Subtracting with Five Extras

Short Course

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

The Five (5) Extra Principle for Subtraction

The five (5) extras principle for subtraction is the reverse of the five (5) extras principle for addition. Instead of adding the integers 1, 2, 3, 4 or 5, we want to subtract them. In this situation, the exact number of beads we want to subtract aren’t available below the bar, but the 5 bead is set. To perform this calculation, we remove the 5 bead (which is too much unless you want to subtract 5) and add the extra.

• • • • We want to subtract 1. Instead, we remove 5 and add the extra, 4. (-5 + 4).

      • We want to subtract 2. Instead, we remove 5 and add the extra, 3. (-5 + 3)

      • We want to subtract 3. Instead, we remove 5 and add the extra, 2. (-5 + 2)

      • We want to subtract 4. Instead, we remove 5 and add the extra, 1. (-5 + 1)

      • We want to subtract 5. Nothing extra (-5 + 0)

This is five (5) extras principle for subtraction: Remove 5 and add the extra.

Subtracting using the Five (5) Extras Principle

When we need to subtract the integers 1, 2, 3, 4, or 5, but the beads we need below the bar aren’t available and the 5 bead is in use, then we can use the five (5) extras principle for subtraction. In this principle, we remove the 5 bead from above the bar (clear 5) and then add (set) the extra beads to the bar to get the number that you originally wanted to subtract.

Important: To apply the five (5) extra principle for subtraction, the most efficient way to move your fingers is to apply the beads below the bar first and then clear the 5 bead in one continuous motion. So we execute the steps of the five (5) extras principle for subtraction 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.

Examples

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

• Example: 5 - 1

• Example: 5 - 2

• Example: 5 - 3

• Example: 5 - 4

• Example: 5 - 5

• Example: 876 - 433

• Example: 5,687 - 2,543

• Example: 875,567 - 441,237

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.