Adding Decimals and Columns of Decimals

Short Course

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

Entering Decimals

The only difference between adding integers and adding decimals is the location of the decimal point. When using the Cranmer Abacus, the decimal point is called the unit mart. You may recall, from previous chapters, we pointed out that the Cranmer Abacus (as purchased from the American Printing House for the Blind) contains 4 raised marks on the bar in the middle of the abacus. 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.

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 several examples of how to enter decimal numbers.

• Example: Enter $483.30

• Example: Enter the number for Pi ( to 12 decimals places)

Adding Decimals

Now, let’s add 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 add the digits of each of the numbers directly or using the ten (10) extras principle and the five (5) extras principle for addition and subtraction like you did in previous chapters. You would ask these questions:

• Can the digit be added directly?

• If not, can the digit be added using the five (5) extras principle?

• If not, can the digit be added digit using the ten (10) extras principle and the five (5) extras principle for addition or subtraction?

Examples

Now, let’s look at several examples .that willLet’s see how this works in some examples:

• Example: 3.7692 + .0419

• Example: 6.5926 + 596.7465

• Example: 38,208.33 + 9,448.48

Adding Columns of Decimal Numbers

Now, let's learn how to add decimal numbers and columns of decimal numbers. The same principles that you have learned before also apply to adding columns of decimal numbers. Just be sure to determine the unit mark and keep all of the numbers you are adding correctly aligned with this unit mark.

Examples

Here are some examples:

• Example: $8.26 + $8.82 + $201.17 + $250.62

• Example: $345.60 + $606.69 + $5.98 + $167.95

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.