Short Division
Single 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
Let’s review how to setup a division calculation. 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 Cranmer 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 your Cranmer 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 to the left of the dividend.
Short Division with Integer Remainders
Let’s review the division process. First, we divide the first digit of the divisor into the first digit or the first two digits of the dividend. The location of the partial quotient is determined by the first digit of the divisor.
If the number of digits we use in the divisor equals the number of digits we use in the dividend, we apply the “equal, shift 2 left” principle. This means we move 2 columns to the left of the dividend and then set the result of the division calculation in this column.
If the number of digits we use in the divisor doesn’t equal the number of digits we use in the dividend, we apply the “not equal, shift 1 left” principle. In this case we move 1 column to the left and set the results of the division calculation in this column.
Now multiply the number that you just entered by the divisor. Remember, in this book, the product of two single digits is always a 2 digit number. Then subtract the result from the dividend. This gives you a partial dividend.
If the partial dividend is greater than the divisor, repeat the division process by dividing the first digit of the divisor into either the first digit or first 2 digits of the new partial dividend, setting the result in the correct column, multiplying the result by the divisor and subtracting the product from the partial dividend.
The division process ends when the partial dividend is 0 or less than the value of the divisor.
The columns for the quotient are determined by adding the number of digits in the divisor and adding 1 for the process of division. The quotient is the number to the left of this column. The remainder is the number to the right of this column.
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
Example: 674,825 divided by 7
Example: 161,832 divided by 8
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 would shift the dividend 3 columns to the left. So, a four digit dividend would be entered in column 7, 4 columns for the dividend and 3 columns for the remainder.
The divisor is entered from the left edge of the Cranmer abacus regardless of whether the remainder is an integer or a decimal.
Then we follow the short division process. This process remains 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: 7,458 divided by 8
Example: 19,799 divided by 5
Example: 75,339 divided y 6
Example: 66,489 divided by 3
Example: 949,364 divided by 9
Example: 7,750,373 divided by 7