Multiplying large numbers

I saw this handy program on TV last night whilst doing some posts on 606v2 last night.

It was one of those seemingly annoying infomercials with loads of excited voices carrying on about this thing called brainetics.

Basically, it was about these young kids who have been taught this method of multiplying and dividing large numbers...and coming up with the answers very quickly without the use of a calculator, which I admit I'm always grabbing for in my line of work.

It suddenly struck me how handy these techniques would have been in my job/s if I had known them years ago.

If you're an engineer, surveyor, architect, accountant or have to deal with big numbers on a daily basis; then the following is good to know:


For multiplying numbers between 90 and 100

....95 (5)
X..96 (4)

number in brackets is number less than 100

first two digits of answer is 100-(5+4)
last two digits of answer is 5 x 4

so 95 x 96 = 9120

very simple isn't it? It's much quicker than breaking it down into separate equations...then adding them together.

....92 (8)
X..97 (3)

= 8924

For multiplying numbers between 100 and 110,

....107
X..105

first number is always 1
add last 2 numbers (5+7) for the next 2
multiply last 2 numbers for the last 2

= 11,235

....109
X..104
= 11,336

For square numbers,

....85
X..85

square 1st number (8x8=64)
square 2nd number (5x5=25)
now double the last number in 85 (2x5)
and multiply by the 1st number in 85 (2x5x8=80)

so, write down 64 and 25, and 80 underneath 2nd and 3rd digits, then add them together

...6425
....80
= 7225

....93
X..93

...8109
....54
= 8649

I saw them doing much larger ones (e.g.328x47) and tricky divisions (78/39) in a matter of seconds but they didn't show the method.

Is this something that has been known for a while or is it a simplification of older methods? All I know is that in my time at school, the 12x tables was the limit. The kids of today will have a huge boost in confidence dealing with numbers - great for quick calculations of things.

What do people think? Does anyone know the other clever tricks like how to multiply bigger numbers or divide them quickly?

A simpler way of squaring two numbers that end in 5

multiply the 1st number by 1 more than that number, then add the 25 at the end.

....85
x...85

8x9=72, (are the first two digits)
then add 25 at the end
=7,225

....65
x...65
=4,225

....95
x...95
=9,025

Wow interesting stuff, keep this open I want to have a read later! Would be handy, seeing as I'm a Quantity Surveyor!

Must admit I've never seen any of these mental tricks that are quite so detailed and complicated (but still very nice!)

I do use lots of simpler tricks myself though for doing mental arithmetic

Just little things like if I'm asked 29x78 I can much easier to 30x78 and then subtract 78 from the answer

The other thing I do a lot if forced to do some arithmetic without benefit of a calculator is to try to be aware of what the answer should *approximately* be .. so if I was asked to calculate 85x85 (as in the original post), I'd be aware that 80x80 was 6400 and that 90x90 was 8100 so the answer should be somewhere in between. If I then came to an answer like 11,400 I'd *know* from my guts that I'd done something wrong (even if I'd used a calculator - could still have input it wrongly)

Far too many people these days rely too much on what electronic devices tell them and accept it without question, not realizing that they may have input the query wrongly.

like ordering 3 pints of beer and a whisky and coke in a bar and being charged £41.60. A young barperson with no intuitive grasp of numbers wouldn't question that if that's what the cash register said. They'd never consider that they may have entered it wrongly

Yes, that's what I used to do as well Davie.

Get to the nearest 10, 100, 1000 or whatever and then subtract the 10-x, 100-x, 1000-x, etc. They do a similar thing - with added tricks on their site.


For instance, there's a good one for multiplying numbers where the last 2 digits equal '10', like:

...46
x..44

multiply first number by n+1 = 4+1 = 5

so 4 x 5 = 20 (first two numbers)

then multiply the last two numbers, 6 x 4 = 24 (last two numbers)

= 2024

...83
x..87

= 7221