Long Division
Double Abacus Approach
72,357 divided by 87 = 831.689 (to 3 decimal places)
Short Course
This is a short course (slide show) in long division. All of the examples in this show use two digit divisors.
Long Division
In the Short Division section, we divided a single digit into large numbers. To do this, we asked how many times we can subtract/divide the divisor from either the first digit or the first two digits of the dividend. We would continue this process until the divisor was larger than the dividend or the dividend equaled 0. It is reasonable to assume that we would follow this same process with two-digit divisors. There is only one problem. This process only works for a small group of 2-digit divisors or larger divisors.
We need to use a better method for 2-digit or larger divisors. The Double-A Long Division Method addresses this issue with a simple process the works for divisors of 2 or more digits. Instead of using the first digit of the divisor we mentally add 1 to the first digit and divide it into the dividend. The result of this division is set in the top abacus. Then we multiply the result of this division by each digit of the original divisor and subtracted the product from the dividend. This process continues until the dividend is 0 or less than the divisor.
Since we are using a higher divisor (only for the initial division), the result of the division my need to added in the same column of the previous division. We call this upward adjustment.
When the first digit of the divisor is nine (9), we will not be able to use a higher divisor. In this situation, we will need to divide the first digits of the dividend by 9 but reduce the quotient by 1. Then we follow the same process division process. This lower quotient is entered into the correct column of the top abacus. Next, we will multiply this number by each digit in the divisor and subtract it from the dividend. This process continues until the dividend is 0 or less than the divisor. Occasionally you may need to upwardly adjust the quotient.
This is the Double-A Long Division approach to division with divisors with 2 digits. It involves using a higher divisor, a lower quotient and upward adjustment. The following examples will help you to better understand these concepts. A more detailed explanation of this method can be found in the Appendix.
The process for setting up the division calculation remains the same as in the previous sections. First, set up the dividend. Enter this number from on the right side of the bottom abacus. If the dividend is a 3digit number, then from left to right, set each digit starting in column 3.
Next, set up the divisor. Start from the left side of the bottom abacus, in column 13, and set each digit of the divisor. A two-digit divisor will be set in columns 13 and 12.
The result of the division calculation is the quotient. We will enter this number in the in the columns in the top abacus.
Examples
Now, let’s look at some more examples of this process. In these examples, the dividend will have many digits, the divisor will be two digits and the remainder will be a decimal. Click on the link to show the steps to calculate the answer.
Example: 868 divided by 41
Example: 636 divided by 93
Example: 6,655 divided by 75
Example: 67,180 divided by 48
Example: 72,357 divided by 87