mystical_life

1. What is the 5’s complement? On an abacus, each rod has: 1 upper bead worth 5 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: 1 → complement is 4 (1 + 4 = 5) 2 → complement is 3 (2 + 3 = 5) 3 → complement is 2 (3 + 2 = 5) 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: Take away the complement Add 1 bead from the upper deck (worth 5) Example: Add 3 + 4 3 lower beads are already there. We can’t add 4 directly (would need 7 beads). Instead: remove the complement of 4 (which is 1), then add the upper bead (5). 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 You have 6 (5 upper + 1 lower). You can’t remove ...