Multiplying any 2 digit numbers together

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 together. This gives the first figure of the answer.

Step 2: Cross-multiply and add. This gives the middle figure.

Step 3: Multiply the tens digit together. This gives the last figure of the answer.

Example: 12 x 23

  

So the answer is 276
This is normally
called long multiplication but actually the answer can be written straight down using the VERTICALLY AND CROSSWISE formula.

• 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.