Ten class (10th)mathematics tricks

1. Multiplying by 11 (Two-digit Numbers)

Trick:
For a number like 52:
Add the digits: 5 + 2 = 7
Place the result in the middle:
52 × 11 = 572

(If the sum is 10 or more, carry over)




2. Square of a Number Ending in 5

Trick:
For a number like 75:
Take the first digit(s): 7
Multiply it by (7 + 1): 7 × 8 = 56
Add 25 at the end: 75² = 5625




3. Quick Percentage Calculation

Trick:
Find 10%, 1%, and build from there.
E.g., 18% of 250
→ 10% = 25,
→ 1% = 2.5
→ 8% = 2.5 × 8 = 20
→ Total = 25 + 20 = 45


4. Squaring Numbers Close to 100

Trick:
E.g., 103²
= 100² + 2×100×3 + 3²
= 10000 + 600 + 9 = 10609




5. Divisibility Rule for 7

Trick:
Double the last digit, subtract from the rest.
If result is divisible by 7, so is the number.
E.g., 203 → 20 - 6 = 14 → Yes!




6. Product of Two Numbers with Same Tens and Ones Adding to 10

Trick:
E.g., 43 × 47
Tens = 4
Ones = 3 and 7 (adds to 10)
→ 4 × (4 + 1) = 20
→ 3 × 7 = 21
→ Answer = 2021




7. Multiplying Two-Digit Numbers Ending in 1

Trick:
E.g., 21 × 31
→ (20 + 1) × (30 + 1)
→ Use distributive property
= 20×30 + 20×1 + 1×30 + 1×1
= 600 + 20 + 30 + 1 = 651




8. Cube of a Two-Digit Number Ending in 5

Trick:
E.g., 15³
= (10 + 5)³
Use binomial expansion: a³ + 3a²b + 3ab² + b³
= 1000 + 3×100×5 + 3×10×25 + 125
= 1000 + 1500 + 750 + 125 = 3375




9. Multiply by 5 Fast

Trick:
Multiply by 10 and divide by 2.
E.g., 86 × 5
→ 860 ÷ 2 = 430




10. Check Divisibility by 3

Trick:
Add all digits. If the sum is divisible by 3, so is the number.
E.g., 372 → 3 + 7 + 2 = 12 → Yes!


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