Abacus Math Program – Lesson 4 – Simple Multidigit Addition and Subtraction
With the basic abacus movements learned in the first 3 lessons on a single rod, we are now ready to apply our knowledge to more than 1 rod. If you have not looked at the first 3 lessons or are new to abacus math, I suggest you take a look at Lesson 1, Lesson 2, and Lesson 3 first which will make your progress easier and faster. The power of abacus math lies in the treatment of problems 1 digit at a time, 1 rod at a time. Reducing arithmetic problems down to single digit operations on the abacus, a fundamental technique of abacus math and the goal of the four arithmetic algorithms, increases calculation speed and improves calculation accuracy. Since each rod on the abacus represents 1 digit of a base 10 number we reduce the required bead movements needed to a single rod.
As we progress we will learn a simple set additional bead movements, 6 in all, that manage interactions between rods, i.e. borrow and carry, and within rods. For now we will restrict our discussion to working with 1 digit at a time, a single rod at a time on the abacus. The methods employed in lesson 4 can be extended to numbers of any size. So for larger numbers we simple treat the numbers one digit at a time from left to right on the abacus. Processing math and arithmetic calculations from left to right which is opposite of how most of us are taught will have the advantage of lining up our calculation method with exactly how we read and say numbers. So abacus math students can immediately begin calculations as numbers are read or heard and do not have to wait until the entire number is known.
In the examples, numbers within a circle show the order in which the beads should be moved. Numbers at the tip of an arrow show the value of the beads to be moved.
Example #1: In this example we start by adding the number 15 to the abacus. First add 1 lower bead with the thumb on rod A and the upper 5 bead with the index finger on rod B. Next add 4 to 15 by adding 4 lower beads with the thumb on rod B. The interim sum on the abacus is now 19. Next subtract 1 from 19 by moving 1 lower bead with the index finger away from the bar on rod B. The interim sum is now 18. Lastly subtract 17 from 18 by firstly subtracting 1 from 1 on rod A. Next subtract 7 from 8 on rod B by removing the upper 5 bead and 2 lower beads with the index finger on rod B. The final sum is 1.
Example #2: In this example we start by adding 17 to the abacus. First add 1 with the thumb on rod A and pinch with the thumb and index finger the upper 5 bead and 2 lower beads on rod B. Next subtract 12 from 17 by first subtracting 1 from 1 on rod A. Then subtract 2 from 7 on rod B by removing 2 lower beads with the index finger. The interim sum is now 5. Add 10 to 5 by adding 1 to 0 on rod A with the thumb. The interim sum is now 15. Lastly, add 4 to 15 by moving 4 lower beads with the thumb on rod B to the bar. The final sum on the abacus is 19.
Example #3: In this example we start by adding 18 to the abacus. First add 1 to rod A by adding 1 lower bead. Then add 8 to rod B by pinching the upper 5 bead with 3 lower beads. Next subtract 6 from 18 on the abacus by first moving the upper 5 bead with the index finger away from the bar on rod B. Then move 1 lower bead with the index finger away from the bar on rod B. The interim sum is now 12. Add 5 to 12 by moving the upper 5 bead with the index finger on rod B to the bar. The interim sum is now 17 on the abacus. Finally, subtract 15 from 17 on the abacus by first subtracting 1 from 1 on rod A. Then subtract 5 from 7 on rod B by moving the upper 5 bead with the index finger away from the bar. The final sum on the abacus is 2.
