Arithmetic Tricks – Impress Anyone with Fast Maths
These arithmetic tricks are not magic — they are elegant applications of the mathematical rules you have already learned. Understanding why they work reinforces the underlying principles.
Trick 1 – Multiplying by 11
For a two-digit number: add the digits, place the sum between them.
36 × 11: 3 + 6 = 9 → answer: 396
Trick 2 – Squaring Numbers Ending in 5
85²: multiply (8 × 9) and append 25 → 72 | 25 = 7,225
Trick 3 – Multiply by 9 Using Your Fingers
Hold up 10 fingers. Fold down the nth finger (for n × 9). The fingers to the left = tens digit; to the right = ones digit.
7 × 9: fold 7th finger → 6 fingers left, 3 right → 63
Trick 4 – Casting Out Nines (Check)
Add the digits of any number. If the result is a multiple of 9, the original is too. Works for checking multiplication.
Check 36 × 27 = 972: 9+7+2=18 (multiple of 9) ✓
Trick 5 – Percentage Swap
x% of y = y% of x. Use the easier version.
18% of 50 = 50% of 18 = 9
Trick 6 – Doubling and Halving
32 × 25 = 32 × 100 ÷ 4 = 3,200 ÷ 4 = 800
Key Takeaways
- Tricks are not cheating — they are efficient use of mathematical properties.
- Understanding why a trick works prevents misapplying it.
- Combine estimation with tricks to spot when you have used one incorrectly.
Practice Questions
- Use the ×11 trick to find 47 × 11.
- Use the ×9 finger trick to find 8 × 9.
- Calculate 65² using the ×5 ending trick.
- Use percentage swap to find 4% of 75.
- Use doubling/halving to calculate 48 × 25.