The 49 to 50 Exchange

Counting to 50 with your fingers

In the previous sections,  we counted to 5 and 10 using our fingers. Now, in this section, we will continue counting to 50 using both hands. 

1. 1. To start, make sure that none of your fingers are touching a surface

   2. To count from 10 to 40, by pressing each finger on your left hand to the surface. Don’t press you thumb down yet.

   3. Next, with all four of your fingers toughing the surface, count from 1 to 4 by pressing each finger on your right hand to the surface.  You have counted to 44.

   4. Continuing to count to 45, press your thumb on your right hand to the surface and raise the other four fingers in one continuous motion.

   5. Now, to count from 6 to 9, keep your thumb on the surface and press each finger, in order, until the remaining 4 fingers, on your right hand, are touching the surface.  You have now counted to 49.

   6. The final step to count to 50, is to first clear all your fingers on your right hand and then clear all the fingers in your left hand at the same time you press your left thumb to the surface.  This leaves only your left thumb touching the surface.

Why does this work?  As you earlier , each finger has a value of 1 and the thumb has a value of 5. So, the value of each number is increased by 1 as we press the finger to the surface. One finger equals 1, two fingers equal 2, three fingers equal 3 and four fingers equals 4.  The thumb has a value of 5 so pressing just the thumb to the surface equals 5.  Pressing the thumb and one finger (5 + 1) equals 6. The thumb and 2 fingers (5 + 2) equal 7. The thumb and 3 fingers (5 + 3) equal 8 and the thumb and 4 fingers equal 9. The fingers on your left had have a value of 10 and the left thumb has a value of 50.  

Counting to 50 with the Abacus

How do we count to 49 and then count to 50 with an abacus?  In each step, we push 1 bead to the bar.  Then when all the beads are used below the bar, we push the 5 bead to the bar and clear the 4 beads below the bar.  To count from 9 to 10, we push 1 bead to the bar in the tens column and clear all the beads in the ones column.

Adding using the 49 to 50 Exchange

As you saw in the previous section, counting to 5 involves using all the beads below the bar and the 5-bead.  Now, let’s add some single numbers and use the 49 to 50 exchange: 

• Add:  49 + 1

• Add: 48 + 2

• Add:  47 + 3

• Add:  46 + 4

Examples

These examples we will use the 49 to 50 exchange in any column when no beads are available below the bar and the 5-bead is not being used in the column to its left.  Each addition will start in the left most column and continue in each column moving to the right until all the columns have been added. 

• Example:  39 + 13

• Example:  24 + 29

• Example:  261 + 262

• Example:  2,917 + 2,530

• Example:  13,138 + 21,916

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.