Vedic Maths for Kids· Lesson 8 of 10
இரட்டிப்பாக்கல் மற்றும் பாதி — பெருக்கல் வழி
Doubling and Halving for Multiplication
~10 min
15 × 16 = 15 × 8 × 2 = 240. By doubling one factor and halving the other, hard multiplications become easy. Learn this elegant trick and its limits.
By the end of this lesson you will be able to— இந்த பாடத்தின் இறுதியில்
- Apply doubling and halving to simplify multiplication
- Know when it helps (one number can be halved cleanly) and when it doesn't
- Solve: 15×16, 25×12, 50×18 using this technique
Let's Learn
What you will learn today
Simplify multiplication by doubling one factor and halving the other until the problem becomes easy.
Which is easier to multiply?
Which would you rather calculate: 15 × 16 or 30 × 8? Both have the same answer (240). What about 25 × 12 vs 100 × 3? (Both = 300.) The trick: they're the same problem in disguise.
The key insight: a × b = (2a) × (b/2) when b is even. You can double one factor and halve the other without changing the product. Do this repeatedly until one factor becomes a round number — then multiply.
The rule
If you want to compute a × b:
- Check: is b even? If yes, you can halve it.
- Double a, halve b. The product stays the same.
- Repeat until one factor is a convenient number (round number, power of 10, etc.)
- Multiply the simplified version.
📐 Example: 15 × 16
16 is even. Keep doubling/halving:
- 115 × 16 → 30 × 8 (double 15, halve 16)
- 230 × 8 → 60 × 4
- 360 × 4 → 120 × 2
- 4120 × 2 = 240
- 515 × 16 = 240 ✓
📐 Example: 25 × 12
12 is even. Try halving 12, doubling 25:
- 125 × 12 → 50 × 6
- 250 × 6 → 100 × 3
- 3100 × 3 = 300
- 425 × 12 = 300 ✓
When to use this technique
This technique shines when doubling one factor makes it a round number (10, 50, 100, 200...) while the other becomes an easy integer. Not every multiplication simplifies nicely — 13 × 17, for example, doesn't benefit from this approach.
Why does this work?
Because multiplication is a rectangle of area a × b. Doubling one side and halving the other keeps the same area. Mathematically: (2a) × (b/2) = 2ab/2 = ab. The product is preserved exactly.
Challenge Round
Challenge: 35 × 14
Apply doubling and halving. What does 35 eventually become, and why does that help?
Doubling and halving: a×b = (2a)×(b/2). Keep going until you reach a convenient factor. Why it works: preserves the product (rectangle area argument).
↪ Next: Quick Division Patterns — shortcuts for dividing by 5, 25, and 9.
Key Points
- ✓a × b = (2a) × (b/2) when b is even
- ✓Double one factor, halve the other — product unchanged
- ✓Repeat until you reach a round/easy number
- ✓Best when doubling leads to multiples of 10 or 100
Glossary
சொல் அகராதி
Double
இரட்டிப்பு
Halve
பாதி
Equivalent
சமம்
Simplify
எளிமைப்படுத்து
Practice Activities
Speed Drill · விரைவு பயிற்சி
Doubling & Halving Drill
Quizவினாடி வினா
Answer each question to check your understanding.
Why does doubling one factor and halving the other keep the product the same?
Fill in the Blanksஇடைவெளி நிரப்புக
Type the missing word and press Check or Enter.
Type the missing word and click Check or press Enter.