Fast ways to do Arithmetic mentally

[RedAlert]

Do you guys know of any particular strategies to use when doing when arithmetic in your head, so that you can solve your problem quickly and correctly?

[Dapthar]

Do you guys know of any particular strategies to use when doing when arithmetic in your head, so that you can solve your problem quickly and correctly?

Always try to work with round numbers, and split up decimals into more manageable parts. For example, say you wanted to purchase 5 items that are $1.17 each. Now, you could try to work out $1.17[math]\cdot[/math]5 in your head, but let's try another way.

 

Now, we know that 5[math]\cdot[/math]$1.00 = $5.00, so keep that in mind.

 

Also, $.17 is not a very round number, so let's use $.20, which is $.03 off. Now, we know that 5[math]\cdot[/math]$.20 = $1.00. So our "guess" is $6.00.

 

However, remember we were $.03 off on each item, so we need to correct for that. So, how much are we off? Exactly 5[math]\cdot[/math]$.03 = $.15. Thus, we will pay $6.00 - $.15 = $5.85.

[Callipygous]

i just do it one place at a time

 

5*1.00 = $5.00

5 * .10= $.50

thats $5.50

5*.07= .35

thats 5.85

 

thats the order i always do it in too, not sure why. seems like it would be easier if i started with the smaller stuff.

[YT2095]

divisibility with 9`s

 

if I give you the number: 18855 if you add each number as an idividual like: 1+8+8+5+5= 27

now add the 2 and 7 you get 9.

 

so 18855 is divisible by 9 (infact it goes in 2095 times).

 

this works with ANY number that 9 will go into perfectly

 

also you know that 3 will too.

[darth tater]

i just do it one place at a time

 

5*1.00 = $5.00

5 * .10= $.50

thats $5.50

5*.07= .35

thats 5.85

 

thats the order i always do it in too' date=' not sure why. seems like it would be easier if i started with the smaller stuff.[/quote']

 

This is exactly the way I have always done it. Or as Dapthar does it, it is pretty much the same thing.

 

All it takes is memory enough to recall the "saved" equasions in your head for later addition.

[Johnny5]

Do you guys know of any particular strategies to use when doing when arithmetic in your head, so that you can solve your problem quickly and correctly?

 

Suppose you are asked to add a small amount of numbers:

 

376

229

145

 

As a first approximation, you have:

 

300

200

100+

=600

 

if you screw up the rest of the process, the correct answer is still reasonably close to 600. So you could now say, "the correct answer is approximately 600." In order to improve the approximation, you have to add the numbers in the tens column...

 

70

20

40+

=130

 

And then add this to your first approximation, which you had to hold in memory. Remembering that it was 600, you now have to add 130 to this, to obtain 730

 

730 is now your second approximation to the exact answer, and you must remember this number if you want to find a better approximation. To obtain a better approximation, you now have to add the numbers in the ones column.

 

6

9

5+

=20

 

730+20=750

and you are done, this is the exact answer.

 

It's just a different way to approach addition of numbers, then what is usually taught.

[dan19_83]

divisibility with 9`s

 

if I give you the number: 18855 if you add each number as an idividual like: 1+8+8+5+5= 27

now add the 2 and 7 you get 9.

 

so 18855 is divisible by 9 (infact it goes in 2095 times).

 

this works with ANY number that 9 will go into perfectly

 

also you know that 3 will too.

 

 

 

That's not a general maths rule or anything, is it?

Does it only work for 9 and 3.

[dan19_83]

i just do it one place at a time

 

5*1.00 = $5.00

5 * .10= $.50

thats $5.50

5*.07= .35

thats 5.85

 

thats the order i always do it in too' date=' not sure why. seems like it would be easier if i started with the smaller stuff.[/quote']

 

 

That's my way of doing it too. it's fast and easy and you know that if you get the answer worng, then at least you'll be close to the answer.

[RedAlert]

Hmm.....Thanks a lot for the responses. They really helped.

 

What about dividing and subtracting?

[YT2095]

That's not a general maths rule or anything' date=' is it?

Does it only work for 9 and 3.[/quote']

 

sure it is, it`s great for verifying x9 multiplications, sort of a quick way to check.

 

that particular one works for 9`s and obviously for 3`s as a result.

 

don`t take my word for it, test it out for yourself

 

 

I used to know one for 7`s as well, but I`ve forgotten it

[RICHARDBATTY]

If its x5 do x10 and halve it. ie £1.17 x10 add 0 £11.70 halve it £5.85

[Callipygous]

sure it is' date=' it`s great for verifying x9 multiplications, sort of a quick way to check.

