Best Answer:
The more digits there are, the more work it is.

Hardly anyone can multiply 4-digit numbers in their head, and even 3-digits can pose a challenge.

There's a reason calculators are so popular!

The so-called "lightning calculators" who put on shows and

multiply huge numbers (9, 10, or more digits) have

lots of specialized tricks which aren't worth learning

for most people.

If you can do 2-digit numbers, you'll be miles ahead

of most people any way.

What I would suggest is that you reverse the process

most of us are taught. Do the "big numbers" first.

I find it easier to add small numbers to large numbers

than the other way around.

Let me illustrate with 2-digit numbers for brevity:

Let's do 43 x 64.

Here's the standard way to do it:

..43

..64

-----

4 x 3 = 12, write down 2, carry the 1

......2

4 x 4 = 16, add the 1 you carried, 17

Stick the 17 in front of the 2

..172

6 x 3 = 18, write down 8, carry the 1

...8_

6 x 4 = 24, add the 1, 25

stick than in front of the 8_

.258_

-------

add

...172

..258_

--------

bring down the 2

......2

7+8 = 15, write down 5, carry the 1

....52

1+5 = 6, add the carried 1, gives 7

...752

bring down the other 2

2752

What a lot of work --- and very difficult to do in your head .

In large part, I think, that is because you're adding big numbers

to small numbers and working right to left, so you have

lots of carries and things to worry about and keep track of.

Instead, start with the big parts and add the smaller parts:

43 x 64 = (40 + 3) x (60 + 4)

40 x 60 = 2400

+ 3 x 60 = 180.... 2580

+ 40 x 4 = 160 ....2740

+ 3 x 4 = 12 .... 2752

With practice you do these quickly, so you don't have

to stop and think how many 0's to do.

3 x 6 = 18, 3 x 60 = 180 for example.

At the beginning, you have zeroes on the right end

so there's less to remember and less carrying.

That makes it easier, too.

I recommend this method for pencil-and-paper work

too - it's a lot less work once you understand it.

With 3 digits or more in the numbers, it helps

to have a few more tricks up your sleeve, but

give this a try and see how it goes.

Do a hundred or so of them written down and

I bet when you're done you'll be doing half of

the work in your head already. Do another hundred

and presto! the answers will just pop out!

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