Addition with soroban

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This chapter is of utmost importance for learning calculation with the soroban. My advice is to do as many exercises as possible in order to master the addition rules that we will see.

As a general rule, there are two steps:

• You have to represent the first term of the addition on the sorban
• Add the digits of the second term to it, preferably starting with the units place.

However, there are cases where the beads to be added are not available. The solutions for each case will be developed in this chapter.

Case with all beads to be added available

For example, consider the operation :

31 + 12

First, the first term 31 must be entered on the soroban, of course by activating a One Bead in the units column and 3 One Beads in the tens column:

Then you continue with the previous state and to add 12,

• you activate 2 more One Beads in the units column and
• 1 One Bead on the tens column.

You then read the result on the soroban which is the number 43 :

Another example:

62 + 17

Write the first term 62 on the soroban, by activating

• 2 One Beads in the units column and
• the Five Bead and a One Bead in the tens column:

Then you continue with the previous state and to add the number 17,

• you activate the Five Bead and 2 additional One Beads on the units column
• and 1 One Bead on the tens column.

You then read the result on the soroban which is the number 79 :

Example involving the hundreds column:

254 + 630

Let's write the first term 254 on the soroban, by activating

• 4 One Beads in the units column,
• the Five Bead in the tens column and
• 2 One Beads in the hundreds column:

Then, to add 630, you continue with the previous state and activate

• 3 more One Beads in the tens column and
• the Five Bead and 1 One Bead on the hundreds column.

You then read the result on the soroban which is the number 884:

3^rd exercise

In this exercise you will have a series of addition operations to perform on the virtual soroban.

Click on the following button to start:

Case with beads to be added not available

For example, the operation :

24 + 43

The first term 24 must be entered on the soroban, by activating

• 4 One Beads in the units column and
• 2 One Beads in the tens column:

Then, to add the number 43, you continue with the previous state and you would activate

• 3 more One Beads in the units column and
• 4 One Beads on the tens column.

However, the beads needed for activation are not available. In such cases, you should use the Five Bead if it is available:

• Instead of activating 3 One Beads, we proceed with the activation of the Five Bead and the deactivation of 2 One Beads. Indeed: 3 = 5 - 2
• Instead of activating 4 One Beads, we proceed to the activation of the Five Bead and the deactivation of 1 One Beads. Indeed: 4 = 5 - 1

We then read the result on the soroban which is the number 67 :

Remember the following rules:

Adding	Solution (*)	Indeed	Rule to remember (*)
1	+ 1 FB – 4 OB	1 = 5 - 4	+ 1 OB equivalent to + 1 FB – 4 OB
2	+ 1 FB – 3 OB	2 = 5 - 3	+ 2 OB equivalent to + 1 FB – 3 OB
3	+ 1 FB – 2 OB	3 = 5 - 2	+ 3 OB equivalent to + 1 FB – 2 OB
4	+ 1 FB – 1 OB	4 = 5 - 1	+ 4 OB equivalent to + 1 FB – 1 OB

(*) FB = Five Bead - OB = One Bead.

4^rd exercise

In this exercise you will have a sequence of addition operations to perform on the virtual soroban. The 4 rules above must be well known to perform this exercise.

Click on the following button to start:

Other cases with beads to be added not available

For example, the operation :

38 + 84

The first term 38 must be entered on the soroban, by activating

• 3 One Beads and the Five Bead in the units column and
• 3 One Beads in the tens column:

Then, to add the number 84, you continue with the previous report and you would activate

• 4 more One Beads in the units column and
• the Five Bead and 3 One Beads on the tens column.

However, the beads needed for activation are not available. In these cases, 1 One Bead from the column following the current column must be used, which id counted 10 :

• Instead of adding 4, we will add 10 (Activate 1 OB on the tens column) and subtract 6 (Deactivate 1 OB and 1 FB on the units column). Indeed: 4 = 10 - 6
• Instead of adding 8, we will add 10 (Activate 1 OB in the hundreds column) and subtract 2 (deactivate 2 OB in the tens column). Indeed: 8 = 10 - 2

We then read the result on the soroban which is the number 122 :

Remember the following rules:

