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Shortcut for multiply numbers together up to 19

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Is this quicker than multiplying normally?

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Shortcut for multiply numbers together up to 19 [#permalink] New post 29 Jul 2012, 22:01
Example:

19*18=

1. Take the first number and add it with the units digit of the second number.
19+8=27

2. Multiply the result by 10
27*10=270

3. Multiply the units digit of the first number with that of the second number
9*8=72

4. Add the result of step 2 and 3 together
270+72 = 342
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Re: Shortcut for multiply numbers together up to 19 [#permalink] New post 01 Aug 2012, 05:29
Expert's post
arnivorous wrote:
Example:

19*18=

1. Take the first number and add it with the units digit of the second number.
19+8=27

2. Multiply the result by 10
27*10=270

3. Multiply the units digit of the first number with that of the second number
9*8=72

4. Add the result of step 2 and 3 together
270+72 = 342


It would be much better to know the multiplication tables of numbers up to 19. Numbers up to 19 are used often and knowing their tables can speed up your calculations considerably
Then 18*19 is straight forward.
18*9 = 162. Write 2 and carry 16
18*1 = 18. Add 16 to get 34. You get 342.

Also, learning tables is not as hard as you might imagine.
e.g. 18*2 we know is 36. 18*3 is 18 more than 36

18*5 = 90 (12*5 = 60, 13*5 = 65, 14*5 = 70 and so on...). 18*4 is 18 less than 90. 18*6 is 18 more than 90

18*10 = 180. 18*9 is 18 less than 180.

All you really need to learn up is 18*7 and 18*8.
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Re: Shortcut for multiply numbers together up to 19 [#permalink] New post 01 Aug 2012, 06:25
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arnivorous wrote:
Example:

19*18=

1. Take the first number and add it with the units digit of the second number.
19+8=27

2. Multiply the result by 10
27*10=270

3. Multiply the units digit of the first number with that of the second number
9*8=72

4. Add the result of step 2 and 3 together
270+72 = 342


This is a translation of the algebraic multiplication of two numbers of the form 1a * 1b = (10+a)(10+b) = 100+10a+10b+ab. The latest expression we can also written it as (10+a+b)10+ab=(1a+b)10+ab.

I don't think the algorithm can be a real time saver. And its usage is quite limited (numbers below 20).
Many times, depending on the numbers, we can find specific shortcuts.
For example, 19 * 18 I would do it as (20 - 1) * 18 = 360 - 18 = 342, as it is always easy to multiply by 10 and 2.
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Re: Shortcut for multiply numbers together up to 19   [#permalink] 01 Aug 2012, 06:25
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