Multiplying any 2 digit numbers together by mere mental arithmetic!
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An easy way to multiply a 2 digit number by a 2 digit number using Rainbow Multiplication.

Step-1: Multiply the ones digit of both the numbers together and write down the ones; carry, if any. This gives the first figure of the answer.

Step-2: Cross-multiply and add plus carried digit; write down the ones and carry. This gives the middle figure.

Step-3: Multiply the tens digit of both the numbers together and add carried digit; write it down.

Example: 12 x 23

This is done using the VERTICALLY AND CROSSWISE formula; also called Rainbow Multiplication.

Further Example,
• 21 x 23 = 483
We first put, or imagine, 23 below 21:

There are 3 steps:

a) Multiply vertically on the left: 2 x 2 = 4. This gives the first figure of the answer.
b) Multiply crosswise and add: 2 x 3 + 1 x 2 = 8. This gives the middle figure.
c) Multiply vertically on the right: 1 x 3 = 3. This gives the last figure of the answer.

Similarly,
• 61 x 31 = 1891

• 6 x 3 = 18; 6 x 1 + 1 x 3 = 9; 1 x 1 = 1

Carries

There were no carries in the method given above. However, there only involve one small extra step, if there is any carries in any place.
• 21 x 26 = 546
The method is the same as above except that we get a 2-figure number, 14, in the middle step, so the 1 is carried over to the left (4 becomes 5).
So, 21 × 26 = 546

• 33 x 44 = 1452
There may be more than one carry in a sum:

Vertically on the left we get 12. Crosswise gives us 24, so we carry 2 to the left and mentally get 144.

Then vertically on the right we get 12 and the 1 here is carried over to the 144 to make 1452.