5-விதி: கழித்தல்
5-Rule: Subtracting Across Five
When lower beads aren't showing enough to subtract, lift the upper bead and add back the partner. This is the mirror image of the addition rule.
Let's Learn
What you will learn today
Use the 5-complement rule to subtract when lower beads can't give enough.
Recall: 5-rule for addition
In the last lesson: to add 4 when lower beads are full, you pushed the upper bead down (+5) and 1 lower bead down (−1). Net: +4. Now we reverse the logic for subtraction.
Here's the new problem: your abacus shows 7 (upper bead down, 2 lower beads up). You need to subtract 4. You look at the lower beads — only 2 are showing! You can't remove 4 lower beads. The 5-rule rescues you again — but in reverse.
கழித்தல் கூட்டலின் எதிர் — 5-விதியும் எதிர்திசையில் செல்கிறது.
When does the 5-rule for subtraction apply?
The 5-complement subtraction rule applies when:
- The upper bead is currently DOWN (showing 5 or more is shown via upper bead)
- There are not enough lower beads showing to subtract the number directly
- The result of the subtraction will still be positive
The 5-complement rule for subtraction
When you can't remove N lower beads directly, do this instead:
- Push the upper bead UP (this subtracts 5 from your value)
- Then push the 5-complement of N lower beads UP (this adds back the excess)
- The net result is exactly −N
📐 Worked example: 7 − 3
Start: abacus shows 7 (upper bead down, 2 lower beads up). You need to subtract 3.
- 1Can I push 3 lower beads down? Only 2 lower beads are showing — I can't remove 3.
- 2Use 5-rule: push upper bead UP (subtracts 5 → value 7−5=2)
- 3The 5-complement of 3 is 2. Push 2 lower beads UP (adds 2 → value 2+2=4)
- 4Result: abacus shows 4. And 7 − 3 = 4 ✓
📐 Worked example: 6 − 4
Start: abacus shows 6 (upper bead down, 1 lower bead up). You need to subtract 4.
- 1Can I push 4 lower beads down? Only 1 lower bead is showing. Cannot remove 4.
- 2Use 5-rule: push upper bead UP (−5 → value 6−5=1)
- 3The 5-complement of 4 is 1. Push 1 lower bead UP (adds 1 → value 1+1=2)
- 4Result: abacus shows 2. And 6 − 4 = 2 ✓
Addition vs Subtraction — the mirror
See how the two rules are exact mirrors of each other:
The rule in words
Addition rule: upper bead DOWN, complement lower beads DOWN. Subtraction rule: upper bead UP, complement lower beads UP. The direction of everything reverses — that's the pattern.
Common error: moving in the wrong direction
Students sometimes push the upper bead DOWN when subtracting (because addition uses 'down'). Remember: for subtraction, the upper bead goes UP. The goal of subtraction is to reduce the value, so UP removes the bead's contribution.
Try it: show 8, then subtract 3
Set your abacus to 8. Then subtract 3 using the 5-rule. What should it show? (Answer: 5)
🎯 Goal: Show the number 8
Challenge Round
Challenge: 9 − 4
Start with 9. Subtract 4 using the 5-rule. What is the result?
🎯 Goal: Show the number 9
When lower beads can't give enough: push upper bead UP (−5), push 5-complement of N lower beads UP (+comp). Net = −N.
↪ Next: 10-Rule Adding — when numbers cross from the ones rod to the tens rod.
Key Points
முக்கிய குறிப்புகள்
- ✓5-rule subtraction: when lower beads can't give enough, use the upper bead
- ✓Push upper bead UP (−5), then push 5-complement of N lower beads UP (+comp)
- ✓Net result is exactly −N
- ✓Mirror of addition: everything is the same, but directions reverse
Glossary
சொல் அகராதி
5-complement rule
5-நிரப்பு விதி
Upper bead up
மேல் மணியை மேலே தள்ளு
Lower bead up
கீழ் மணியை மேலே தள்ளு
Net subtraction
நிகர கழித்தல்
Practice Activities
Speed Drill · விரைவு பயிற்சி
5-Rule Subtraction Drill
5-விதி கழித்தல் பயிற்சி
Guided Additionவழிகாட்டு கூட்டல்
Follow every step on the abacus — you must earn each move!
Follow each step — the abacus starts at the right number. No jumping to the final answer!
Step 1
Show 8 (upper bead down, 3 lower beads up). Subtract 4: only 3 lower beads showing. Not enough. Use 5-rule.
Your abacus shows: 8
Quizவினாடி வினா
Answer each question to check your understanding.
Your abacus shows 6. You subtract 3. Which direction does the upper bead move?