Quick Multiplication up to 20 x 20

“I’m having trouble above 10×10.”

This was a statement I heard many times while interacting with students preparing for competitive examinations including CAT. This was in response to my appeal to them to memorize tables up to 20×20.

Today I am posting here on QuickerMaths.com, the method which I recommend to my students too.

How to multiply up to 20×20 in your head?

Assumption: You know your multiplication table reasonably well up to 10×10.

I am trying to explain this with an example,

Say you want to multiply – 16 x 13

Step 1 – Add the unit’s digit of one to the other number –

Here, add 16 + 3 = 19

Or, add 13 + 6 = 19

Step 2 – Put a zero after the number (i.e. multiply it by 10)

Here, 19 becomes 190

Step 3 – Multiply unit’s digit of both the numbers

Here, 6×3 = 18

Step 4 – Add the product to the result of Step 2

Here, 190 + 18 = 208

Simple!! Isn’t it?

Another example, 17×19 =  (17+9)*10 + (7*9)  = 260 + 63 = 323

(10+a) * (10+b) = 100 + 10b + 10a + a*b
= (10+a+b) * 10 + a*b
==========
This can be extended to sums like 23 * 28
(20+a) * (20+b) = 400 + 20b + 20a + a*b
= (20+a+b) * 20 + a*b
So, 23*28 = (23+8)*20 + 3*8 = 620 + 24 = 644.
==========
& so on.

by NANDEESH H N

Try for yourself. Let me know (by posting a comment below) if you liked it.

Click here for some more fast multiplication tricks

34 thoughts to “Quick Multiplication up to 20 x 20”

  1. hey,is it any specific books available 4 this???????????????????????
    plz tell,i need it…………………………………

  2. Hi Nandeesh

    can you tell me the above formula can be used in any two digit multiplication

    and for three digit multiply what is the formula for ex: 839478*625

    waht are short cut tricks for square, cube root, Division

  3. another trick which suits to all two digit multiplication is
    Eg-25*24
    (5*4) multiplying one’s(here we remains with carry 2 ie 5*4=20)….0
    now multiplying criss cross (5*2)+(4*2)+carry ie 2 is 20…..0
    now multiply ten’s (2*2)+carry ie 2 is….. 6
    the ans is 600

  4. Thumbs up to Sanjay Patel… His method works for any 2 digit and 3 digit numbers multiplication of anytype.. Thanks a lot..

  5. ??? ???? ?? ???????? ?? ????
    235 *142=?
    2 3 5
    1 4 2
    _____
    ????=5*2=10=0
    1 ?????
    ????=?. ?? ?. ?? ???? ?? ?????? ???? ?? ???
    =3*2 + 5*4=6+20=26
    ????? ?? ????=26+1=27=7 ,????? 2

    ?????=2*2 + 5*1 + 3*4
    =21=????? ????=23=3, ??.=2

    ????=2*4 + 3*1=11+??.2=13=3, ??.1

    ???=2*1=2+??.1=3

    ????? ??? ???. ??. ?. ?
    3 3 3 7 0
    ??? ??? ???…

  6. I almost certainly would not have contemplated this was valuable two or three years ago, yet it’s fascinating how age evolves the manner you respond to things, many thanks for the article it really is great to discover something smart now instead of the typical rubbish masquerading as blogs and forums over the internet. Regards

  7. 13*18 = (13+8)*10+3*8 = 234
    23*28 = (23+8)*20+3*8 = 644
    33*38 = (33+8)*30+3*8 = 1254
    43*48 = (43+8)*40+3*8 = 2064
    53*58 = (53+8)*50+3*8 = 3074

      1. Same shortcut does not work everywhere.

        One way of solving your problem is:
        45*487 = 90*487/2 = 43830/2 = 21915

      2. another approach:
        hy can u tell me D shortcut trick of multiplying 45*487

        45*487=(50-5)*487=(487*50)-(487*5)= (487*100/2) – (no need to calculate it now)
        = 24350-2435=21915…just trying it, in this way nos can be calculated mentally ofcourse with practice

    1. Hi Nandeesh,

      Can u tell me short trick for 76*45
      Bcoz above the nos are in 10’s or 20’s or 30’s.

      Thank you

      1. 76*45= simple use the guys method of criss-cross as explained in hindi.

        or u can use 76*(50-5)=its very easy to multiply by 5 ain’t it

        =(76*100)/2- no need to calculate it now= 3800-380=3420…ans

    2. 13 *18 = 1*( 13 + 8 ) l ( 3 * 8 ) = 1*21 l 24 =21 l 24 = 234
      23 *28 = 2*( 23 + 8 ) l ( 3 * 8 ) = 2 *31 l 24 = 62 l 24 = 644
      33 *38 = 3*( 33 + 8 ) l ( 3 * 8 ) = 3 *41 l 24 = 123 l 24 = 1254
      43 *38 = 4*( 43 +8 ) l ( 3 * 8 ) = 4 *51 l 24 = 204 l 24 = 2064
      53 *58 = 5*( 53 + 8 ) l ( 3* 8 ) = 5 * 61 l 24 = 305 l 24 = 3074

  8. Very good!
    (10+a) * (10+b) = 100 + 10b + 10a + a*b
    = (10+a+b) * 10 + a*b
    ==========
    This can be extended to sums like 23 * 28
    (20+a) * (20+b) = 400 + 20b + 20a + a*b
    = (20+a+b) * 20 + a*b

    So, 23*28 = (23+8)*20 + 3*8 = 620 + 24 = 644.
    ==========
    & so on.

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