Fast calculation skills are crucial for excelling in the CLAT exam, especially in the quantitative techniques section. Mastering mathematical tricks for fast calculations in CLAT can save you valuable time and boost your accuracy.
Here, we’ll learn various calculation tricks for CLAT that will help you solve problems quickly and efficiently. From basic operations to mental math strategies, these tips are designed to enhance your calculation speed.
Digit Sum Method: Calculation Trick for CLAT
The Digit Sum Method is a quick and effective technique used to verify arithmetic calculations, especially useful for addition, subtraction, multiplication, and division. It involves reducing numbers to a single digit by repeatedly summing their digits until only one digit remains.
Steps to Use the Digit Sum Method
- Add the digits of a number together.
- If the sum is a multi-digit number, add those digits together.
- Repeat until you obtain a single-digit number.
Examples of Digit Sum Method
Addition: Verify 123 + 456 = 579
- Digit sum of 123: 1 + 2 + 3 = 6
- Digit sum of 456: 4 + 5 + 6 = 15 → 1 + 5 = 6
- Digit sum of 579: 5 + 7 + 9 = 21 → 2 + 1 = 3
- Operation on digit sums: 6 + 6 = 12 → 1 + 2 = 3
Since the digit sum of 579 (3) matches the digit sum of the operation on the digit sums (3), the addition is correct.
Subtraction: Verify 789 – 456 = 333
- Digit sum of 789: 7 + 8 + 9 = 24 → 2 + 4 = 6
- Digit sum of 456: 4 + 5 + 6 = 15 → 1 + 5 = 6
- Digit sum of 333: 3 + 3 + 3 = 9
- Operation on digit sums: 6 – 6 = 0 (if negative, add 9 until it’s positive) → 0 + 9 = 9
Since the digit sum of 333 (9) matches the digit sum of the operation on the digit sums (9), the subtraction is correct.
Multiplication: Verify 23 × 46 = 1058
- Digit sum of 23: 2 + 3 = 5
- Digit sum of 46: 4 + 6 = 10 → 1 + 0 = 1
- Digit sum of 1058: 1 + 0 + 5 + 8 = 14 → 1 + 4 = 5
- Operation on digit sums: 5 × 1 = 5
Since the digit sum of 1058 (5) matches the digit sum of the operation on the digit sums (5), the multiplication is correct.
Division: Verify 144 ÷ 12 = 12
- Digit sum of 144: 1 + 4 + 4 = 9
- Digit sum of 12: 1 + 2 = 3
- Digit sum of 12 (result): 1 + 2 = 3
- Operation on digit sums: 9 ÷ 3 = 3
Since the digit sum of 12 (3) matches the digit sum of the operation on the digit sums (3), the division is correct.
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Benefits of the Digit Sum Method
- Quick Verification: Helps verify calculations quickly without redoing the entire problem.
- Error Detection: Identifies errors in arithmetic operations effectively.
- Easy to Use: Simple and straightforward, requiring only basic addition skills.
Unit Digit Method: Calculation Trick for CLAT
The Unit Digit Method is a quick and efficient technique used to find the last digit of a number resulting from addition, subtraction, multiplication, or exponentiation. This method is particularly useful for verifying the correctness of calculations in CLAT.
Steps to Use Unit Digit Method
- Identify the Unit Digit: Focus only on the unit digits of the numbers involved in the calculation.
- Perform the Calculation on Unit Digits: Perform the required arithmetic operation (addition, subtraction, multiplication, or exponentiation) using only the unit digits.
- Determine the Unit Digit of the Result: The unit digit obtained from the operation on the unit digits is the unit digit of the final result.
Examples of Unit Digit Method
Addition: Find the unit digit of 123 + 456
- Unit digit of 123: 3
- Unit digit of 456: 6
- Add the unit digits: 3 + 6 = 9
- Unit digit of the result: 9
Subtraction: Find the unit digit of 789 – 456
- Unit digit of 789: 9
- Unit digit of 456: 6
- Subtract the unit digits: 9 – 6 = 3
- Unit digit of the result: 3
Multiplication: Find the unit digit of 23 × 47
- Unit digit of 23: 3
- Unit digit of 47: 7
- Multiply the unit digits: 3 × 7 = 21
- Unit digit of the result: 1
Exponentiation: Find the unit digit of 2^5
- Unit digit of 2: 2
- Exponentiation pattern for 2: 2, 4, 8, 6 (repeats every 4)
- 5 mod 4 = 1, so the unit digit is the same as 2^1
- Unit digit of the result: 2
Benefits of the Unit Digit Method
- Speed: Quickly determine the unit digit of a calculation without performing the entire operation.
