Subtracting Decimals and Columns of Decimals

Short Course

This is a short course (slide show) in the basic concepts to subtract using the Five (5) Extras Ten (10) Extras principles.

Entering Decimals

When using the Cranmer Abacus, the decimal point is called the unit point. They are located between the columns 3 and 4, between columns 6 and 7, between columns 9 and 10, and between columns 12 and 13. These raised bumps are called unit marks and organize the columns into groups of three. 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. Count the decimal places in each number that you are subtracting. The number with the largest number of decimal places will determine which unit mark you should use as your decimal point.

2. 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.

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

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

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

Subtracting Decimals

As always, 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 subtraction problem. But the principles for subtracting remain the same. To review from Chapter 12, to subtract two integers, you may need to:

• Subtract a digit directly

• Add or subtract a digit using the five (5) extras principle

• Subtract a digit using the ten (10) extras principle and the five (5) extras principle for addition or subtraction using one or more columns

Before we look at some examples, let’s summarize all the steps we have learned to apply these principles to subtraction calculations.

Examples

Now, let’s look at some examples:

• Example: 9,572.97 – 2,851.53

• Example: 5,892.298 – 205.881

• Example: 61.5510 – 54.1648

• Example: 51,460.31 – 8,323.06

• Example: 515.0076 – 274.0166

• Example: 24.00869 – 7.309

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.