Mental Multiplication

I am always amazed and feel lost when people perform these 3 by 3, 4 by 4 multiplication and so on…
Any help on the methodologies pls…!!!

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@kinma
I will be very grateful if you can help me out on this​:100::100:!
Thanks!

Will do. Give me some time to write something up. Life is busy atm.

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Cross multiplication

I have written about this extensively.
Personally, I always calculate from left to right.

However; for this item, let’s explain the cross multiplication from right to left.
Let’s do an example.

123
456 X

Start with the ones. These are the right most digits:
3 * 6 = 18. Write 8. Carry 1:

123
456 X

____(1)8

Now do the tens. These are the multiplications that end in one zero.
These are 20 * 6 and 3 * 50.
If you locate the numbers, you understand where the term cross multiplication comes from.
The zero in 20 and the zero in 50 are for demonstration purpose only. IRL you multiply without the zero’s:
2 * 6 + 3 * 5 = 12+15 = 27.

Add the carry from the previous step:
27 + 1 = 28. Write the 8, carry the 2:

123
456 X

___(2)88

Now the hundreds or the multiplications that end in two zero’s:
100 * 6 + 20 * 50 + 3 * 400. Again, the zero’s are for demonstration purposes and help you find which numbers to do.
We do 1 * 6 + 2 * 5 + 3 * 4 = 6 + 10 + 12 = 28.
Add the carry from the previous step:
28+2 = 30.

Write 0, carry 3:

123
456 X

__(3)088

After the hundreds come the thousands or 3 zero’s:
100 * 50 + 20 * 400. =>1 * 5+2 * 4 = 5+8=13.
Add carry: 13+3 = 16:

123
456 X
(1)6088

After 3 zero’s come 4 zeros. There is only one:
100 * 400 => 1 * 4 = 4.Add Carry. 4+1 = 5:

123
456 X

56,088. Done.

Do these kinds of calculations for a while and the cross will be stamped into your brain!

Let’s generalize and do a 4x4:

abcd
efgh X

1: d * h
2: c * h + d * g
3: b * h + c * g + d * f
4: a * h + b * g + c * f + d * e
5: a * g + b * f + c * e
6: a * f + b * e
7: a * e

I suggest you start each step with the carry from the previous step, so let’s write out the steps again with carrying:

abcd
efgh X

1: d * h. Write the ones, carry the rest.
2: carry + c * h + d * g Write the ones, carry the rest.
3: carry + b * h + c * g + d * f. Write the ones, carry the rest.
4: carry + a * h + b * g + c * f + d * e. Write the ones, carry the rest.
5: carry + a * g + b * f + c * e. Write the ones, carry the rest.
6: carry + a * f + b * e. Write the ones, carry the rest.
7: carry + a * e. Write all digits.

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awesome stuff kinma, totally dig it. i got the book Math Magic, but didnt get to multiplication yet. Probably similar stuff. But you just made something clear to me which seemed choatic to me before. But using the cross and the letter example it sparked something! so thanks for that!

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