Subtracting Decimals and Columns of Decimals

Entering Decimals

Up to this point, all the numbers that we have entered into our Cranmer Abacus have been integers.  The implied “decimal point” has been at the right edge of the abacus.  This means that each unit mark acts like a comma to separate each group of three digits.  However, to enter a decimal number, we will “move” the decimal point to one of the unit marks. But, how do we know which unit mark to use?

1. First, move your index finger across the bar from right to left.  Make sure that you can feel each unit mark, every three columns.

2. Then, count the decimal places in each number that you are adding. The number with the largest number of decimal places will determine which unit mark you should use as your decimal point.

3. If the largest number of decimal digits you are adding is 3 or less, the first unit mark will be the point you should use to locate your decimal place.  The decimal portion of the number will be entered to the right of the unit mark, in columns 3, 2, and 1.  The integer portion of the number will be entered to left of this mark, in columns 4 through 13.

4. If the largest number of decimal digits is 4, 5, or 6, then use the second unit mark.

5. For numbers with 7, 8, or 9 decimal digits, you should use the third unit mark.

6. Lastly, you will need to use the fourth unit mark for numbers with 10, 11, or 12 decimal digits.

You will need to be careful that you align each number correctly. Misaligning numbers and decimal points will result in an incorrect answer to your addition problem.

Examples

Now let's look at some examples: 

• Example:  Enter $483.30

• Example:  Enter the number (to 12 decimal places) of Pi 

Subtracting Decimals

Now, let’s subtract some decimal numbers. You will use the same principles as you used in previous calculations there are some additional questions that you should ask first:

• • • Which decimal number has the largest number of digits to the right of the decimal point?

    • How many digits are there to the right of the decimal point in this number? 

    • Which unit mark will allow you to set all the digits in this decimal number? Use this unit mark to set the first number.

Then, you can subtract the digits of each of the numbers by pulling beads directly from the bar or using one or more of the exchanges: 5 to 4 exchange, 10 to 9 exchange, 50 to 49 exchange and the 100 to 99 exchange.

Examples

Let’s see how this works in some examples:

• Example:   3.8111 – 1.0419

• Example:  596.7465 – 7.5926  

• Example:  38,208.33 – 9,449.48 

Subtracting Columns of Decimals

In this section, you will learn how to subtract columns of decimal numbers. The same principles that you have learned before also apply to subtracting columns of decimal numbers. Just be sure to determine the unit mark and keep all the numbers you are subtracting correctly aligned with this unit mark. 

• Example:  $468.87 – $8.26 – $8.82 – $201.17   

• Example:  $1,126.22 – $345.60 – $5.98 – $606.69 

Build Your Skill

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