Techniques for Quick Mental Math in Competitive Exams

Mental math skills are essential for competitive exams where time is of the essence. Being able to solve mathematical problems quickly and accurately gives you an edge over others. Here, we explore effective techniques to sharpen your mental math abilities and save valuable time during exams.

1. Learn to Break Numbers Down

Breaking down complex numbers into simpler components makes calculations easier. For example:

To multiply 23 × 48, break it down as: (20×48)+(3×48)=960+144=1104(20 × 48) + (3 × 48) = 960 + 144 = 1104(20×48)+(3×48)=960+144=1104

This decomposition method reduces mental strain and speeds up calculations.

2. Master the Art of Approximation

For questions where exact answers aren’t required, use approximation to quickly zero in on the correct option. For example:

When dividing 482 by 23, approximate it as 480÷24=20480 \div 24 = 20480÷24=20. This method helps you eliminate wrong options swiftly.

3. Memorize Basic Arithmetic Rules and Tables

Knowing multiplication tables up to 20, squares up to 30, and cubes up to 15 can save a lot of time. Here’s how they help:

For 12×1412 × 1412×14, recall (12+2)×12=122+24=144+24=168(12 + 2) × 12 = 12^2 + 24 = 144 + 24 = 168(12+2)×12=122+24=144+24=168.

4. Use the Rule of 9s for Subtraction

When subtracting numbers close to powers of 10, use the Rule of 9s. For example:

1000−648=999−648+1=351+1=3521000 – 648 = 999 – 648 + 1 = 351 + 1 = 3521000−648=999−648+1=351+1=352.

This eliminates the need for borrowing in subtraction.

5. Master Percentage Shortcuts

Competitive exams often include percentage calculations. Use these tricks:

Finding 10%, 20%, or 50%:
- 10%10\%10% of 480 is 484848, 20%20\%20% is 969696, and 50%50\%50% is 240240240.
Reverse Percentages: If 75% of a number is 60, the number is 60÷0.75=8060 \div 0.75 = 8060÷0.75=80.

How to Prepare for the General Knowledge Section in Competitive Exams

6. Apply the Square and Cube Tricks

Squaring numbers ending in 5:

352=(3×4)∣25=122535^2 = (3 × 4) | 25 = 1225352=(3×4)∣25=1225.
Multiply the first digit by the next integer and append 25.

Cubing numbers close to 10 or 100:

1023=1003+3(1002×2)+3(100×22)+23=1061208102^3 = 100^3 + 3(100^2 × 2) + 3(100 × 2^2) + 2^3 = 10612081023=1003+3(1002×2)+3(100×22)+23=1061208.

7. Use the Cross Multiplication Trick

For quick multiplication of two 2-digit numbers:

Multiply 23×4523 × 4523×45:
- Multiply the units digits: 3×5=153 × 5 = 153×5=15.
- Cross multiply and add: (2×5)+(4×3)=10+12=22(2 × 5) + (4 × 3) = 10 + 12 = 22(2×5)+(4×3)=10+12=22.
- Multiply the tens digits: 2×4=82 × 4 = 82×4=8.
- Combine: 8∣22∣15=10358 | 22 | 15 = 10358∣22∣15=1035.

8. Practice Vedic Math Techniques

Vedic math simplifies operations using ancient methods:

Vertically and Crosswise for multiplication:
- For 23×4723 × 4723×47:
  (2×4)∣(2×7+3×4)∣(3×7)=8∣26∣21=1081(2 × 4) | (2 × 7 + 3 × 4) | (3 × 7) = 8 | 26 | 21 = 1081(2×4)∣(2×7+3×4)∣(3×7)=8∣26∣21=1081.

9. Utilize Digital Sum for Verification

Quickly verify calculations using the digital sum method:

For 123×45=5535123 × 45 = 5535123×45=5535:
- Digital sum of 123123123 is 666, 454545 is 999. 6×9=546 × 9 = 546×9=54, digital sum 999.
- Verify 553555355535’s digital sum: 999.

10. Develop Number Sense with Daily Practice

Practicing mental math daily with puzzles and mock tests strengthens your number sense. Apps like Mental Math Trainer or Mathway provide excellent resources.

Conclusion

Mastering mental math for competitive exams requires dedication, practice, and the use of efficient techniques. By breaking down numbers, memorizing tables, and using smart shortcuts, you can significantly improve your speed and accuracy. Dedicate a few minutes daily to practicing these methods, and you’ll see remarkable improvements in no time!

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