Video 29- Addition of 5's complements on Abacus Tool @kidsknowledgepoint
1. What is the 5’s complement?
On an abacus, each rod has:
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1 upper bead worth 5
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4 lower beads worth 1 each
The 5’s complement of a number is the number you must add to it to make 5.
Example:
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1 → complement is 4 (1 + 4 = 5)
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2 → complement is 3 (2 + 3 = 5)
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3 → complement is 2 (3 + 2 = 5)
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4 → complement is 1 (4 + 1 = 5)
2. Why is it important?
a) Faster Addition
When adding a number that would go beyond 5 on a rod, we don’t count one bead at a time.
Instead, we:
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Take away the complement
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Add 1 bead from the upper deck (worth 5)
Example: Add 3 + 4
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3 lower beads are already there.
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We can’t add 4 directly (would need 7 beads).
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Instead: remove the complement of 4 (which is 1), then add the upper bead (5).
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Now total is 7 — done in fewer moves.
b) Faster Subtraction
When subtracting a number larger than the current lower beads, we borrow using complements.
Example: Subtract 4 from 6
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You have 6 (5 upper + 1 lower).
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You can’t remove 4 directly from 1 lower bead.
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Instead: remove the upper bead (5) and then add the complement of 4 (which is 1) to the lower deck.
c) Mental Math Boost
Understanding 5’s complements trains the brain to think in “shortcuts” rather than counting one by one — this is the essence of abacus speed.
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