Trick to Multiply Numbers Close to 100

The Trick

Imagine that you are solving a long problem in the exam. In the middle of it, you are required to multiply numbers close to 100. Let us take an example: 106 × 107 or 98 × 109 etc. Don’t worry! You can solve these types of problems in 2 seconds.

Steps to Follow

1. First, we write all the numbers as two digit numbers. These numbers are how much they exceed or are less than 100.
   For example: 106 exceeds 100 by 6, so we write it as 06.
   107 exceeds 100 by 7, so we write it as 07.
2. After Step 1, we multiply these pair of two-digit numbers i.e. 06 × 07 = 42. If on multiplication we get only a single digit number, then we write it with a preceding 0. i.e. 02 × 01 = 02 etc.
3. On another side of the line, we do cross addition i.e. either we do ‘106 + 07’ or ‘107 + 06’. Observe that they will always produce the same result.
4. If the product in Step 2 is less than 100, then these are the last two digits of the final product. And the product in Step 3 are the first three digits of the final product. The final product is obtained by putting these five digits together. This can be seen in Example 1.
5. If the product in Step 2 is either negative or more than 100, then a few more steps are involved. What we do in these cases is illustrated in the examples below:

Example 2:

Here, one number exceeds 100 by 04, while one number is less than 100 by 02. So we multiply +04 and -02 to get -08. Since we get a negative number, we borrow 1 from the left side. This 1 translates to 100 units when taken to the right side.

Now we add this 100 to the -08. So the result is 92 on the right side. And on the left side, we have 102-1 = 101. So we finally get a five digit number i.e. 10192.
Example 3:

Here, on the right we get a product greater than 100. So we reduce 100 from the right, leaving behind a two digit number. Then we give this 100 to the left side where it translates to 1 unit. This 1 gets added to the number on the left. And you now get a five digit number 12208.