🔢 Multiplication Short Tricks

1. Multiply by 11 Trick

👉 Rule: Digits को अलग करो और बीच में उनका sum डाल दो।

• Example:
  $32 × 11 = 3 \_ 2$
  बीच का sum → $3 + 2 = 5$
  Answer = 352

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2. Number ending with 5 का Square (n5 × n5)

👉 Formula: $(n5)^2 = n × (n+1) | 25$

• Example:
  $35 × 35 = 3 × 4 | 25 = 1225$

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3. Multiply by 9, 99, 999... Trick

• $67 × 99 = (67 × 100) – 67 = 6700 – 67 = 6633$

• $84 × 999 = (84 × 1000) – 84 = 84000 – 84 = 83916$

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4. Vedic Maths Trick (For 2-digit numbers close to 100)

👉 Formula: $(100 – a)(100 – b) = 100(100 – (a+b)) + (a×b)$

• Example:
  $97 × 96$
  $a = 3, b = 4$
  Step 1: $100 – (3+4) = 93$
  Step 2: $3 × 4 = 12$
  Answer = 9312

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5. Cross Multiplication Trick (2-digit × 2-digit)

👉 Example: $23 × 47$

1. Last digit multiply: $3 × 7 = 21$ → write 1, carry 2

2. Cross multiply: $(2×7) + (3×4) = 14 + 12 = 26$ + carry 2 = 28 → write 8, carry 2

3. First digit multiply: $2 × 4 = 8$ + carry 2 = 10

Answer = 1081

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6. Multiply by 5, 25, 50, 75

• $n × 5 = (n ÷ 2) × 10$
  👉 $468 × 5 = (468 ÷ 2) × 10 = 2340$

• $n × 25 = (n ÷ 4) × 100$
  👉 $64 × 25 = (64 ÷ 4) × 100 = 1600$

• $n × 50 = (n ÷ 2) × 100$
  👉 $86 × 50 = (86 ÷ 2) × 100 = 4300$

• $n × 75 = (n ÷ 4) × 300$
  👉 $36 × 75 = (36 ÷ 4) × 300 = 2700$

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7. Numbers close to 50 (Vedic Style)

👉 Formula: $(50+a)(50+b) = 2500 + 50(a+b) + ab$

• Example:
  $53 × 48$
  $a=+3, b=–2$
  Step 1: $2500 + 50(3–2) + (3×–2)$
  Step 2: $2500 + 50(1) – 6 = 2544$

Answer = 2544

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8. Multiply by 99, 999 in 1 step

👉 Shortcut: Just subtract from 100, 1000...

• $54 × 99 = 54×100 – 54 = 5400 – 54 = 5346$

• $73 × 999 = 73×1000 – 73 = 73000 – 73 = 72927$

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9. Multiply by 125

👉 Formula: $n × 125 = (n × 1000) ÷ 8$

• Example:
  $48 × 125 = (48 × 1000) ÷ 8 = 48000 ÷ 8 = 6000$

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10. Easy Trick for Double Numbers (Like 23×22, 45×44)

👉 Formula: $n(n–1)$ at end + 2nd digit squared

• Example:
  $23 × 22$
  Step 1: $23 × 22 = (22 × 22) + 22 = 484 + 22 = 506$