- Simplicity: Focuses only on the last digits, making the method easy to apply and understand.
- Verification: Useful for checking the correctness of answers in competitive exams.
Multiplication & Division Calculation Tips for CLAT
Multiplying by 5
Multiply the number by 10 and then halve the result.
For example:
34 × 5 = (34 × 10) / 2 = 340 / 2 = 170.
Squaring Numbers Ending in 5
For numbers ending in 5, use the formula (n × (n+1)) and append 25 at the end.
For example:
25² = 2 × 3 = 6, then append 25 = 625.
Using the Distributive Property
Break down the multiplication into smaller parts.
For example:
23 × 47 can be calculated as-
= (20 + 3) × (40 + 7)
= 20 × 40 + 20 × 7 + 3 × 40 + 3 × 7
= 800 + 140 + 120 + 21
= 1081
Dividing by 5
Multiply the number by 2 and then divide by 10.
For example:
230 ÷ 5
= (230 × 2) / 10
= 460 / 10
= 46.
Using Estimation
Round the divisor and the dividend to the nearest multiple of 10 to simplify the division, then adjust the result.
For example:
483 ÷ 12 can be estimated as 480 ÷ 12 = 40.
Multiplication Tables
Memorize tables at least up to 12 × 12. Practice regularly to ensure quick recall.
Square Roots
Know the square roots of perfect squares at least up to 15.
For example:
- √1 = 1
- √4 = 2
- √9 = 3
- √16 = 4
- √25 = 5
- √36 = 6
- √49 = 7
- √64 = 8
- √81 = 9
- √100 = 10
- √121 = 11
- √144 = 12
- √169 = 13
- √196 = 14
- √225 = 15
Using Vedic Mathematics for CLAT
Vedic Mathematics is an ancient system of calculation that simplifies complex arithmetic operations using unique techniques. These methods are derived from ancient Indian scriptures called the Vedas. Vedic Math offers quick and efficient ways to perform basic mathematical operations, making it ideal for competitive exams like CLAT.
Vedic Math includes several techniques that can be particularly useful for CLAT. Two of the most effective methods are the Vertically and Crosswise method for multiplication and the Base method for squaring numbers. These techniques can significantly speed up your calculations and improve accuracy.
Vertically and Crosswise Method for Multiplication
The Vertically and Crosswise method is a quick way to multiply two-digit numbers.
Example: Multiply 23 by 45.
- Step 1: Multiply the units digits: 3 × 5 = 15. Write down 5 and carry over 1.
- Step 2: Cross-multiply and add the results: (2 × 5) + (3 × 4) = 10 + 12 = 22. Add the carry over 1 to get 23. Write down 3 and carry over 2.
- Step 3: Multiply the tens digits: 2 × 4 = 8. Add the carry over 2 to get 10. Write down 10.
- Result: Combine the results from each step to get 1035.
Base Method for Squaring Numbers
The Base method is used to square numbers that are close to a base (like 10, 100, 1000, etc.).
Example: Square 98.
- Step 1: Identify the base (100) and the difference from the base: 98 is 2 less than 100 (Base – 2).
- Step 2: Calculate the square of the difference: 2² = 4.
- Step 3: Subtract the difference from the number: 98 – 2 = 96.
- Step 4: Write down the result from step 3, followed by the result from step 2. Since the base is 100, ensure the squared difference fits the place value: 9604.
- Result: The square of 98 is 9604.
Common Mistakes to Avoid in CLAT Calculation Tricks
- Misplacing Decimal Points: Be careful with decimal points, especially in percentage and division calculations, as small errors can lead to incorrect answers.
- Overcomplicating Simple Calculations: Stick to simple and straightforward methods. Overcomplicating can lead to confusion and errors.
- Rushing Through Problems: Take your time to understand the problem and apply the appropriate trick. Rushing can lead to mistakes.
- Neglecting Practice: Regular practice is crucial. Ensure you consistently apply these tricks to build speed and accuracy.
Wrapping Up:
Quantitative Techniques in CLAT is a subject where you can score full marks with the right preparation and techniques. By mastering easy calculation tips and tricks for CLAT, such as the Digit Sum Method, Unit Digit Method, and Approximation Method, you can enhance your speed and accuracy.
To further boost your preparation, it’s crucial to practice regularly with:
These resources help you familiarize yourself with the CLAT exam pattern and identify areas for improvement.
Additionally, consider enrolling in reputable and top CLAT coaching to receive expert guidance and structured study plans.