For example, if you were trying to add 93, 472, 65 and 3551, you would add a 0 to 472 and a 00 to 93 and 65, so that each of these numbers had the same amount of columns. This would give you 4 rows. Row 1 would have 0093, row 2 would have 0472, row 3 would have 0065, and row 4 would have 3551.
For example, in the units or ones column of 0093 + 0472 + 0065 + 3551, add 3 from 0093, 2 from 0472, 5 from 0055, and 1 from 3551. This total would be 11, which would need to be subtracted due to the rule of 11. This would give you a value of 0.
Using 0093, 0472, 0065, and 3551 as an example, this would tally up to one 11 subtracted in the ones column, two 11s subtracted in the tens column (9 + 7 = 16 - 11 and 5 + 6 = 11- 11), xero 11s subtracted in the hundreds column, and zero 11s subtracted in the thousands column. So add a row with 0021 below the added value of 3950 (since 3 + 2 + 5 + 1 - 11 = 0, 9 + 7 - 11 + 6 - 11 + 5 = 5, 0 + 4 + 0 + 5 = 9, and 0 + 0 +0 +0 = 3).
Using the added value of 3950 with an 11s row of 0021, the ones digit of your final total would be 1.
For example, with the numbers 3950 and 0021, add the L shape patterns of 5, 2, and 1; 9, 0, and 2; and 3, 0, and 0. Then, final total in your tens column would be 8 (5 + 2 + 1), it would be 1 in the hundreds column (9 + 0 + 2, which equals 11, carry the 1 because the rule of 11 now no longer applies) and it would be 4 in the thousands column ( 3 + 0 + 0 +1 the carried one). Therefore, your final total (and the correct answer) would be 4181. Voila!
For example, if you’re trying to multiply 972 by 18, add 2 0’s before you do any real mental multiplication so your multiplicand is now 00972.
If you were multiplying 00972 by 18, your first outer pair would be 8 and 2, your second outer pair would by 8 and 7, your third outer pair would be 8 and 9, your fourth outer pair would be 8 and 0, and your fifth outer pair would be 8 and 0.
Your first inner pair of 00972 x 18 would be 1 and nothing, your second pair would be 1 and 2, your third pair would be 1 and 7, your fourth pair would be 1 and 9, and your fifth pair would be 1 and 0. (1 would not be paired with the final 0, since it always has to be to the right of the outer pair. ) If your multiplier is 3 digits or more, no problem! Just know you’ll have 2 inner pairs, the first 1 digit to the right of the outer pair, and the second 2 digits to the right. Both inner pairs will remain unpaired at first and you’ll add up the total of all three digit pairs each time.
For example, the first number (the number in the ones column) of your final total value for 00972 x 18 would be 6, because 8 x 2 = 16 and 1 is not yet paired. Add the 6 (the ones value) to the final total, and carry the 1. The number in the 10s column would be 9 because 56 (8 x 7) + 2 (1 x 2) + 1 (carried) = 59, the number in the hundreds column would be 4 because 72 (8 x 9) + 7 (1 x 7) + 5 (carried) = 84, the number in the thousands column would be 7 because 0 (8 x 0) + 9 (1 x 9) + 8 (carried) = 17, and the number in the ten thousands column would be 1 because 0 (8 x 0) + 0 (1 x 0) + 1 (carried) =1. That would make the final answer 17,496.
For example, if you were dividing 9471 by 77, bring the 9 down to your PD row and divide that 9 by 7. This equals 1 which now makes the first place value of your quotient. The remainder is irrelevant.
If you were dividing 9471 by 77, your NT product would be 7, because N (7 X 1 = 07) + T (7 x 1 = 07, the tens placement is 0) = 7.
After getting an NT product of 7 for 9471, subtract 7 (the NT product) from 9 for a value of 2.
After carrying 2 (the PD 9 - NT 7 value) to the W fig row of 9471, carry down the 4 to create a value of 24 in the W fig row.
For 9471, subtract the remaining units of your NT, 7 (because 7 x 1 = 07), from your working figure of 24 to get a value of 17. Place 17 in the PD row next to 9.
Using 9471/77 as an example, after getting 17 for your PD row, divide 17 by the 7 in 77 for a value of 2. Add the 2 next to 1 in your final quotient (not worrying about the remainder). Now, you know the first two digits of your final quotient will be 12.
Using this method, the final quotient of 9471 divided by 77 = 123, with W figs of 24 (PD 9 - NT 7, carry down the 4), 27 (PD 17 - NT 15, carry down the 7), and 01 (PD 23 - NT 23, carry down the 1) and PDs of 9, 17 (W fig 24 - U 7), 23 (W fig 27 - U 4), and 0 (W fig 1 - U1).
