08: MULTIPLY BY RAINBOW METHOD (PART I)

SUTRA (Algorithm):

This is a VARIATION of previous method

DEMONSTRATION

Work and Write from Right to Left
Right Digit;
Add Two, Two Digits;
Left Digit

01) Consider: 514 x 32 = ?

The digits 2 & 3 of 32, in that order,
Multiply each digit of _514_, from Right to Left
as DESCRIBED & DEMONSTRATED below.
     
2x0 + 3x5|2x5 + 3x1|2x1 + 3x4|2x4 + 3x0
15|13|14|8
16|14|14|8
A very practical suggestion:
The curved lines above, connect two digits, in some 'pattern'.
This pattern is very important.

Note the detailed explanation is lo - - - - ng;
but actual working is just 1 step.

Step 1:
Unit's digit 2 multiplies unit's digit 4.
Always this is the starting point.
Next digit 3 has NO digit before (to the right of) 4 to multiply.
 
514 x 32 =   - - - - -   8

Step 2:
Now unit's digit 2, multiplies the digit 1 after moving to the left of 4.
And now the ten's digit 3 multiplies the digit 4, on the right of 1.
Results are added; we get 14.
 
514 x 32 =   - - -   14 8
514 x 32 =   - - -   14 8
Step 3:
Now moving one digit further, we get (2x5)+(3x1) = 13 and
in the next step (2x nothing)+(3x5) = 15

514 x 32 =   -  13 14 8
514 x 32 =   -   14 4 8
514 x 32 =   1514 4 8
514 x 32 =   16  4 4 8

02) Consider: 738 x 64 = ?

4x0 + 6x7|4x7 + 6x3|4x3 + 6x8|4x8 + 6x0
42|46|60|32

738 x 64 = 42 46 60 32
Step by step:
738 x 64 =                  32
738 x 64 =                   32
738 x 64 =                   32
738 x 64 =              60 32
738 x 64 =              63   2
738 x 64 =        5 2   3   2
738 x 64 =  4 7    2   3   2

738 x 64 = 47232     Note this is done in ONE STEP, from right to left !

WORKED EXAMPLES:
(Practice and improve your fluency.)
REMEMBER it is done in 1 step.

1.312 x 21 = 6552   5. 468 x 83 = 38688424
2.423 x 23 = 917129   6. 947 x 64 = 60666028
3.615 x 24 = 14271620   7. 503 x 52 = 2611156
4.214 x 75 = 16203520