Last week we used complements to do multiplication by the Nikhilam method, for which both the numbers being multiplied need to be near the same base. This week let us look at using complements to multiply numbers whose base may not be the same.
To refresh our memory let us look at two important steps that we used last week:
1. Multiplication of the complements to get the units digit.
2. Cross subtraction of the complements and the given numbers.
Example: 96 x 8
In this problem the numbers do not have the same base, so the Nikhilam method is not possible. But we can still use complements.
■ First write the complements of each of the numbers.
96 x 8
14 2 (complements)
■ Multiply the complements. So we get 2 x 4 = 8 and 2 x 1 =2 which we have written below it.
96 x 8
14 2
28
■ Now to get the digits of the answer correctly we need to append a zero below 8, the units digit, and continue our calculations.
96 x 8
14 2
28
0
■ Cross subtract the complement from the number. 8 - 4 = 4 (or 6 – 2 = 4) and 8 - 1 = 7 (or 9 – 2 = 7) and write them below as shown.
96 x 8
14 2
28
740
■ Add the digits normally to get the answer.
96 x 8
14 2
28
740
768
■ Answer: 768
Let us try one more problem: 83 x 9
8 3x9
2 7 1
2 7 (multiplication of the complements)
7 2 0 (cross subtract the complement and the number)
7 4 7
Answer: 747
We can use this method for bigger numbers when the complements are small and it is easy to arrive at the answer.
Now you can try doing these problems.
1. 49 x 94. 69 x 8
2. 87 x 85. 99 x 7
3. 97 x 7