 

that particular one works for 9`s and obviously for 3`s as a result.

 

don`t take my word for it, test it out for yourself

 

 

I used to know one for 7`s as well, but I`ve forgotten it [/quote']

 

 

if always heard that that is how people do like 3 digit multiplications in their head in like 2 seconds, but i dont see how. how does that help? what do you do with that?

[uncool]

That's not usually how they do 3 digit multiplication in their heads. I have done two-digit multiplication by using difference of square things, and it seems to work out well, usually. I expect that that could be extended to 3 digit multiplication.

Divisible by 7: Take the last digit, remove it from the number. Multiply the digit by 2, and subtract it from the rest of the number. Repeat until it's one digit long. This should leave you with a number divisible by 7 if the original is divisible by 7.

 

My own generalization:

For any number a not divisible by 2 or 5, to determine if a number b is divisible by it:

Take the lowest multiple c of a that ends in one.

Then replace the 2 in the example for 7 with (c-1)/10, and 7 with a.

For example:

To determine if a number is divisible by 17, take the last digit and remove it from the number. Multiply the digit by 5 (from 51 = 3 * 17) and subtract that product from the rest of the original number. Repeat until it is down to a small number. if the original is divisible by 17, then this last number, and all intermediate numbers will be divisible by 17.

 

Ask me for proof of this later if you want.

 

Example: 65569 = 17*3857

6556 9

6556 45

6511 = 17*383

651 1

651 5

646 = 17*38

64 6

64 30

34 = 17*2

Oh, and 99...9 (a 9's)^2 = 999... (a-1 9's)8000...(a-1 0's)1

-Uncool-

[coquina]

Regarding the "nines" - if you are trying to balance your check book and you are off, try dividing the amout you are off by 9. If it is an integer, you have probably transposed a number somewhere.

[Dave]

I was talking to my dad the other day, and he was saying how he'd watched a documentary on this a while back (don't know the name, sorry). One of the more interesting methods of doing this is actually to learn how to properly use an abacus to work out the multiplications, divisions and additions.

 

The documentary was all about a class of kids that trained their mind on using the abacus for a couple of hours a day - I think it was in one of the Eastern countries. After a couple of years of doing this, they were able to abandon the abacus completely and just picture it in their minds. These kids are able to multiply two 5 figure digits in their head and give you the answer within a couple of seconds.

 

Now, I'm not saying that you should do this - it's probably never going to be necessary for you to multiply large numbers in your head - but it does give an interesting insight into how powerful the human brain is if applied correctly.

[Rekkr]

I have heard that autistic savants do their math my similar means. They supposedly associate an individual symbol for every single number. When they think, the symbols just "blur" together into an answer.

[Ophiolite]

Practice.

[RedAlert]

I guess so in the end. My parents tell me the same thing. I was just wondering if there was a particular strategy I could practice.

[dan19_83]

You could do your parents taxes for them!!

 

Seriously though, i think the best thing is to get a maths book and start doing some of the difficult sums without using a calculator. If you do enough of them in your head you'll be a whizz after a while. Practices makes perfect is what i've been told!

[Ophiolite]

Redalert, I was not meaning to be trivial with my one word response. Several methods and 'tricks' have been suggested, but none of them work without the practice.

May I suggest carrying this out when you are waiting in a queue, or sitting on a bus. In other words anytime you have nothing else to do to occupy your mind. (It also might help to learn your times tables up to say thirty three rather than twelve.)

It is worth the effort. Unjustifiably, people often asume someone who is fast at mental arithmetic is also intelligent. I've fooled a lot of people that way.

[ski_power]

Or you could buy a book on Vedic Mathematics. It gives plenty of short cuts for any mathematical operations including but not limited to solving quadratic and simultaneous equations in the mind. The human brain indeed is very powerful. And once you get a hang of vedic maths which is really easy anyway, you'll do exponentials inside your skull.

[RICHARDBATTY]

http://www.vedicmaths.org

OMG Even me the perpetual amoeba can do it why is this not compulsory education.

[RedAlert]

Is this true or are you guys joking with me??

[RedAlert]

OMG!!!!

 

IT REALLY WORKS!

 

MATH WAS REALLY THIS EASY?!

 

Just wait till I show my parents this!

[RedAlert]

I searched the internet for a free source to learn it from.....and I couldn't find a single one.

 

I also found another system called the Trachtenberg system, but you have to pay to learn that too.

 

Isn't there anything in the world that is free!?

 

Any of you know this stuff? Would you be willing to tell me?