விரைவு வகுத்தல் — வடிவங்களை கண்டுபிடி
Quick Division: Spotting Patterns
Division looks hard, but many everyday divisions follow simple patterns. From dividing by 5 (double and divide by 10) to dividing by 25, learn the shortcuts that make remainders rare.
Let's Learn
What you will learn today
Divide mentally by 5, 25, and 9 using transformation shortcuts.
What is 340 ÷ 10?
34. Easy — just remove a zero. What about 340 ÷ 5? This seems harder, but there is a trick: ÷5 is the same as ×2 ÷10. So 340 × 2 = 680, ÷10 = 68. Done.
Division by certain numbers — 5, 25, 9 — has beautiful shortcuts that come from their relationship with powers of 10. Instead of dividing by 5, you double and divide by 10 (much easier). Instead of dividing by 25, you multiply by 4 and divide by 100.
வகுத்தல் குறுக்குவழிகள் — 5, 25, 9 இவற்றுக்கு சிறப்பு வழிகள்.
Dividing by 5: double and divide by 10
Why does this work? Because 5 = 10/2. So ÷5 = ÷(10/2) = ×2/10 = (×2) then (÷10).
- 340 ÷ 5: double → 680, divide by 10 → 68
- 475 ÷ 5: double → 950, divide by 10 → 95
- 123 ÷ 5: double → 246, divide by 10 → 24.6
Dividing by 25: multiply by 4 and divide by 100
Why? Because 25 = 100/4. So ÷25 = ÷(100/4) = ×4/100 = (×4) then (÷100).
- 350 ÷ 25: ×4 → 1400, ÷100 → 14
- 675 ÷ 25: ×4 → 2700, ÷100 → 27
- 200 ÷ 25: ×4 → 800, ÷100 → 8
Dividing by 9: the digit pattern
For whole-number multiples of 9, the 9-times table has a pattern that makes mental division easy: if you know the 9-times table, reverse it. 81÷9: you know 9×9=81, so 81÷9=9. More useful: recognise multiples of 9 by their digit sum.
- A number is divisible by 9 if its digit sum is divisible by 9
- 72: 7+2=9 → divisible by 9 → 72÷9=8
- 108: 1+0+8=9 → divisible by 9 → 108÷9=12
When is the shortcut most useful?
These shortcuts shine in mental calculation, estimation, and checking. For division by 5: double-and-divide-by-10 always works. For division by 25: multiply-by-4-then-divide-by-100 always works. For division by 9: digit sum tells you if it divides evenly.
Challenge Round
Challenge: 480 ÷ 5 and 750 ÷ 25
Apply the shortcuts. Show your working for both.
÷5 = ×2 then ÷10. ÷25 = ×4 then ÷100. ÷9: check digit sum divisibility and reverse times table. These transform hard divisions into easy ones.
↪ Next: Speed Maths Challenge — all techniques together in a final mixed set.
Key Points
முக்கிய குறிப்புகள்
- ✓÷5 = double then divide by 10 (because 5=10/2)
- ✓÷25 = multiply by 4 then divide by 100 (because 25=100/4)
- ✓÷9: divisibility check via digit sum; reverse the 9× table
- ✓Transforms hard divisions into easier operations
Glossary
சொல் அகராதி
Division
வகுத்தல்
Divisor
வகுக்கும் எண்
Shortcut
குறுக்கு வழி
Pattern
வடிவம்
Practice Activities
Quizவினாடி வினா
Answer each question to check your understanding.
Why does ÷5 = ×2 then ÷10?
Fill in the Blanksஇடைவெளி நிரப்புக
Type the missing word and press Check or Enter.
Type the missing word and click Check.