Improving ones maths ability?

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1

Does anyone have any tips on how to improve ones basic maths ability? Recently I have found that simple things such as addition, subtraction and multiplication are leaving me stumped.

For instance today when marking test papers I needed to use a calculator to calculate that 64 - 27 = 37 :s

Also splitting the bill at restaurants always leaves me confused about how much each person should pay.

Is there an App or any tips that you could recommend? I heard that the “brain training” game for the Nintendo DS is supposed to be quite good.

Thanks

2

Start off by learning the “times table”, 1x1=1 etc, up to 10x10.
Practice a few subtractions of the sort you had trouble with - a pattern emerges pretty fast.
But dividing by three can be pretty tough, so maybe think first about how many friends you’re going to have dinner with.

3

‘Brain Training DS’ is great, though a bit simple. If you have a DS, definitely get it.

However, If you don’t own one, there are brain training or even specific “math training” apps for iphone or Android. Buying a cheap off-contract Android smartphone will give you far more value than a DS, as you can also use it for mandarin study and as an electronic dictionary.

4

From a mental arithmetic point of view, it can be helpful to break things down to simpler tasks or rough estimates if you can.

For example, 64 - 27. 6 -2 = 4. Therefore 64 -20 = 44. leaves 7 , 7 from 44 is 37.

You go to a restaurant and the bill is 1752 dollars for 3, round it up to 1800 and divide by 3. Roughly 600 dollars. Want to be exact, look at the difference, which is 48 between 3 , 16 each. or 584 dollars each.

Go out and get a bill for 5, thats 20%, calculate 10% which is easy and double it.

KISS. keep it simple stupid, no need to do the kind of math you learned at school in your head. Break it down to simple tasks that make sense and then refine the answer if you need to.

5

You could just ask someone Taiwanese to work it out for you.
They expect all bignoses to be retarded at maths.
I always laugh when they tell me how great Taiwanese are at maths.
I’ve got a Masters degree in it.

6

Also, learn the division shortcuts. Dividing by 10, 2, or even 5, is pretty easy, but learn the others from 1-10 (seven is the only one that doesn’t follow a simple rule). i.e. To determine if a number is divisible by 3, you add up all of the digits. If necessary, you add those digits again. You do this until you get the smallest possible number. If that is divisible by three, then your original number is divisible by 3, e.g. Is 14,826 divisible by three? Yes. 1 + 4 + 8 + 2 + 6 = 21. 2 + 1 = 3. So, let’s say you get a bill for 755NTD and there are three of you. Is that divisible by three? 7 + 5 + 5 = 17 = 1 + 7 = 8. Not divisible by 3. What to do? Round it up to the nearest number that is. How do you do that? Reverse engineer it. Well, the digits need to add up to 9. So, you make it 1 + 8, which is 18 which is 7 + 5 + 6. So, divide 756 by 3. So, that’s 7 divided by 3 (2, with a remainder of 1), 15 divided by three (because of the 1 remainder, so 5), then 6 divided by 3, so 2. So, each person pays 252, but one person pays 251 (because you rounded up by one at the start).

Learn factor trees, e.g. Want to divide a number by 72? 72 = 2 x36 = 2 x 2 x 18 = 2 x 2 x 2 x 9 = 2 x 2 x 2 x 3 x 3. So, if you want to divide a number by 72, divide it by 2, then 2 again, then 2 again, then 3, then 3 again. e.g. What’s 1872 divided by 72? It’s 936 x 2 = 468 x 2 x 2 = 234 x 2 x 2 x 2 = 78 x 2 x 2 x 2 x 3 = 26 x 2 x 2 x 2 x 3 x 3. 1872/72 = 26. It sounds ridiculously simple, but I do this kind of thing almost on a daily basis.

As has been mentioned already, learn how to take an estimate and then become more accurate from there. What’s 19 x 18? 19 = 20 - 1. So, it’s (20 x 18) - (1 x 18). That’s 360 - 18 = 342. That’s a lot easier than doing 19 x 18 the long way.

