Avoiding the carry

Mental Calculation, Mathematics, and Puzzles
1

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.

3 Likes
2

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.

3

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4

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.

1 Like
5

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

6

It’s a wrong
22
×38
=836

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

7

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

1 Like
8

Thank you

9

tbh i just answering this randomly and its probs wrong because I know like no mental math methods but how @kinma describes this is that the question becomes
40| -2
x40|+2
so 4x4=16 x 100 1600 then you -2x38 or 76 so 1524 then you add 42x2 or 84 which becomes 1604 then you add -2 x 2 or -4 which becomes 1600 but thats wrong because using the one method I know I can work out that it is 1596 because (30 x 42=1260 then add 8 x 42 and you get ( 40 x 8 = 320 + 16=336) 1596. this is something I find hard so im trying to get used to mental math but noone seems to be truely helpful. anyway I believe kinma explained it but I got confused lol. it seems to add more to the question

10

@_Shadow01

38 × 42

there is difference of 4 numbers between them.
Square the middle and subtract 4 (2²)

40² - 4 => 1600 - 4 => 1596.

2 Likes
11

thanks that helps. I actually kind of understand so yours helped more for me than kinmas. thank you