Adding 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 Addition

In the previous pages, we studied the five (5) extras principle. We learned how to add and subtract the integers 1, 2, 3, 4, and 5 when the exact number of beads isn’t available.

The five (5) extras principle is:

• Set (add) 5 and clear (remove) the extra

• Clear (remove) 5 and set (add) the extra.

Now, let’s consider the situation where you want to add 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. In this situation, you will add 10 (which will be too many) and then remove the extra. For example:

• We want to add 1. Instead, we add 10 and remove the extra, 9. (10 – 9).

• We want to add 2. Instead, we add 10 and remove the extra, 8. (10 – 8)

• We want to add 3. Instead, we add 10 and remove the extra, 7. (10 – 7)

• We want to add 4. Instead, we add 10 and remove the extra, 6. (10 – 6)

• We want to add 5. Instead, we add 10 and remove the extra, 5. (10 – 5)

• We want to add 6. Instead, we add 10 and remove the extra, 4. (10 – 4)

• We want to add 7. Instead, we add 10 and remove the extra, 3. (10 – 3)

• We want to add 8. Instead, we add 10 and remove the extra, 2. (10 – 2)

• We want to add 9. Instead, we add 10 and remove the extra, 1. (10 – 1)

This is the ten (10) extras principle: Add 10 and remove the extra.

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

Adding using the Ten (10) Extras Principle

This seems simple enough. When we need to add 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. In this principle we will set 1 bead left (to add 10) and then clear (remove) the extra beads from the bar to get the number that you originally wanted to add.

Examples

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

• Example: 9 + 1

• Example: 9 + 2

• Example: 9 + 3

• Example: 9 + 4

• Example: 9 + 5

• Example: 9 + 6

• Example: 9 + 7

• Example: 9 + 8

• Example: 9 + 9

• Example: 64 + 96

• Example: 123 + 987

• Example: 987 + 239

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.