Subtracting with Ten Extras

Short Course

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

The Ten (10) Extras Principle for Subtraction

In the Abacus Addition pages, you studied the ten (10) extras principle for addition and applied it to addition calculations. Now, let’s see how this principle is applied to subtraction.

Let’s consider the situation where you want to subtract an integer 1, 2, 3, 4, 5, 6, 7, 8, or 9 and the exact number of beads isn’t available, and the 5 bead isn’t available. This means that we can’t use the five (5) extras principle for subtraction. In this situation, you will subtract 10 (which will be too many) and then add the extra. For example:

• • • • We want to subtract 1. Instead, we subtract 10 and add the extra, 9. (-10 + 9).

      • We want to subtract 2. Instead, we subtract 10 and add the extra, 8. (-10 + 8)

      • We want to subtract 3. Instead, we subtract 10 and add the extra, 7. (-10 + 7)

      • We want to subtract 4. Instead, we subtract 10 and add the extra, 6. (-10 + 6)

      • We want to subtract 5. Instead, we subtract 10 and add the extra, 5. (-10 + 5)

      • We want to subtract 6. Instead, we subtract 10 and add the extra, 4. (-10 + 4)

      • We want to subtract 7. Instead, we subtract 10 and add the extra, 3. (-10 + 3)

      • We want to subtract 8. Instead, we subtract 10 and add the extra, 2. (-10 + 2)

      • We want to subtract 9. Instead, we subtract 10 and add the extra, 1. (-10 + 1)

This is the ten (10) extras principle for subtraction: Subtract 10 and add the extra.

Important: To apply the ten (10) extras principle in subtraction, the most efficient way to move your fingers is to remove the beads from the column to the left (subtract 10) first and then add extra beads in the current column. So we execute the steps of the ten (10) extras principle in the same order as the way we just described. This technique will become important as you develop more speed in your calculations.

Subtracting using the Ten (10) Extras Principle

This principle is the opposite technique from the one we used to add integers. But this should make sense because subtraction is all about removing integers. When we need to subtract the integers 1, 2, 3, 4, 5, 6, 7, 8, or 9, but the beads we need aren’t available, then we can use the ten (10) extras principle for subtraction. In this principle we will clear 1 bead left (to subtract 10) and then add (set) the extra beads to the bar to get the number that you originally wanted to subtract.

Examples

Let’s look at some examples of how this principle is applied:

• Example: 10 - 1

• Example: 10 - 2

• Example: 10 - 3

• Example: 10 - 4

• Example: 10 - 5

• Example: 10 - 6

• Example: 10 - 7

• Example: 10 -8

• Example: 10 - 9

• Example: 62 - 54

• Example: 78 - 59

• Example: 841 - 655

• Example: 3,834 - 2,945

• Example: 73,844 - 19,155

• Example: 88,527 - 19,589

• Example: 400 - 2

• Example: 90,000 - 11

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.