நிரப்பு இணைகள் என்றால் என்ன?
What Are Complements?
Before learning the rules, you need to understand the idea: every number has a partner that makes a target. Discover the 5-family and 10-family pairs that unlock all abacus speed.
Let's Learn
What you will learn today
Understand what complement pairs are and why knowing them unlocks all abacus speed.
Quick recall from Level 1
Before we begin: how many lower beads are on each rod? What is the upper bead worth? What is 5 + 3 on the abacus? Good — you are ready for Level 2!
Welcome to Level 2! You already know every number 0–9 on the abacus and how to do simple addition. Now comes the real secret of abacus speed — complement pairs. Once you know these pairs, your fingers will move faster than your mind can count.
அபாகஸ் வேகத்தின் இரகசியம் இதோ — நிரப்பு இணைகள்.
What is a complement?
A complement is a partner number. Every number has a partner that adds up to a target. The target we care about most on the abacus is 5 and 10 — because those are the points where the abacus changes gears.
- The 5-target: which pairs of numbers add to 5?
- The 10-target: which pairs of numbers add to 10?
📐 5-complement pairs
These are the only two pairs that matter for the 5-family rule:
- 11 + 4 = 5 → (1 and 4 are each other's 5-complement)
- 22 + 3 = 5 → (2 and 3 are each other's 5-complement)
- 35 + 0 = 5 → (5 and 0 — but we rarely use this one)
📐 10-complement pairs
These are the pairs that matter for the 10-family rule (crossing to the tens rod):
- 11 + 9 = 10 → (1 and 9 are each other's 10-complement)
- 22 + 8 = 10
- 33 + 7 = 10
- 44 + 6 = 10
- 55 + 5 = 10
Why do we need these pairs?
On the abacus, sometimes you cannot add or subtract a number directly. The beads in the right position are not there. When that happens, you use the complement to approach from the other direction. The complement pair is your rescue partner.
Memory trick for 5-complement pairs
Hold up 5 fingers. Count: 1 finger is separate from 4 fingers. 2 fingers are separate from 3 fingers. The two groups are the complement pairs. You can always check by counting to 5.
5 விரல்களை நிமிர்த்துங்கள் — இரு குழுக்களில் பிரியுங்கள்.
Common confusion: mixing up 5-complement and 10-complement
Students sometimes use the wrong family rule. The question to ask yourself is: 'Am I working on one rod (ones only)? Then 5-family. Am I about to cross to the tens rod? Then 10-family.' More on this in Lessons 2–5.
Challenge Round
Recall challenge
Without looking above: what is the 5-complement of 3? What is the 10-complement of 4? What is the 10-complement of 9? Recall these before checking the answer.
You now know the two families of complement pairs: 5-family (1↔4, 2↔3) and 10-family (1↔9, 2↔8, 3↔7, 4↔6, 5↔5). These are the building blocks of all Level 2 work.
↪ Next: 5-Rule Adding — using the 5-complement to add when lower beads are full.
Key Points
முக்கிய குறிப்புகள்
- ✓5-complement pairs: 1↔4, 2↔3
- ✓10-complement pairs: 1↔9, 2↔8, 3↔7, 4↔6, 5↔5
- ✓A complement is the 'partner number' that reaches the target (5 or 10)
- ✓These pairs are your rescue plan when direct addition or subtraction fails
Glossary
சொல் அகராதி
Complement
நிரப்பு
5-family
5 குடும்பம்
10-family
10 குடும்பம்
Partner
இணை
Target
இலக்கு
Practice Activities
Quizவினாடி வினா
Answer each question to check your understanding.
4-இன் 5-நிரப்பு என்ன?
What is the 5-complement of 4?
Match the Termsபொருத்துக
Click a term on the left, then click its matching definition on the right.
Click a term, then click its matching definition.
Terms
Definitions