Vedic Maths for Kids· Lesson 5 of 10
10-க்கு அருகில் உள்ள எண்களை பெருக்கல்
Multiply Numbers Near 10
~11 min
When two numbers are both close to 10, their product has a beautiful shortcut. 9 × 8, 7 × 9, 8 × 8 — all solved in your head using the base-10 method.
By the end of this lesson you will be able to— இந்த பாடத்தின் இறுதியில்
- Find the deficiency of each number from 10
- Apply Nikhilam: cross-subtract and multiply deficiencies
- Solve: 9×8, 7×9, 8×8 and similar problems
Let's Learn
What you will learn today
Multiply any two numbers that are both close to 10 using the Nikhilam base method.
How far from 10?
How far is 9 from 10? (1) How far is 7 from 10? (3) How far is 8 from 10? (2) These 'distances' are called deficiencies — and they are the key to today's technique.
When two numbers are both close to 10, their product has a hidden structure. 9 × 8 = 72. You can find this without multiplying directly — using only the distance each number is from 10. Once you see the pattern, you will never think about near-10 multiplication the same way again.
The Nikhilam base-10 method
For two numbers both close to 10:
- Find the deficiency of each number from 10
- Cross: take either number, subtract the OTHER number's deficiency
- Multiply the two deficiencies together → this is the units (ones) part
- Combine: cross-result | units-result = final answer
📐 Example: 9 × 8
Deficiency of 9 from 10: 1. Deficiency of 8 from 10: 2.
- 1Cross: 9 − 2 = 7 (or: 8 − 1 = 7 — same result either way)
- 2Units: 1 × 2 = 2
- 3Combine: 7 | 2 = 72
- 49 × 8 = 72 ✓
📐 Example: 7 × 8
Deficiency of 7: 3. Deficiency of 8: 2.
- 1Cross: 7 − 2 = 5 (or: 8 − 3 = 5)
- 2Units: 3 × 2 = 6
- 3Combine: 5 | 6 = 56
- 47 × 8 = 56 ✓
Why does this work?
Let a = 10 − p and b = 10 − q (where p, q are deficiencies). Then a × b = (10−p)(10−q) = 100 − 10p − 10q + pq = 10(10−p−q) + pq = 10(a−q) + pq. So the tens part is (a − q) and the units part is (p × q). That is exactly what the cross and units calculations give.
When units product exceeds 9
If the deficiency product is ≥ 10 (e.g., 7 × 6: deficiencies 3 and 4, product 12), carry the tens digit into the cross result: cross=3, units=12 → 3+1=4 tens, 2 units = 42. Verify: 7×6=42 ✓
Common error: using the wrong deficiency in the cross
The cross uses one number minus the OTHER number's deficiency. Not one number minus its own deficiency. 9 × 7: cross = 9 − 3 (3 is 7's deficiency) = 6. Not 9 − 1 (which would be 8, wrong).
Try: 8 × 8
Both are 8. Deficiency of each from 10 is 2. Apply the method.
Challenge Round
Challenge: 6 × 7
Both are close to 10. Apply the method. Watch the units product carefully.
Base-10 Nikhilam: find deficiencies from 10, cross-subtract for tens part, multiply deficiencies for units part. If units ≥ 10, carry.
↪ Next: Base-100 — the same method scaled up to numbers near 100.
Key Points
- ✓Deficiency = how far the number is below 10
- ✓Cross: either number minus the OTHER's deficiency → tens part
- ✓Units: multiply the two deficiencies → ones part
- ✓If units ≥ 10, carry to the tens part
Glossary
சொல் அகராதி
Deficiency
குறைபாடு
Base
அடிப்படை
Cross-subtraction
குறுக்கு கழித்தல்
Nikhilam
நிகிலம்
Practice Activities
Speed Drill · விரைவு பயிற்சி
Base-10 Speed Drill
Quizவினாடி வினா
Answer each question to check your understanding.
What is 9 × 6 using the base-10 method?
Fill in the Blanksஇடைவெளி நிரப்புக
Type the missing word and press Check or Enter.
Type the missing word and click Check or press Enter.