Abacus for Children — Level 3· Lesson 4 of 10

மூன்று இலக்கங்களில் 5-விதி

5-Rule in Three-Digit Numbers

~13 min

Free

Apply the 5-complement rule to hundreds, tens, and ones rods independently. The same rule you know from single-digit work now operates on three rods.

By the end of this lesson you will be able to— இந்த பாடத்தின் இறுதியில்

  • Apply the 5-complement rule to any rod in a three-digit calculation
  • Recognise which rod needs the 5-rule in a given problem
  • Solve problems where 5-rule fires on the ones, tens, or hundreds rod

Let's Learn

What you will learn today

Apply the 5-complement rule on any rod in a 3-digit addition or subtraction problem.

🔁

Recall: the 5-rule

5-rule for addition: when lower beads can't fit the number directly on ONE rod, push upper bead DOWN (+5) and 5-complement lower beads DOWN (−complement). 5-rule for subtraction: upper bead UP (−5), 5-complement lower beads UP (+complement).

The 5-rule from Level 2 applies to every single rod — ones, tens, or hundreds. When you are adding or subtracting on one rod and need the 5-rule, you apply it on that rod only. The other rods are unaffected. Same rule, bigger numbers.

5-rule on the ones rod (in a 3-digit context)

Example: 143 + 4 = 147. Hundreds and tens are unchanged (1 and 4 stay). Ones: 3 + 4 → 5-rule on ones: upper bead down (+5), 1 lower bead down (−1). Net: 3+4=7. Others: unchanged.

  • Hundreds: 1 (unchanged)
  • Tens: 4 (unchanged)
  • Ones: 3 → add 4 → 5-rule: upper bead down, 1 lower bead down → 7

📐 143 + 4 = 147

Ones rod: starts at 3. Add 4: 3+4=7. Need 5-rule (can't push 4 lower beads when only 1 space left). Upper bead down (+5), complement of 4 is 1 → 1 lower bead down (−1). Result: upper + 2 lower = 7.

Hunds
|
Tens
|
Ones
147

5-rule on the tens rod

Example: 131 + 30 = 161. Ones: 1 unchanged. Tens: 3 + 3 → 5-rule on tens: upper bead on tens down (+50), complement of 3 is 2 → 2 lower beads on tens down (−20). Net: +30. Hundreds: 1 unchanged.

  • Adding 3 to the tens rod showing 3: 3+3=6
  • Can't push 3 lower beads (room for only 2)
  • 5-rule: upper bead on tens DOWN (+50), 2 lower beads on tens DOWN (−20). Net: +30. Rod now shows 6.

📐 131 + 30 = 161

Ones: 1 unchanged. Tens: 3 + 3 = 6 (5-rule on tens rod). Hundreds: 1 unchanged.

Hunds
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Tens
|
Ones
161

📐 5-rule on the hundreds rod

Example: 314 + 200 = 514. Hundreds: 3 + 2 → 5-rule on hundreds: upper bead on hundreds down (+500), complement of 2 is 3 → 3 lower beads on hundreds down (−300). Net: +200. Rod now shows 5 (upper bead only = 500).

Hunds
|
Tens
|
Ones
514
💡

The 5-rule never crosses rods

This is key: the 5-rule always stays on one rod. It does not affect tens when you apply it on ones. It does not affect hundreds when you apply it on tens. You adjust upper and lower beads on the same rod only.

🔍

Don't confuse 5-rule with 10-rule

5-rule: result fits on ONE rod (0–9 or 0–9 × rod's value), but you can't add directly. 10-rule: result overflows the rod (e.g., ones gives > 9 → must carry to tens). If the rod shows 7 and you add 4: 7+4=11 → that overflows the ones rod. That is NOT the 5-rule — it needs the 10-rule!

✏️

224 + 3 = 227

Add 3 to the ones rod of 224 using the 5-rule if needed.

🎯 Goal: Show the number 227

Hunds
|
Tens
|
Ones
Your abacus shows: 0

Challenge Round

313 + 30 = 343

Start with 313. Add 30 (only the tens rod changes). Apply the 5-rule on the tens rod.

🎯 Goal: Show the number 343

Hunds
|
Tens
|
Ones
Your abacus shows: 0
🌟

The 5-rule from Level 2 applies to any rod: ones, tens, or hundreds. Always apply it on the single rod where you can't add/subtract directly without crossing 5. The other rods are untouched.

Next: 10-Rule Carry in Three-Digit Addition.

Key Points

  • 5-rule applies to ONE rod at a time — ones, tens, or hundreds
  • On the ones rod: same as Level 2
  • On the tens rod: upper bead (+50), 5-complement lower beads (−10 each)
  • On the hundreds rod: upper bead (+500), 5-complement lower beads (−100 each)
  • The 5-rule never causes a bead to move to a different rod
G

Glossary

சொல் அகராதி

5-complement

5-நிரப்பு

Same rod

அதே தண்டு

Upper bead (hundreds)

நூறுகள் மேல் மணி

No carry

கொண்டுசெல்வதில்லை

In-rod rule

உள் தண்டு விதி

Practice Activities

Speed Drill · விரைவு பயிற்சி

5-Rule Practice — Any Rod

8 problemsType the answer, press EnterYour time is recorded — try to beat it next time!

Quizவினாடி வினா

Answer each question to check your understanding.

Question 1 of 4

3 உள்ள ஒன்றுகள் தண்டில் 4 கூட்டுகிறீர்கள். விடை 7. எந்த விதி?

You are adding 4 to the ones rod which shows 3. The result (7) fits on one rod. Which rule applies?

Match the Termsபொருத்துக

Click a term on the left, then click its matching definition on the right.

MMatch terms to their definitions

Click a term, then click its matching definition.

Terms

Definitions

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