How's your mental arithmetic?

gerry87

I'm trying to work on my mental arithmetic, just wondering if people around here would consider themselves to have good mental arithmetic? If you'd say you're good, have you always been quick or did you take time to learn it? Any tips?

I've been trying out some of those system things like tratchenberg and playing http://www.jimmyr.com/blog/speed_math.swf that game, anyone know any other games or things to practice?

Cheers!

namenotavailablE

I'd be considered pretty quick by my students- when there's a column of values on the board to add-up, I typically would have the answer calculated before any of them have inputted the individual values into their calculators.

I have a few tricks that sometimes are handy eg squaring numbers ending in 5 => multiply the number before the 5 by the number which is one greater than that. The result goes before the digits 25 and you've got your answer
Example: 45 x 45 => 4 x 5 = 20 => answer is 2025

Squaring numbers ending in 9 (a harder one for me) => square the number that is 1 greater than your desired number. Subtract from the result the sum of (your number + the number which is 1 greater) => that's your answer.
Example:39 x 39 => 40 x 40 =1600 => 1600-(40+39)=1521

To be honest, I'm probably 'old school'- we were drilled in primary and my father was also very quick at mental arithmetic so it probably just brushed off on me. I remember seeing a couple of good Youtube videos by an Indian instructor that are worth checking out eg multiplying numbers close to 100 and suchlike.

LeixlipRed

Maybe you should teach the students the reasons behind these tricks? And not let them use calculators

namenotavailablE

If they were all about 12 years younger I would consider it

Unfortunately they are all in their late teens/ early 20's and I have a 'syllabus of stuff' to get through.....

On occasion, I've shown the tricks to a group (usually in the earlier stage of a semester) when they ask "Did you prepare the answer in advance? How did you know that's the answer" !

LeixlipRed

Ah ok, I just assumed it was Junior Cert stuff or something.

namenotavailablE

Another one (courtesy of Youtube) handy for squaring numbers close to 100:

Example: 98^2

• 98 is 2 away from 100 => subtract 2 from 98 => 96.
• 2 ^ 2 is 04 => append 04 to 96 => answer is 9604

Or again: 96^2

• 96 is 4 away from 100 => subtract 4 from 96 => 92.
• 4 ^ 2 is 16 => append 16 to 92 => answer is 9216

Works every time!

Fremen

Squaring numbers is fairly easy in general. All you need is the formula

(x+y)^2 = x^2 + 2xy + y^2

Now, to square 67, say, let x=60 and y=7. Now, instead of one difficult multiplication, you have four easy multiplications and two easy additions. It's just a matter of keeping a running sum in your head while doing the multiplications.

hivizman

A combination of memory and pattern-spotting often works. For example, I sometimes use the "difference of two squares" formula x^2 - y^2 = (x+y)*(x-y) to do multiplications quickly. If I was asked to multiply 116 by 84, I'd notice that 116 is 100+16 and 84 is 100-16 and immediately calculate the answer to be 9,744 (100^2 = 10,000, minus 16^2 = 256). I remember the squares of numbers up to around 40, and use Fremen's formula for squares greater than 40.

When adding up columns of figures (I used to be an accountant in the pre-computer era, so had to do this a lot), I often group numbers together. So if I see a 4 and a 6, I mentally combine these and add 10 to my total - I do more complex groupings like combining a 5, a 7 and an 8 into 20. For more simple additions I often add from left to right rather than from right to left - after some practice, you can make the necessary adjustments for carrying numbers over in your head as you go.

Also, use of approximations can be helpful. So, if asked to multiply 49.5 by 25.65, I'd immediately multiply 50 by 25 and say that the answer is about 1,250 (it's actually 1,269.675) - a lot of people using calculators will either input the numbers incorrectly or get the decimal point in the wrong place. For many purposes, this approximation will be just as useful as working out a precise answer and then rounding it.

Davidius

I'm not quick with the mental arithmetic, even when using techniques and such. I just don't process information that fast.

LeixlipRed

I have a M.Sc in Maths and my mental arithmetic is fairly slow. It's no big deal in most real life scenarios. Slow and steady and what not :P

gerry87

Thats what i've been wondering whether arithmetic is engrained in people who are good at maths/have done higher level maths, also whether the people who are very quick have specifically practiced it, or is it just a natural thing.

I've got a trading interview and there's a mental maths test for part of it, I was wondering if i'd be at a huge dis-advantage against maths/physics grads (i'm finance). I guess it's just a matter of practice.

sponsoredwalk

We've all learned our 12 times tables and, not surprisingly most of us stopped there.

The odd time a teacher asked what is 15 x 15, maybe one crazy classmate had learned up to there by themselves and could answer, but that was an odd thing for a person to bother with.

This book, however, really does have easy and intuitive tricks for mental arithmetic that should become a staple of primary school education.

http://www.amazon.com/Secrets-Mental-Math-Mathemagicians-Calculation/dp/0307338401

I believe that using if children used this book at an early age it would help to do away with this fear of numbers that so many students seem to acquire. I stress the use of the word "students" as it is through mis-education that people seem to develop this aversion to numbers.

