Long Division with Larger Divisors
Double Abacus Approach
25,986 divided by 5,121 = 5.074 (to 3 decimal places
Short Course
This is a short course (slide show) in long division with larger divisors. All of the examples in this show use tow or more digits in the divisors.
Long Division with Larger Divisors
The process for setting up the division calculation remains the same. 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. In the last example below, we will show you how to enter a divisor when there aren’t enough rows available in the bottom abacus.
The result of the division calculation is the quotient. We will enter this number in the in the columns in the top abacus.
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 multi-digit divisors.
So, we introduced, in the Long Division section, a better method for dividing with multi-digit divisors. Instead of using the first digit of the divisor we mentally add 1 (or more) to the column 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, the result of the division may need to be 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.
Now, let’s apply this process to 3 and 4-digit divisors in the following examples.
Examples
Now, let’s look at some more examples of this process. In these examples, the dividend will have many digits, the divisor will have 3 or more digits and the remainder will be a decimal (to 3 places). Click on the link to show the steps to calculate the answer.
Example: 474 divided by 177
Example: 5,537 divided by 486
Example: 85,096 divided by 203
Example: 26,645 divided by 321
Example: 52,288 divided by 682
Example: 570,491 divided by 943
Example: 7,008 divided by 4,003
Example: 25,986 divided by 5,121
Example: 1,411,805 divided by 5,941