This technique can be used to multiply a

This technique can be used to multiply a number with a series of 9 like 99, 9999, 99999 etc. It cannot be used to multiply a number with a number like 87, 865 etc. You will be amazed to see the speed at which we get the answer !

There are different cases we use here: A) Multiplying a number with an equal number of 9’s B) Multiplying a number with a higher number of 9’s C) Multiplying a number with a lower number of 9’s

CASE A Multiplying a number with equal number of 9’s (Q) Multiply 549 by 999 In this case, the multiplicand 549 has 3 digits. The multiplier 999 also has 3 digits. It means both are equal

549 x 999 • We subtract 1 from 549 and write down half the answer as 548. The answer at this stage is 548 • Now, we will be dealing with the number 548. Subtract each of the digits 5, 4, and 8 from 9 and write them in the answer one by one. (9) - 5 = 4 (9) - 4 = 5 (9) - 8 = 1 We had already obtained the numbers 548. We suffix the numbers 451. The final answer is 548451

(Q) Multiply 8889 by 9999 In this case, the multiplicand 8889 has 4 digits. The multiplier 9999 also has 4 digits. It means both are equal

8889 x 9999 • We subtract 1 from 8889 and write down half the answer as 8888. The answer at this stage is 8888 • Now, we will be dealing with the number 8888. Subtract each of the digits 8, 8, 8 and 8 from 9 and write them in the answer one by one. (9) - 8 = 1 We had already obtained the numbers 8888. We suffix the numbers 1111. The final answer is 88881111

Let us check the following examples where both the multiplicand multiplier have equal digits (a)64 x 99 = 63 36 (b) 67567 x 99999 = 67566 32433 (c) 4007 x 9999 = 4006 5993

Let’s move to the next case. Multiplying a number with a higher number of 9’s

CASE B Multiplying a number with higher number of 9’s (Q) Multiply 549 by 9999 In this case, the multiplicand 549 has 3 digits. The multiplier 9999 has 4 digits. It means nine’s are higher. So, it falls in Case B

SOLUTION Write the number 549 as 0549. Now the question becomes 0549 multiplied by 9999 It means both the multiplicand multiplier now have 4 digits. Therefore, we can use the same steps that we used in Case ‘A’ !

0549 x 9999 • We subtract 1 from 0549 and write down half the answer as 0548. The answer at this stage is 0548 • Now, we will be dealing with the number 0548. Subtract each of the digits 0, 5, 4, and 8 from 9 and write them in the answer one by one. (9) - 0 = 9 (9) - 5 = 4 (9) - 4 = 5 (9) - 8 = 1 We had already obtained the numbers 0548. We suffix the numbers 9451. The final answer is 05489451

(Q) Multiply 682 by 99999 In this case, the multiplicand 682 has 3 digits. The multiplier 99999 has 5 digits. It means 9’s are more

We convert the number 682 as 00682. The new question now becomes 00682 by 99999. It means both the multiplicand multiplier now have 5 digits. Let’s proceed to the solution…

• We subtract 1 from 00682 and write down half the answer as 00681. The answer at this stage is 00681 • Now, we will be dealing with the number 00681. Subtract each of the digits 0, 0, 6, 8, 1 from 9 and write them in the answer one by one. (9) - 0 = 9 (9) - 6 = 3 (9) - 8 = 1 (9) - 1 = 8 We had already obtained the numbers 00681. We suffix the numbers 99318. The final answer is 0068199318

Let us check the following examples which have more nine’s than the digits. They all fall under Case B. (a)64 x 999 = 063 936 (or simply 63936) (b)47 x 9999 = 0046 9953 (or simply 469953)

Let’s move to the last case. Multiplying a number with a lower number of 9’s

CASE C Multiplying a number with lower number of 9’s (Q) Multiply 549 by 99 In this case, the multiplicand 549 has 3 digits. The multiplier 99 has 2 digits. It means nine’s are lower. So, it falls in Case C.

CASE C of Vedic Mathematics uses a different approach. In this case, we cannot use the technique we used in Case A and B. In this case, we use the normal method of multiplication. but with a difference The question is ‘Multiply 549 by 99’ We will write the number 99 as (100 – 1) and then do the question.

Let us do the problem : 549 x (100 – 1) = 54900 – 549 = 54351 This technique is so obvious that it does not need further elaboration. With this we conclude the technique on multiplication with a series of nine.