracting 20 we get 180, then adding 32 we get 212, or just adding 30 we get 210 which is close enough for most purposes.

These kinds of ideas and techniques come up all the time. After a while you see right through the seemingly difficult to handle problem. The solution is just a matter of breaking the problem down into smaller pieces that are easy to calculate, then combining in the required manner.

The approximation of a square root using differentials is fairly easy too, i'll elaborate at another time if you have never done this before. After that we'll do partial differential equations in our heads (just kidding there)

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Ratchit said:

9/5 is 20% less than 2, not 10%.

Ratch

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Ian Rogers said:

Yep! Simple .... Using the discount and 100 are the two constants I need... I have no idea why it didn't come to me before!!

Cheers Spec..

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Ian Rogers said:

Ohh!! Fight..... 9/5 = 1.8 also 2 * 0.9 = 1.8 .. 2 / 10 = 0.2.. 2 - 0.2 = 1.8.. Sorry Ratch I'm with MrAl..

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spec said:

No sweat Ian.

I got caught badly by the down and up thing when I was discussing costs with an accountant at work. I was just on the point of telling him he couldn't do basic maths when I realized.

Where this really bites is in stocks and shares: Your shares go down by 10% but they need to go up 10.1% to make up that loss. I often wondered why shares went down easier than up.

spec

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Ratchit said:

When you use two different bases of comparison for percentage calculations, then the percentages differ. Think of it this way, a value goes from 100 units to 90 units for a value decrease of 10 units. An increase of 10 value units will bring it back to 100 units where it was before.

Ratch

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Ratchit said:

When you use two different bases of comparison for percentage calculations, then the percentages differ. Think of it this way, a value goes from 100 units to 90 units for a value decrease of 10 units. An increase of 10 value units will bring it back to 100 units where it was before.

Ratch

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Ratchit said:

9/5 is 20% less than 2, not 10%.

Ratch

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Ian Rogers said:

Ohh!! Fight..... 9/5 = 1.8 also 2 * 0.9 = 1.8 .. 2 / 10 = 0.2.. 2 - 0.2 = 1.8.. Sorry Ratch I'm with MrAl..

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Ratchit said:

I don't understand what being "with" MrAL means. Please explain.

Ratch

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strantor said:

Yes I have to agree after re-reading what I wrote. I worded that very badly from start to finish. I sincerely apologize.

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MrAl said:

Hi,

Ratch i just think either you did not wake up all the way yet today or didnt go to bed last night
We're discussing basic percentages, if we cant get that right, one of us did not have our coffee yet

Percentage can be expressed either as a whole number like 100 or as a fraction like 1.00, and this last one is just a fractional percentage. The fractional percentage is easier to work with because we can just multiply.

Example 1:
What is 1 percent of 100?
100*0.01=1
Here i used the fractional percentage of 0.01 for 1 percent.

Example 2:
What is 3 percent of 50?
50*0.03=1.5

Example 3:
What is 10 percent of 100?
100*0.10=10

Example 4:
What is 10 percent of 200?
200*0.10=20

A statement like: "180 is 10 percent less than 200" means we subtract 10 percent of 200 from 200: So first what is 10 percent of 200?
200*0.10=20 as above, and 200-20=180

In fractional form, 9/5=1.8, and 2/1=2.0, and 10 percent of 2.0 is 0.20, and the statement: "1.80 is 10 percent less than 2.00" means:
Take 10 percent of 2.00 which equals 20, then subtract that from 2.00 which then equals 1.80, which in fractional form is 9/5. So the statement: "9/5 is 10 percent less than 2" must be correct.

Sometimes the statement of being "with" someone simply means that you agree with them on the point being discussed. To the contrary, being "not with" someone means you dont agree with them in the context of a dispute among several people or groups.

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Mikebits said:

I have to admit, Ratch had me confused, but your explanation was very good.

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MrAl said:

Hi,

Ratch i just think either you did not wake up all the way yet today or didnt go to bed last night
We're discussing basic percentages, if we cant get that right, one of us did not have our coffee yet

Percentage can be expressed either as a whole number like 100 or as a fraction like 1.00, and this last one is just a fractional percentage. The fractional percentage is easier to work with because we can just multiply.

Example 1:
What is 1 percent of 100?
100*0.01=1
Here i used the fractional percentage of 0.01 for 1 percent.

Example 2:
What is 3 percent of 50?
50*0.03=1.5

Example 3:
What is 10 percent of 100?
100*0.10=10

Example 4:
What is 10 percent of 200?
200*0.10=20

A statement like: "180 is 10 percent less than 200" means we subtract 10 percent of 200 from 200: So first what is 10 percent of 200?
200*0.10=20 as above, and 200-20=180

In fractional form, 9/5=1.8, and 2/1=2.0, and 10 percent of 2.0 is 0.20, and the statement: "1.80 is 10 percent less than 2.00" means:
Take 10 percent of 2.00 which equals 20, then subtract that from 2.00 which then equals 1.80, which in fractional form is 9/5. So the statement: "9/5 is 10 percent less than 2" must be correct.
To compare, 4/5 is 20 percent less than 1.
The real question though is why did i think 9/5 was 20 percent less than 2 also before i calculated the true percentage. I think it is because it looks almost like 4/5 at first to us and we get locked on that for some reason. Doing the calculation on a calculator makes it more apparent that it is 10 percent.
Of course we also know that 2 is approximately 11.1 percent GREATER than 1.8 too (the other discussion about percentage) because 1.8*0.11 is approximately 0.20 .

Sometimes the statement of being "with" someone simply means that you agree with them on the point being discussed. To the contrary, being "not with" someone means you dont agree with them in the context of a dispute among several people or groups.

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Ian Rogers said:

I don't get your meaning..... The statement 9/5 is 10% less the 2 looks right to me.... 9/5 is 1.8 1.8 is 10% less than 2....

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Ratchit said:

Yes, as explained in post #36, I used the wrong base to calculate the percentage. Sorry for the confusion.

Ratch

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Colin said:

I buy something for $1.00 and get 10% discount. Then 10% tax is added. The answer is not $1.00 !!!! A trap for the uneducated.

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