#Shortcut Methods and Tricks for Numerical Calculations:

1. Multiplication:

• Fast Doubling: To quickly multiply a number by 2, simply shift all its digits one place to the left and add a zero at the end.
• Tricks for Numbers Ending with 5:
• To multiply a number ending in 5 by any single-digit number, first, multiply the single-digit number by 10, and then add half of that result to itself.
• Multiplying by 9, 11, or 12:
• Multiplication by 9: To multiply a number by 9, subtract the number from its reverse, and then append a zero to the end.
• Multiplication by 11: To multiply a number by 11, add the digits in the odd positions and then add the digits in the even positions. Finally, append these two sums together.
• Multiplication by 12: To multiply a number by 12, first multiply it by 11 and then add the number back to itself.

2. Division:

• Division by 11: To divide a number by 11, alternately subtract and then add the individual digits, starting from the rightmost digit, and place these differences/sums below the digits of the number. If any difference/sum is greater than or equal to 10, subtract/add 11 to get its remainder.
• Rounding off Quotients: When dividing a number by another, you can quickly estimate the quotient by dropping the last digit of the divisor and then moving the decimal point of the dividend one place to the left.

3. Percentages:

• Direct Percentage Calculations: To calculate a percentage directly without using a calculator, first multiply the number by the whole percentage (e.g., 25% = 0.25), and then move the decimal point two places to the left (for % values less than 100) or one place to the right (for % values greater than 100).

• Percentage Change Formula: To find the percentage change between two numbers, subtract the smaller number from the larger number, divide the difference by the smaller number, and then multiply by 100.

4. Square Roots:

• Estimation Technique: To quickly estimate the square root of a number, find the largest square that is less than or equal to the given number. The square root of the number will be slightly greater than the side length of this largest square.

5. Powers and Roots:

• Squaring a Double-Digit Number: To quickly square a double-digit number, add 5 to the first digit, multiply the result by 10, and then add the square of the second digit.
• Cubing a Double-Digit Number: To cube a double-digit number, multiply the squared result (obtained in the previous trick) by the second digit.

6. LCM (Least Common Multiple)

• Prime Factors Method: List the prime factors of each number and identify the common prime factors. The LCM is the product of all these common prime factors.

7. HCF (Highest Common Factor)

• Prime Factors Method: Similar to the LCM process, list the prime factors of each number and identify the common prime factors. The HCF is the product of the lowest power of each common prime factor.

8. Mental Arithmetic Tricks:

• Addition: You can mentally add two numbers by adding their digits in pairs, starting from the rightmost digits, and carrying over any tens when needed.
• Subtraction: When subtracting a smaller number from a larger number, subtract the digits in pairs from right to left, borrowing when necessary.
• Multiplication: Certain numbers, like 11, 99, or numbers ending with zeros, have specific mental multiplication tricks that make calculations easier.

These shortcut methods can help you perform numerical calculations quickly and efficiently, without the use of a calculator.