Another thing that is really helpful is learning squares. Our year eight mathematics teacher made us memorise these. I can still tell you that 18 x 18 is 324 without having to think about it. An even more useful trick is learning the formula for calculating the squares of numbers ending in a 5. What’s 65 squared? It’s (60 x 70) + 25 = 4225. See what I did there? I took the nearest 10 below and multiplied it by the nearest 10 above, and then added 25.

Learn some common fractions as percentages. This is immensely useful on a daily basis. Obviously, one half is 50%. What’s 4/9 as a percentage? I just know that 1/9 = ~11%, so it’s pretty close to 44%. What’s 9/14 as a percentage? I just know that 1/14 is ~7%, so it’s pretty close to 63%. Also, get a “feel” for percentages or decimals. I have no idea what 36% of 840 is (I just calculated it), but if I am presented with 3,024, 302.4 and 30.24, I can tell you it’s the second one because it should be roughly a third, and the first (3,024) is obviously too large and the third (30.24) is obviously too small. Likewise, because I know it should be about a third, I know the first number should be a 3. So, if I see 402.4, I know that’s wrong and someone’s having a laugh and trying to rip me off.

There are tons of things like this. I think being good at everyday mathematics, or the kind of mathematics you do up until the end of primary/elementary school often involves knowing all sorts of short cuts and tricks, as well as just memorising fairly commonly occurring things (this is why knowing multiplication tables is a must, as is knowing what every digit added and subtracted from every other digit is). There’s a reason why that stuff used to be absolutely core to education, just like why people used to learn how to spell and this was really laboured at length in primary/elementary school. In a sense, these little things are like the phonics rules for spelling, only English has lots of exceptions with spelling rules. Mathematics doesn’t have exceptions, so if you learn the basic rules, you’re golden in probably 90% of the cases where you’ll need to use mathematics on a daily basis (obviously, if you’re doing something like building a shed, you might have to bust out some trigonometry).

7

When did dividing by 72 become basic maths? :smiley:

8

Another alternative would be to buy one of those pocket calculators.
From what you say, you dont need a really fancy one, just a basic one that costs a few hundred NT$.
Just in case there are no Taiwanese handy when it comes to paying the bill (like maybe they all went to the bathroom).

9

When you know that 72 is not a difficult number because of all of its factors. Dividing by 73 would be a real bitch, and even dividing by 77 would be a major pain (7 x 11, both annoying numbers to divide by), but 72, not at all. It’s actually really easy because the factors are all divisible by 2 or 3. It’s like if you see 48. There’s no reason to be intimidated at all because it’s just like dividing by 2 x 2 x 2 x 2 x 3. 108? No problem. 108 = 2 x 54 = 2 x 2 x 27 = 2 x 2 x 3 x 9 = 2 x 2 x 2 x 3 x 3 x 3. 180? Piece of cake as it’s 10 x 18 = 5 x 2 x 18 = 5 x 2 x 2 x 9 = 5 x 2 x 2 x 3 x 3.

10

It is important for brain health and longevity -meaning keeping a sharp mind in your later years- to exercise all parts of the brain. Those of us who basically use our language side for a living tend to overlook this. I remember literally feeling the burn when I was doing my MBA, especially in Accounting -3 times- and Economics -twice- courses, because you are activating areas that normally are not used that extensively… or not at all.

So the OPs inquiry can even be answered from a health point of view. I have been wanting to take on some additional number related courses -more finance maybe, more accounting just for the masoquist in me, probably better stick to a buxiban’s elementary or high school level Math courses- because of the same reason: finding yourself slowed down doing a simple operation and knowing it is important to be able to function in this area independently of technology.

11

I also suggest remembering up to 12. 11 is easy. A trick my grandfather taught me at an early age. Add the two numerators (top number as in 32 X 11. Add the 3+2 and put it between the two top numbers of 32. Thus answer is easy at 352. That is 3+2 and between the other 2 numbers in the top number.(the numerator) If the total is higher like 89X11, just transfer the extra 10s to the left. . Thus 89X11 results in a quick mental calculation of 8+9 = 17 Carry the 1 over to the left and the 8 it becomes 9 and the single digit of 7 goes between so 979. I also like to do math problems in my head while on the MRT. It intrigues me and also a good way to fall asleep.On a side note, I have to agree that all my students have better math ability than I do. I opened a private GMAT class that extensively tests math. I got all "A"s all the way through advanced calculus but that was years ago and I struggled all day to figure out the book’s problems. I was so proud! I gave the math section to my students and they finished - all 100% correct - in about 20 minutes. Sigh.
However, all Taiwanese KNOW that ALL African American’s are all great basketball players.
Thus, I admit that the math ability may be skewed to those students that have ambition.

