Subtraction with soroban

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If you have worked well the exercises in the previous chapter, then this chapter will be easy for you, as subtraction is the opposite of addition. However, I strongly advise you to do as many of the exercises in this chapter as possible.

Case with beads to be subtracted all available

Let's take the operation :

43 - 12

First, you have to enter the first term 43 on the soroban, of course by activating

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

Then you continue with the previous state and to subtract 12, you deactivate

• 2 One Beads in the units column and
• 1 One Bead in the tens column.

You then read the result on the soroban which is the number 31 :

Another example:

79 - 53

Write the first term 79 on the soroban, by activating

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

Then you continue with the previous state and to subtract 53, you deactivate

• 3 One Beads in the units column and

You then read the result on the soroban which is the number 26 :

Example involving the hundreds column :

487 - 205

Write the first term 487 on the soroban, by activating

• the Five Bead and 2 One Beads in the units column,
• the Five Bead and 3 One Beads in the tens column and
• 4 One Beads on the hundreds column:

Then you continue with the previous state and to subtract the number 205, you deactivate

• the Five Bead in the units column and
• 2 One Beads in the hundreds column.

You then read the result on the soroban which is the number 282 :

8^rd exercise

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

Click on the following button to start:

Case with unavailable beads to be subtracted

For example, the operation :

76 - 42

The first term 76 must be entered on the soroban, by activating

• the Five Bead and 1 One Bead in the units column and
• the Five Bead and 2 One Beads in the tens column:

Then you continue with the previous state and to subtract 42, you had to deactivate

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

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

• Instead of deactivating 2 One Beads, I proceed to deactivate the Five Bead and activate 3 One Beads. Indeed: 2 = 5 - 3
• Instead of deactivating 4 One Beads, I deactivate the Five Bead and activate 1 One Bead. Indeed: 4 = 5 - 1

I then read the result on the soroban which is the number 34 :

Remember the following rules:

Subtracting	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.

9^rd exercise

In this exercise you will have a sequence of subtraction 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 subtracted not available

For example, the operation :

216 - 27

The first term 216 must be entered on the soroban, by activating

• the Five Bead and 1 One Bead in the units column,
• 1 One Bead in the tens column and
• 2 One Beads in the hundreds column:

Then you continue with the previous state and to subtract the number 27, you had to deactivate

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

However, the beads needed for deactivation 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 subtracting 7, we subtract 10 (Deactivate 1 OB in the tens column) and add 3 (Activate 3 OB in the units column). Indeed: 7 = 10 - 3
• Instead of subtracting 2, we subtract 10 (Deactivate 1 OB in the hundreds column) and add 8 (Activate 1 FB and 3 OB in the tens column). Indeed: 2 = 10 - 8

We then read the result on the soroban which is the number 189 :

Remember the following rules:

Subtracting	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

10^rd exercise

In this exercise you will have a sequence of subtraction 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 subtracted and also beads to be added not available

For some operations, we need to use a One Bead from the column following the current column (which is 10), but the beads to be added are not available. For example, the operation :

132 - 76

The first term 132 must be entered on the soroban, by activating

• 2 One Beads in the units column,
• 3 One Beads in the tens column and
• 1 One Bead in the hundreds column:

Then you continue with the previous state and to subtract the number 76, you had to deactivate

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

However, the beads needed for deactivation are not available. In these cases, we have to use a One Bead from the column following the current column, which is counted 10 :

• Instead of subtracting 6, we subtract 10 (deactivate 1 OB in the tens column) and we should add 4 (activate 4 OB in the units column). Indeed: 6 = 10 - 4.
  But, as you can see on the abacus, there are no 4 One Beads available to activate. In this case, instead of activating 4 One Beads, we will activate the Five Bead and deactivate 1 One Bead. Indeed: 4 = 5 - 1.
  The overall operation is therefore : -6 equivalent = -10+5-1.
• In the tens column, instead of subtracting 7, we subtract 10 (deactivate 1 OB in the hundreds column) and we should add 3 (activate 3 OB in the tens column). Indeed: 7 = 10 - 3.
  But, as you can see on the abacus, there are no 3 One Beads available to activate. In this case, instead of activating 3 One Beads, we will activate the Five Bead and deactivate 2 One Beads. Indeed: 3 = 5 - 2.
  The overall operation is therefore : -7 equivalent = -10+5-2.

I then read the result on the soroban which is the number 56 :

Remember the following rules:

Subtracting	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

11^rd exercise

In this exercise you will have a sequence of subtraction 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 subtract a digit in a column :

1. Deactivate the necessary beads if they are available. The necessary beads to deactivate according to the number to be deducted are detailed in the 2^nd column of the table below.
2. If at least one bead to be deactivated 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 deactivated and beads from the current column activated 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 activated are not available. In these cases, it is necessary to activate the Five Bead as detailed in the 5^th column of the following table.

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

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

Summary of the rules for performing subtraction operations

As an indication, here are all the subtraction operations and the solutions for performing them. I am not asking you to remember this table, but to remember the procedure explained above.

12^rd exercise

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

Click on the following button to start:

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