Adding	Solution	Rule to remember
1	1 = 10 - 9	+ 1 is equivalent to + 10 and - 9
2	2 = 10 - 8	+ 2 is equivalent to + 10 and - 8
3	3 = 10 - 7	+ 3 is equivalent to + 10 and - 7
4	4 = 10 - 6	+ 4 is equivalent to + 10 and - 6
5	5 = 10 - 5	+ 5 is equivalent to + 10 and - 5
6	6 = 10 - 4	+ 6 is equivalent to + 10 and - 4
7	7 = 10 - 3	+ 7 is equivalent to + 10 and - 3
8	8 = 10 - 2	+ 8 is equivalent to + 10 and - 2
9	9 = 10 - 1	+ 9 is equivalent to + 10 and - 1

5^rd exercise

In this exercise you will have a sequence of addition operations to perform on the virtual soroban. The 9 rules above must be well known to perform this exercise.

Click on the following button to start:

Case with beads to be added and also beads to be subtracted not available

For some operations, we need to use a One Bead from the column following the current column (which is counted 10), and deactivate beads from the current column. But, we find that these are not available.

For example, consider the operation :

75 + 68

The first term 75 must be entered on the soroban, by activating

• the Five Bead on the units column and
• the Five Bead and 2 One Beads in the tens column:

Then, to add the number 68, you continue with the previous state and you would activate

• the Five Bead and 3 One Beads on the units column and
• the Five Bead and 1 One Bead on the tens column.

However, the beads needed for activation are not available. In these cases, a One Bead from the column following the current column must be used, which is counted 10 :

• Instead of adding 8, we will add 10 (Activate 1 OB on the tens column) and we should subtract 2 (Deactivate 2 OB on the units column). In effect: 8 = 10 - 2.
  But, as you can see on the abacus, there are no 2 One Beads available to deactivate. In this case, instead of deactivating 2 One Beads, we will deactivate the Five Bead and activate 3 One Beads. Indeed: 2 = 5 - 3.
  The global operation is therefore: +8 equivalent = +10-5+3.
• In the tens column, instead of adding 6, we will add 10 (Activate 1 OB on the hundreds column) and subtract 4 (deactivate 4 OB on the tens column). Indeed: 6 = 10 - 4.
  But, as you can see on the abacus, there are no 4 One Beads available to deactivate. In this case, instead of deactivating 4 One Beads, we will deactivate the Five Bead and activate 1 One Bead. Indeed: 4 = 5 - 1.
  The overall operation is therefore: +6 equivalent = +10-5+1.

We then read the result on the soroban which is the number 143 :

Remember the following rules:

Adding	Solution	Rule to remember
6	6 = 10 – 5 + 1	+ 6 is equivalent to + 10, - 5 and +1
7	7 = 10 – 5 + 2	+ 7 is equivalent to + 10, - 5 and +2
8	8 = 10 – 5 + 3	+ 8 is equivalent to + 10, - 5 and +3
9	9 = 10 – 5 + 4	+ 9 is equivalent to + 10, - 5 and +4

6^rd exercise

In this exercise, you will have a sequence of addition operations to perform on the virtual soroban. The 4 rules above must be well known to perform this exercise.

Click on the following button to start:

How to perform the operations?

To add a digit in a column :

1. Activate the necessary beads if they are available. The beads to be activated according to the number to be added are detailed in the 2^nd column of the table below.
2. If at least one bead to be activated is unavailable, the solution is to use the Five Bead from the current column as detailed in the 3^rd column of the table below.
3. If neither of the above solutions is possible, then a One Bead from the next column must be activated and beads from the current column must be deactivated as detailed in the 4^th column of the table below.
4. When applying the previous solution, you will find cases where the One Beads to be deactivated are not available. In these cases, it is necessary to resort to the deactivation of the Five Bead as detailed in the 5^th column of the table below.

The cells in the table below with the word "Not avail." indicate impossible cases.

The One Bead to be activated in the next column is marked OB10 because it is counted by 10.

Summary of the rules for performing addition operations

As an indication, here are all the addition operations and the solutions to perform them. I do not ask you to remember this table, but to remember the procedure explained above.

7^rd exercise

In this exercise you will have a sequence of addition operations to perform on the virtual soroban. All the addition rules must be well known to perform this exercise.

Click on the following button to start:

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