Basic Division

Short Course 

This is a short course (slide show) on how to divide with single digits.  All of the examples in this show use one 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 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.   

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 to the left of the dividend.

Basic Division Calculations

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 page, we will limit our calculations to only a single digit divisor and a one- or two-digit dividend. Now, let’s look at the detailed 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?  That depends on the number of digits we use in the divisor and the number of digits we use in dividend:

      • 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. For example, 4 / 2 – both the divisor and dividend are single digits) then we enter the result of division, 2 columns to the left of the dividend.

      • 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. For example, if we want to divide 4 into 12.  We can’t divide 4 into 1, so we divide 4 into 12. In this example, the number of digits in the divisor (1) is not equal to the number of digits used in the dividend (2). So, we enter the result of the division, 1 column to the left of the dividend.

      • 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 (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 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

This may sound a little complicated. So let’s use some examples to show how the process works. Click on the link to show the steps to calculate the answer. 

• Example: 9 divided by 3

• Example: 24 divided by 6

• Example: 36 divided by 4

• Example: 42 divided by 7

• Example: 56 divided by 8

• Example: 72 divided by 9

Build Your Skill

Now you are ready to try some calculations on your own. Click on problems and their solutions to test your skill.