Multiplication of Numbers with a Series of 9’s

Generally, students find difficulty Multiplication of Numbers with 9’s. But it is exactly the opposite – the higher the number of 9’s in the question, the easier to calculate the correct answer. Using the method given below, we can Multiplication of Numbers with a Series of 9’s.
In other words, we can quickly multiply any number with 99, 999, 9999, 99999, etc. The technique is divided into 3 cases. In the first case, we will be multiplying a given number with an equal number of 9’s. In the second case, we will be multiplying a number with a higher number of 9’s. In the third case, we will be multiplying a number with a lower number of 9’s.

Case 1: Multiplying a number with an equal number of 9’s

Ex-1. Multiply 84 by 99.
• In this example, we subtract 1 from 84 and write half the answer 83 as LHS (left-hand side) the part of our answer. The answer at this stage is 83 __
• Now, we will be dealing with 83. Subtract the digits 8, and 3 from 9 and write them in the answer one by one. i.e. 9 – 8 is 1 and 9 – 3 is 6.
• The answer already obtained was 83 and now we put the digits 1 and 6 (16) as RHS (right-hand side) of our answer.
• The complete answer is 8316.

Ex-2. Multiply 734 by 999.
• We subtract 1 from 734 and write half the answer 733 as the LHS (left-hand side) part of our answer.
• Next, we subtract the digits 733 from 9 and write the answer 9 – 7 = 2, 9 – 3 = 6, and 9 – 3 is 6. Now we get 266 as RHS (right-hand side) of our answer.
• The final answer is 733266.

Ex-3. Multiply 9432 by 9999.
• We subtract 1 from 9432 and get 9431 as the LHS (left-hand side) part of our answer.
• Next, we subtract the digits 9431 from 9 and get 0568 as RHS (right-hand side) of our answer.
• The final answer is 94310568.

Now, we take some large digits to multiply.

Ex-4. Multiply 436285 by 999999.
• We subtract 1 from 736285 and get the answer 736284. We write this on the LHS (left-hand side) part of our answer.
• Next, we subtract the digits 736284 from 9 and get 563715 as RHS (right-hand side) of our answer.
• The final answer is 436284563715.

Case 2: Multiplying a number with a higher number of 9’s

Ex-1. Multiply 45 by 999.
• In this example, there are three 9’s in the multiplier. However, the multiplicand 45 has only 2 digits. So we add a 0 (zero) and convert 45 to 045 and make it a 3 digit number. After this, we can carry on with the procedure explained in Case 1.
• First, we subtract 1 from 045 and write it down 044 as LHS (left-hand side) part of our answer.
• Next, we subtract each of the digits of 044 from 9 (9-0=9, 9-4=5, 9-4=5) and we get 955 as RHS (right-hand side) part of our answer.
• The complete answer is 044955 which is 44955.

Ex-2. Multiply 726 by 9999.
• Here are four 9’s in the multiplier. However, the multiplicand 726 has only 3 digits. So we add a 0 (zero) and convert 726 to 0726 and make it a 4 digit number.
• First, we subtract 1 from 0726 and write it down 0725 as LHS (left-hand side) part of our answer.
• Now, we subtract each of the digits of 0725 from 9 and we get 9274 as RHS (right-hand side) part of our answer.
• The complete answer is 07259274 which is 7259274.

Ex-3. Multiply 3845 by 999999.
• Here are six 9’s in the multiplier. But, the multiplicand 3845 has only 4 digits. So we add a two 0s (zero) and convert 3845 to 003845 and make it a 6 digit number.
• We subtract 1 from 003845 and write it down 003844 as LHS (left-hand side) part of our answer.
• Now, we subtract each of the digits of 003844 from 9 and we get 996155 as RHS (right-hand side) part of our answer.
• The complete answer is 003844996155 which is 3844996155.

Case 3: Multiplying a number with a lower number of 9’s

Ex-1. Multiply 682 by 99.
• In this case, there are two 9’s in the multiplier. However, the multiplicand 682 has 3 digits, which are more than the multiplier digits.
• So first, we put ‘0’ to the right-hand side of multiplicand 682. Here, we have two 9’s in the multiplier then we put two 0’s (zeros) right-side to 682. So we get 68200. (If we have one 9’s in the multiplier, we put one 0, three 9’s then put three 0’s and so on…).
• Now, we subtract each of the digits of 682 from 68200 and we get 67518.
• The final answer is 67518.

Ex-2. Multiply 8402 by 999.
• In this example, there are three 9’s in the multiplier. The multiplicand 8402 has 4 digits, which are more than the multiplier digits.
• First, we put ‘0’ to the right-hand side of multiplicand 8402. Here, we have three 9’s in the multiplier so we put three 0’s (zeros) right-side to 8402. Now we get 8402000.
• Next, we subtract each of the digits of 8402 from 8402000 and we get 8393598.
• The answer is 8393598.

Ex-3. Multiply 624593 by 9999.
• In this example, there are four 9’s in the multiplier. The multiplicand 624593 has 6 digits, which are more than the multiplier digits.
• First, we put ‘0’ to the right-hand side of multiplicand 924593. Here, we have three 9’s in the multiplier so we put four 0’s (zeros) right-side to 924593. Now we get 9245930000.
• Next, we subtract each of the digits of 924593 from 9245930000 and we get 6245305407.
• The answer is 6245305407.

We see that this technique is too simple and easy to follow. This is the uniqueness of these systems. You realize how simple and easy it is to find the answer to any problem of mathematics that one encounters in daily life and especially in the exams. And the approach is so different from the traditional methods of calculation that it makes the whole process very easy and enjoyable. But if you any doubt in this, please watch our YouTube video, from where you can easily understand the trick. In this video, you will find the full explanation of Multiplication of Numbers with 9’s method.