# First Figures Adds to 10 and Last Figure is Same

In the previous section First Figures are Same and Last Figure Adds to 10, 100, and so on… we studied a special case of multiplication when “Multiply ab x ac where b+c=10s”.

In this section, we are going to study another typical scenario when the First Figure adds to 10 and the Last Figures of 2 numbers are Same, i.e. Multiply ba x ca where b+c=10.

Sutra used: Adyamadyenantyainantyena (The First by the First and The Last by the Last)

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

For example: 24 x 84 = ?

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

The result comprises of 2 parts:

• 1st part or Left figure = multiply the digits and add the common last digit
• 2nd part or Right figure = square the common digit

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. Another example:

63 x 43 = ? Let us practice more:

a 36 × 76                       b 85 × 25                       c 17 × 97

d 41 × 61                       e 23 × 83                       f 54 × 54

g 19 × 99                       h 77 × 37                       i 66 × 46

j 23 × 83