For our 12th MATH-Inic Special for Christmas, we will now show how we can use a base to make division easier. It would be difficult to solve our example, 12,014 ÷ 89, using long division because of the large digits in the divisor. But with base division, finding the quotient is easy using the following steps:
- In the space for the divisor, we place 89 and its complement, 11, underneath it.
- Since we will use 100 as a base, we separate the last two digits of the dividend by a remainder bar.
- Bring down the first digit of the dividend, 1, as the first digit of the quotient. This is because we have the same number of 89s as there are hundreds in the dividend.
- We then multiply it by 11 which is the remainder for every hundred and and place the product under the second and third digits of the dividend.
- The sum obtained in the second column (2 +1 = 3) will be the second figure in the answer.
- Write the product of this latest answer figure and 11 under the 3rd and 4th columns of the dividend as shown.
- The sum of the figures in the 3rd column will be the third answer digit (0 + 1 + 3 = 4).
- Multiply 4 by 11 and place the product as shown.
- Add all the figures after the remainder bar (4th and 5th columns) to get the remainder.
For more examples and review problems, watch out for our coming “30 Master Strategies in Computing”