12

When you know that 72 is not a difficult number because of all of its factors. Dividing by 73 would be a real bitch, and even dividing by 77 would be a major pain (7 x 11, both annoying numbers to divide by), but 72, not at all. It’s actually really easy because the factors are all divisible by 2 or 3. It’s like if you see 48. There’s no reason to be intimidated at all because it’s just like dividing by 2 x 2 x 2 x 2 x 3. 108? No problem. 108 = 2 x 54 = 2 x 2 x 27 = 2 x 2 x 3 x 9 = 2 x 2 x 2 x 3 x 3 x 3. 180? Piece of cake as it’s 10 x 18 = 5 x 2 x 18 = 5 x 2 x 2 x 9 = 5 x 2 x 2 x 3 x 3.[/quote]

11 is simple, too. Alternatively add and subtract the digits of the number. If the sum is a multiple of 11 then the original number is divisible by 11. 2607 => 7-0+6-2=11, so it’s divisble by 11 (11x237), but 2730 => 0-3+7-2 = 2, so it’s not divisible by 11. (2730 = 2x3x5x7x13).

13

I also suggest flash cards up to and including 12X12. I recall this was what my mother did for multiplication. Gpops helped with the 11s but the rest was flashcards. Long hand division and square roots seem to be a lost talent due to calculators.
EDIT: Hell, even store clerks have to use a calculator to give you change. WTF

14

Didn’t know 2Enigma’s method, but did know a similar one to Neon’s method. It’s still a little cumbersome though.

15

I had to pay my water fee one month when I lived in Bangkok.
At the time water was 10 baht per unit (cubic meter).
I’d used 3 units.
So the concierge used her calculator and figured out that 3*10=30.
What I dont get is how she knew she had got it right.
But it goes to show that even dumb people can use calculators and get the same result that Einstein would have acheived.

16

That’s fantastic.

17

When you know that 72 is not a difficult number because of all of its factors. Dividing by 73 would be a real bitch, and even dividing by 77 would be a major pain (7 x 11, both annoying numbers to divide by), but 72, not at all. It’s actually really easy because the factors are all divisible by 2 or 3. It’s like if you see 48. There’s no reason to be intimidated at all because it’s just like dividing by 2 x 2 x 2 x 2 x 3. 108? No problem. 108 = 2 x 54 = 2 x 2 x 27 = 2 x 2 x 3 x 9 = 2 x 2 x 2 x 3 x 3 x 3. 180? Piece of cake as it’s 10 x 18 = 5 x 2 x 18 = 5 x 2 x 2 x 9 = 5 x 2 x 2 x 3 x 3.[/quote]

11 is simple, too. Alternatively add and subtract the digits of the number. If the sum is a multiple of 11 then the original number is divisible by 11. 2607 => 7-0+6-2=11, so it’s divisble by 11 (11x237), but 2730 => 0-3+7-2 = 2, so it’s not divisible by 11. (2730 = 2x3x5x7x13).[/quote]

Interesting but I’m not sure why you wanted to know it was divided by 11 first? Are you working a process of elimination using the easiest methods first to identify the factors?
And if it is not divisible by 11, being an odd number which factors must it be divisible by (assuming it is not a prime number). Is it then more likely to be divisible by 13?

I’m not very good with doing exact maths in my head, but I use mental estimates and percentage/factor calculations all the time in my job. This works fine for me as I am dealing with forecasts and fluctuating currencies so using exact figures would also be an estimate.

If anybody has any tips for currency exchange calculations I’m all ears.

I like to pick out patterns in numbers, that’s a useful skill, simply scanning numbers and see what pops out.