Short Division
Double Abacus Approach
949,364 divided by 9 = 105,484.888 (to 3 decimal places)
Short Course
This is a short course (slide show) in basic division and short division. on how to divide with single digits. All of the examples in this show use single digit divisors.
Setting up Division Calculations
Setting the numbers that are used in a division calculation is a simple process. It is important to remember, that in this book, the first number in our division calculation is the dividend. The second number is the divisor. The back slash “/” (stands for divided by) separates the dividend and the divisor.
First, set up the dividend. Enter this number from on the right side of the bottom abacus. If the dividend is a 3 digit 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.
These are same positions that you used when you did division calculations using pencil and paper (or literary Braille) techniques. The divisor was on the right and the dividend was on the left.
The result of the division calculation is the quotient. We will enter this number in the in the columns in the top abacus.
Short Division with Integer Remainders
In order to calculate the quotient, we start the division calculation by dividing the first digit of the divisor into the either the first digit or the first two digits of the dividend. The result is set in the columns to right of the dividend. Then this single digit is multiplied by each digit of the multiplier and subtracted from the dividend creating a partial dividend. This process continues until the partial dividend is 0 or is smaller than the divisor. This is the final quotient. Any number that is “left over” is called the remainder
In this chapter, we will limit our calculations to only a single digit divisor and a one- or two-digit dividend. Now, let’s look at the process we need to follow to calculate the quotient:
Divide the first digit of the divisor into the first digit or the first two digits of the dividend. In which column to you set the result of the division? The result is set in the top abacus, in the column above the last digit you are dividing. If the last digit is in column 2 of the bottom abacus, the result will be set in column 2 in the top abacus.
Then multiply the number you just entered, by the divisor. Remember, in this book, the product of two single digits is always a 2-digit number (for example, 2 * 2 = 04). Then subtract the result from the dividend. This gives you a partial dividend.
If the partial dividend is 0 or less than the value of the divisor, then you have completed the division calculation.
The quotient is the number in the top abacus. The remainder is the number on the right side of the bottom 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 a single digit and the remainder will be an integer. Click on the link to show the steps to calculate the answer.
Example: 256 divided by 2
Example: 1,281 divided by 3
Example: 8,413 divided by 9
Example: 41,646 divided by 5
Example: 864,528 divided by 6
Short Division with Decimal Remainders
The difference between short division calculations with integer remainders and those with decimal remainders is where the dividend is entered. In the previous calculations (with integer remainders), the dividend is entered on the right edge of the bottom abacus. A four-digit dividend is entered in column 4, 3, 2 and 1 in the bottom abacus.
When we want a decimal remainder, we shift the starting column of the dividend to the left to accommodate the decimal places. If we want to complete the division with 3 decimal places, we will shift the dividend 3 columns to the left. So, a four-digit dividend would be entered in column 7 of the bottom abacus, 4 columns for the dividend and 3 columns for the remainder.
The divisor is entered from the left edge of the bottom abacus. Then we follow the short division process which is the same regardless of the type of remainder.
Examples
Now, let's look at some examples of division calculations with decimal remainders.
Example: 422 divided by 4
Example: 1,248 divided by 5
Example: 19,799 divided by 5
Example: 75,339 divided y 6
Example: 949,364 divided by 9