Mind Math

Soroban Abacus Tutorial

The Soroban is a Japanese abacus used for calculations. It consists of rods with beads that represent numbers.

How to Use:

• Each rod represents a digit in a number.
• The beads above the horizontal bar represent 5 each.
• The beads below the horizontal bar represent 1 each.
• To calculate, move the beads toward the horizontal bar.
• The first rod is the rightmost one and it is the ones place, the second one is the tens place, and so on.

Keyboard Navigation:

• Right and left arrow key to move between the columns
• Up and down arrow key to add or to remove the lower beads to the horizontal bar
• Page Up and page down key to add or to remove uppoer bead to the horizonal bar
• Shift + Up Arrow and Shift + Down Arrow key to add or to remove the upper bead to the horizontal bar
• Shift + Enter to reset the abacus

Example:

To represent the number 7, on the first rod,:

• Move one bead above the bar (5).
• Move two beads below the bar (1 + 1).

To represent the number 27, on the first rod,:

• Move one bead above the bar (5).
• Move two beads below the bar (1 + 1).
• On second rod, move two beads below the bar (1 + 1).

Big Friend Formula:

When we need to borrow 10 from the next (left) rod to add or subtract a number, it is called the "Big Friend" formula. For example, we want to add 8 to 7. So the first rod already has 7. Where do we get another 8 to add? In this case, we need to borrow 10 from the next (left) rod, that is, we add 1 to the next rod and subtract 2 from the first rod. So the sum is 15. So for addition the Big Friend formulas are:

• +9 = +10 -1
• +8 = +10 -2
• +7 = +10 -3
• +6 = +10 -4
• +5 = +10 -5
• +4 = +10 -6
• +3 = +10 -7
• +2 = +10 -8
• +1 = +10 -9

Similarly, for subtraction Big Friend formulas are:

• -9 = -10 +1
• -8 = -10 +2
• -7 = -10 +3
• -6 = -10 +4
• -5 = -10 +5
• -4 = -10 +6
• -3 = -10 +7
• -2 = -10 +8
• -1 = -10 +9

Small Friend Formula:

The Small Friend formula is, on the other hand, used when adding or subtracting numbers require borrowing from the SAME rod. For example, you already have one bead, now you want to add four more with it. In this you do not have four free beads. So you need to borrow the upper bead 5 and remove the lower bead 1. So all these small friend formulas are,

• +4 = +5 -1
• +3 = +5 -2
• +2 = +5 -3
• +1 = +5 -4

Similarly,

• -4 = -5 +1
• -3 = -5 +2
• -2 = -5 +3
• -1 = -5 +4

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