I'm studying from this book for a half an hour every few days, I spread it out so that I wont overload & I recommend you do the same. This book could become a fun activity with young children before bedtime as a way to make numbers a game.

It would also help avoid the extraneous labour of picking up a calculator or actually scribbling out those long winded polynomial multiplications that seem to pop up.

________________________________________________________

(32) x (11) = 352
(81) x (11) = 891

To multiply any two digit number by 11 take the two digits, add them & stick the result in the middle.
3 + 2 = 5 hence
352.

53 x 11= 583

If the addition goes over 10 add the one to the first digit, i.e.

86 x 11= 946

---

> 8+6=14 so (8+1)46 = 946
39 x 11= 429


(85)² = 7225

Squaring anything that ends in 5 instantly means it ends in 25,
when squaring a no. that ends in 5, take the first digit, 8, and
multiply it by the number that follows it, 9, and you get, 72 - 25
7225. :rolleyes:

some more,
(25)² = 625
(55)² = 3025


(32 x 38) = 1216

Why..?

...Get the book and find out.


btw: I'm not trying to pitch or sell the book for my gain or anything, I just think this stuff should of been taught to all of us when we were 11 & there's no better time to rectify past mistakes like the present.

hinault

LeixlipRed wrote: »

I have a M.Sc in Maths and my mental arithmetic is fairly slow. It's no big deal in most real life scenarios. Slow and steady and what not :P

I was very good at maths..........and I used to be pretty good at mental arithmetic but I'm getting old now and I do find that my speed is diminishing somewhat.

gerry87

sponsoredwalk wrote: »

We've all learned our 12 times tables and, not surprisingly most of us stopped there.

The odd time a teacher asked what is 15 x 15, maybe one crazy classmate had learned up to there by themselves and could answer, but that was an odd thing for a person to bother with.

This book, however, really does have easy and intuitive tricks for mental arithmetic that should become a staple of primary school education.

http://www.amazon.com/Secrets-Mental-Math-Mathemagicians-Calculation/dp/0307338401

I believe that using if children used this book at an early age it would help to do away with this fear of numbers that so many students seem to acquire. I stress the use of the word "students" as it is through mis-education that people seem to develop this aversion to numbers.

I'm studying from this book for a half an hour every few days, I spread it out so that I wont overload & I recommend you do the same. This book could become a fun activity with young children before bedtime as a way to make numbers a game.

It would also help avoid the extraneous labour of picking up a calculator or actually scribbling out those long winded polynomial multiplications that seem to pop up.

________________________________________________________

(32) x (11) = 352
(81) x (11) = 891

To multiply any two digit number by 11 take the two digits, add them & stick the result in the middle.
3 + 2 = 5 hence
352.

53 x 11= 583

If the addition goes over 10 add the one to the first digit, i.e.

86 x 11= 946

---

> 8+6=14 so (8+1)46 = 946
39 x 11= 429


(85)² = 7225

Squaring anything that ends in 5 instantly means it ends in 25,
when squaring a no. that ends in 5, take the first digit, 8, and
multiply it by the number that follows it, 9, and you get, 72 - 25
7225. :rolleyes:

some more,
(25)² = 625
(55)² = 3025


(32 x 38) = 1216

Why..?

...Get the book and find out.


btw: I'm not trying to pitch or sell the book for my gain or anything, I just think this stuff should of been taught to all of us when we were 11 & there's no better time to rectify past mistakes like the present.

I read that one, its good, especially for up to three digit multiplication. I've looked at a couple of the other systems, tratchenberg and vedic are two others, they're good for big mental sums like 341894 * 234, but they seem slower (for me anyway) and you don't really get an idea of the magnitude of the number until the sum is finished, unlike in that book.

here's the author of that book in his emm.... mathemagic show
http://www.ted.com/talks/arthur_benjamin_does_mathemagic.html

sponsoredwalk

gerry87 wrote: »

here's the author of that book in his emm.... mathemagic show
http://www.ted.com/talks/arthur_benjamin_does_mathemagic.html

:eek::eek::eek::eek:

Woah, that guy is crazy! Brilliant! That 15 minutes of mathemagic was amazing. I've seen that guy before doing other math related stuff. For some reason I had an image of Oliver Sacks or a lookalike who was very reclusive, but this guy reminds me of people I went to school with. Thanks for the link.

just-joe

Hmmm.. I used to have fairly good mental arithmetic, could multiply 2 digit numbers in my head, but lack of practice over the last few years (ironically while doing a maths degree) has sent it down the drain..

I think practice is the most important thing, as in the end it boils down to how much you can learn by rote, and remember quickly.. eg when it comes to squares at first its hard to work out 13 squared or whatever, but after a while you just know its 179 (:p). Ha yeah I imagine if you keep practicing you'll just get better and better.