 Avoiding the carry

One of the difficult things in mental calculation is to keep track of a carry when you are juggling numbers.

In a lot of cases we can avoid the carry.
An example will make this clear, I hope.

Let’s say we need to calculate:
79
89
__X

Doing this calculation the traditional way leads to a lot of carrying.

However:
79 is pronounced ‘seventy nine’, meaning 70 + 9.
Instead of this, try to see 79 as ‘80 minus one’, which is the same number of course.

89 then becomes ‘90-1’.
Let’s change the calculation to reflect this. We have ‘80 - 1’ times ‘90 - 1’.
I will add extra spacing, but try to see the 8 as 80 and the 9 as 90:

8 - 1
9 - 1
_____X

Now, if we do left to right cross multiplication we get:
1: 80 X 90 = 7200
2: -80 - 90= - 170 (or -1 X 80 -1 X 90)
Subtract 170 from 7200 to get: 7030
3: -1 X - 1 = 1
Add to 7030 = 7031.
Done.

(Technically, in subtracting 170 from 7200 there is a small carry, but most people will hardly notice this and immediately see that 200 - 170= 30.)

I hope you see that this makes the calculation a lot easier.

For practice, start by trying to see ‘38’ as ‘40-2’.
And ‘67’ as ‘70-3’.
Then mentally multiply them.

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This technique is especially handy when we multiply number close to a round number.
Example:

38
42
__X

Try to do the cross multiplication and notice the amount of carrying.

Now try to see it as:

4 -2
4 2
____X

The second step of the cross multiplication cancel each other out (-2X4 +2X4).
We are left with 1600 - 4, which is easy to do mentally.

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This is terrific! What a difference it makes with 38 x 42. I like the cross multiplication method, my only problem with it is remembering the original numbers. I am trying to do all calculations mentally without trying to write anything down.

Or, just work from left to right: 7200 - 170 = 7200 - 100 - 70

It’s a wrong
22
×38
=836

3-8
3 8
=-24+11
=3500-4=3496

How do you get to 3500? Your setup is right:

1. 3x3=9 or 30x30=900 if you prefer
2. cross multiplication cancels out (-24+24)
3. -8x8=-64

Gives you 900-64=836

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Thank you