First Figures are Same and Last Figure Adds to 10, 100, and so on…

In this section, we are going to study one typical scenario when the First Figures of 2 numbers are Same and the Last Figure adds to 10, 100, and so on, i.e. Multiply ab x ac where b+c=10s.

Sutra used: Ekadhikena Purvena (One more than the previous one)

Let us start with 2-digit numbers.

Here, 2-digit numbers start with the same digit and the sum of their last digits is 10. In such cases, the product of the two numbers can be easily computed.

For example: 42 x 48 = ?

Here, the first digit of both numbers are same, i.e. 4 and the last digit of both numbers add to 10, i.e. 2+8.

The result comprises of 2 parts:

• 1st part or Left figure = multiply the digit with One more than the digit
• 2nd part or Right figure = multiply both the digits

Remember that since the 2 digits add to 10, so the right figure will contain 2 digits, i.e. if the product of 2 digits is, say 9 then it will be written as 09.

This method can be extended to more than 2 digit numbers such that the leftmost digits are same and the rightmost digits add to 10, 100, and so on.

Let us take another example:

378 x 322 = ?

Here, the first digit of both numbers are same, i.e. 3 and the last digit of both numbers add to 100, i.e. 78+22.

The result comprises of 2 parts:

• 1st part or Left figure = multiply the digit with One more than the digit
• 2nd part of Right figure = multiply both the digits

Let us practice more:

a 63 × 67                       b 58 × 52                       c 71 × 79

d 104 × 106                   e 32 × 38                       f 104 × 106

g 91 × 99                        h 77 × 73                      i 597 × 593

j 203 × 207

⇐ Multiplication by 11, 111, 1111 and so on…