Division by bigger numbers using complements
In the last few weeks we have seen diferent methods of division using complements. We have been through the methods used to divide by 9, 8, 7. Similar principles can be used to divide by numbers like 99, 98, 97 etc.
Let us start with 1534 / 99
The divisor is 99. So the base is 100. The complement of 99 is 01. And the number of digits that we have to set aside for the remainder will be 2.
We write the numbers as follows:
99 1 5 3 4
01
Bring 1 down and multiply it by the complement. Write the answer below the next two digits. Remember the complement is 01 and the so the product is 01 and is written below the next two digits 5 and 3.
99 1 5 3 4
01 0 1
1
Now we have to add 5 + 0 and 3 + 1 and write the answers below.
99 1 5 3 4
01 0 1
1 5 4
Multiply 5 by the complement and write the answer below the next two digits
99 1 5 3 4
01 0 1
0 5
1 5
Add the digits vertically and you get 4 and 9 in the remainder column. Since we have got numbers below all the digits of the given number we stop our calculations here.
99 1 5 3 4
01 0 1
0 5
1 5 4 9
Answer: The quotient 15 and the remainder 49
Let us try a number with more digits,
349714/ 99
The base is 100, the complement is 01 and the number of digits for the remainder is 2.
99 3 4 9 7 1 4
01
Bring the 3 down. Then multiply it by 01 and write the answer below the next two digits. Add the second set of numbers vertically.
99 3 4 9 7 1 4
01 0 3
3 4
Multiply 4 by the complement and write the answer below the next two digits. Add the next set of digits vertically (9+3+0).
99 3 4 9 7 1 4
01 0 3
0 4
3 4 12
Multiply 12 by the complement and put the answer below 7 and 1. Add the next set of digits vertically (7+4+1)
99 3 4 9 7 1 4
01 0 3
0 4
1 2
3 4 12 12
Multiply 12 by the complement and put the answer below the last two digits. Add vertically.
99 3 4 9 7 1 4
01 0 3
0 4
1 2
1 2
3 4 12 12 4 6
Finally we carry over the tens digits in the two 12s to the previous digit to get the final answer.
3 4 12 12 4 6
3 5 3 2 4 6
Answer: The quotient is 3532 and the remainder is 46