Division

How do I find the quotient when I have the divisor and the dividend?

Ever stuck on questions like what is 868 divided by 7? Or something like 137 divided by 11? Want to solve the simple fractions without using pen and paper? This module might be for you ;)

To find the division of a number, you can easily do so using the following steps:

  1. Start with dividing the divisor with the first number on the left side of the dividend. This will give you the leftmost digit of your quotient.

  2. Move to the right side with every step and get more and more digits for your quotient.
    If the division gives you a remainder, then keep the remainder as the tens digit when moving to the next number.
    If the number is smaller than the divisor, then place a zero in the quotient and keep the entire digit in the divisor as the remainder and move to the next digit. When you reach the end of the number with no remainder, you get to the final answer. However, if you reach the end of the number with remainder, you should treat '0' as the next digit and the remainder as the number in the tens place. In the quotient, you should add a decimal to mark the end of the dividend followed by the result you get by dividing the remainder with the divisor.

Let's try this by dividing 868 by 7:

  1. Dividing the leftmost digit of the dividend with the divisor, i.e. 8 ÷ 7. Since 7 × 1 + 1 = 8, this gives us the first digit of the quotient, i.e. 1. This also gives a remainder of 1.

  2. Moving to the next digit in the dividend, i.e., 6. But since we had a remainder of 1 from the previous step, we keep 1 as the tens digit, therefore, we can say the next digit is equivalent to '16'. 16 ÷ 7 gives us 2 in the quotient and 2 as the remainder. The quotient is now 12.

  3. Moving to the next digit in the dividend, i.e., 8. But since we had a remainder of 2 from the previous step, we keep 2 as the tens digit, therefore, we can say the next digit is equivalent to 28. 28 ÷ 7 gives us 4 in the quotient and no remainder. The quotient is now 124. We have reached the end of the number with no remainder, hence the final answer is 124.

Let's try the above method for 137 divided by 11:

  1. Dividing the leftmost digit of the dividend with the divisor, i.e. dividing 1 with 11. Since 11 × 0 + 1 = 1, this gives us the first digit of the quotient, i.e. 0. This also gives a remainder of 1.

  2. Moving to the next digit in the dividend, i.e., 3. But since we had a remainder of 1 from the previous step, we keep 1 as the tens digit, therefore, we can say the next digit is equivalent to 13. 13 ÷ 11 gives us 1 in the quotient and 2 as the remainder. The quotient is now 01 or 1.

  3. Moving to the next digit in the dividend, i.e., 7. But since we had a remainder of 2 from the previous step, we keep 2 as the tens digit, therefore, we can say the next digit is equivalent to 27. 27 ÷ 11 gives us 2 in the quotient and 5 as the remainder. The quotient is now 12.

  4. There are no digits after 7, however, we treat 0 as the next digit and add a decimal to mark the end of the dividend. But since we had a remainder of 5 from the previous step, we keep 5 as the tens digit, therefore, we can say the next digit is equivalent to 50. 50 ÷ 11 gives us 4 as the next digit in the quotient and 6 as the reminder. The quotient is now 12.4.

  5. Since we still have a remainder, we treat 0 as the next digit. But since we had a remainder of 6 from the previous step, we keep 6 as the tens digit, therefore, we can say the next digit is equivalent to 60. 60 ÷ 11 gives us 5 as the next digit in the quotient and 5 as the reminder. The quotient is now 12.45.

  6. At the end of the 5th step, we get to a situation similar to the one we had at the end of step 3, hence sending us into an infinite loop of steps 4 and 5. The quotient is therefore 12.45454545...

If you find the above method easy, you can increase your pace by learning about intervals in case of some divisors. This will help you to determine all the digits after the decimal whenever there is a remainder even after you have reached the end of the remainder. Below are the intervals for the first 10 integers:

1 - 0
2 - 0.5
3 - 0.333...
4 - 0.25
5 - 0.2
6 - 0.166...
7 - 0.142857142...
8 - 0.125
9 - 0.111...
10 - 0.1

Example:

What is 230 divided by 9?
Dividing 230 by 9 using until the 0 in units place gives us 25 as the answer with a remainder of 5. To determine the digits after the decimal, multiply 5 with the interval for 9, i.e., 0.111... This will give us the digits as 0.555...
Therefore, the answer is 25.5555...