Mental multiplication - direct methods for 11, 5 and 2

It turns out there are 'short cuts' or 'tricks' you can use when multiplying, however these tricks are specific to a number being multiplied. This module provides learning tricks and practice for the numbers 11 , 5 and 2. There exist other tricks for other digits and numbers like 3,4,6,7,8,9 and 12, but they are more complicated and involve more steps, to the point where it's probably easier to use a different technique. ( If you are interested, these techniques form part of the 'Trachtenberg' system of mental maths. )

Note The techniques described here work far better if you have studied the practice modules on this website for "memory systems" as this helps you to "see" the numbers and keep track of them as you proceed with the calculation.

Multiplication by 11

If the digits of the number being multiplied by 11 add to to 9 or less, just add them and sandwich inside the original. For example:

11 x 34 = 374
11 x 71 = 781
11 x 27 = 287

If the digits add up to more than 9, there's a bit more work to do - you will need to carry. Work from the right hand side leftwards. For example:

11 × 48

Step 1) Remember the 48. This is a 'roof' in the Major memory system.
Step 1) 4 + 8 = 12. Think 2 with a carry. Put the 2 next to the 8: 28 - you can think of this as 'navy.'
Step 3) Add the carry (which is always 1 !) to the last digit 4, to make 5. Put the 5 in place: 528
- 528 is the answer.

For longer numbers ( practised at difficulty level 3 ) just repeat the above process, working right to left as usual:

11 × 234 ( a longer number, but easy because there are no carries : )

Step 1) Think 4
Step 2) 3+4 = 7, put the 7 next to the 4: 74
Step 3) 3 + 2 = 5, put the 5 in: 574
Step 4) Just add the last digit which was 2: 2574


11 × 678 ( This is harder, as it involves carries : )

Step 1) Think 8
Step 2) 7 + 8 gives 15 ( 5 with carry ) . Place the 5 next to the 8 : 58
Step 3) 7 + 3 is 13, plus a carry is 14. Place the 4 next to the running answer: 458
Step 4) 6 + the carry gives 7. Place the 7: 7458

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Multiplication by 5

Rule: Halve the number being multiplied by 5, and times by 10.

Example:

18 x 5
Step 1) Halve the 18, to give 9.
Step 2) Add a zero on to give 90, the answer.

46 x 5
Step 1) Halve the 46, to give 23.
Step 2) Add a zero on to give 230, the answer.

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Multiplication by 2

Rule: working right to left, double each digit with a carry.

NoteThis is equivalent to 'column multiplication by 2' on paper, but for 'mental maths' this technique only really makes sense when used with memory images.

Example

76892 x 2

1)  2 x 2 = 4                       4
2)  9 x 2 = 18                     84    ( 'car' with carry )
3)  8 x 2 = 16 + carry = 17       784    ( 'shoe' with carry,  car )
4)  6 x 2 = 12 + carry = 13      3784    ( 'Mike' + 'car' )
5)  7 x 2 = 14 + carry = 15    153784    ( 'Doll' + 'mike' + car )

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Difficulty Levels - typical questions:

1: 11 x 14
2: 11 x 57
3: 11 x 315