More Mental Math Tricks for Quick Calculations

1. Advanced Multiplication Tricks

Multiplying by 99

  • Multiply by 100 and subtract the original number.
     Example: 36 × 99 = (36 × 100) - 36 = 3600 - 36 = 3564
    A Simple Guide to GCSE Chemistry Equations.

Multiplying Two Numbers Close to 100

Use the formula:

(a−x)×(b−x)+x2(a - x) \times (b - x) + x^2

Example: 97 × 96

  • Difference from 100: (100 - 97 = 3), (100 - 96 = 4)

  • Multiply: 3 × 4 = 12

  • Subtract from 100: (97 - 4 = 93)

  • Answer: 9312

Multiplying Any Number by 12

Double the number, then add the original number shifted one place to the left.
 Example: 46 × 12

  • 46 × 2 = 92

  • Shift 46 left: 460

  • Add: 460 + 92 = 552

2. Quick Division Shortcuts

Dividing by 5

  • Multiply by 2 and move the decimal one place left.
     Example: 135 ÷ 5

Dividing by 25

  • Multiply by 4 and move the decimal two places left.
     Example: 300 ÷ 25

    • 300 × 4 = 1200

    • Move decimal: 12

Dividing by 9 Trick

  • Sum the digits until you get a single-digit number.
     Example: 387 ÷ 9

    • 3 + 8 + 7 = 18

    • 1 + 8 = 9, so it’s divisible by 9.

3. Smart Addition & Subtraction

Adding Three or More Numbers Easily

Group numbers to make 10s or 100s.
 Example: 27 + 46 + 53 + 74

  • (27 + 74) = 101

  • (46 + 53) = 99

  • 101 + 99 = 200

Subtracting Large Numbers Using Rounding

  • Round the number up, subtract, then adjust.
     Example: 924 - 389

    • Round 389 to 390 → 924 - 390 = 534

    • Add 1 (since we subtracted extra): 535

4. Squaring Special Numbers

Squaring Numbers Near 50

Use the formula:

(50+x)2=2500+100x+x2(50 + x)^2 = 2500 + 100x + x^2

Example: 52²

  • 2500 + (100 × 2) + 2²

  • 2500 + 200 + 4 = 2704

Squaring Numbers Ending in 1

Use the trick:

(n−1)2+n+(n−1)(n-1)^2 + n + (n-1)

Example: 41²

  • 40² = 1600

  • 1600 + 40 + 41 = 1681

5. Cube Tricks for Small Numbers

Cubing Numbers Ending in 5

Use the formula:

(a×(a+1))2+125(a × (a+1))^2 + 125

Example: 15³

  • (1 × 2) = 2 → 2² = 4 → 4 followed by 125 → 3375

Cubing Numbers Close to 10

Use the formula:

(a+x)3=a3+3a2x+3ax2+x3(a + x)^3 = a^3 + 3a^2x + 3ax^2 + x^3

Example: 12³

  • 10³ + 3(10² × 2) + 3(10 × 2²) + 2³

  • 1000 + 600 + 120 + 8 = 1728

6. Percentage and Fraction Conversions

Finding 1% and Multiples of It

  • 1% = Move decimal two places left.
     Example: 1% of 450 = 4.5
    7% = Find 1%, then multiply by 7.
     Example: 7% of 450 → 4.5 × 7 = 31.5

Converting Common Fractions to Percentages

  • ⅛ = 12.5%

  • ⅙ = 16.66%

  • ⅖ = 40%

  • ⅝ = 62.5%

  • ⅞ = 87.5%

These tricks will make you a math whiz in no time!  Keep practicing, and soon you’ll be calculating faster than a calculator!  Let’s connect for affordable Online GCSE Classes.

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