## Tips for Faster Calculations

__1. Squaring a number ending with 5__Multiply the rest of the number leaving the 5 in the unit digit with its successive number and write the result with 25 in the end.

For e.g. 45^2 can be written as = (4 * (4+1)) 25 = (4*5) 25 = 2025

**natural numbers’ square is the sum of the two numbers. (n+1)2 – n2 = n + (n+1).**

__2. Difference between two consecutive__Use this fact to find the square of a number if square of its previous natural number is known.

For e.g. 46^2 = 45^2 + 45 + 46. We know 452 from the technique (1).

**:**

__3. Tip for finding any square__Choose a base closer to the number whose square is to be found.

Find the deficiency if the number is smacker to its base.

Add the deficiency to the number.

Multiply the result with the base.

Add the product of the square of the deficiency with the result of of the above point.

For e.g. 982.

Choose 100 as base.

Deficiency = 98-100 = -2

Number + Deficiency = 98 + (-1) = 96

Multiplying result with base = 96*100 = 9600

Adding above result with square of deficiency = 9600 + (-2)2 = 9604 which is the result 982

**4. To multiply by 5**,it is easier to add a zero at the end (*10) and divide the result by 2.

__5. To find the complement of a number (difference from the next highest power of 10)__Subtract all but the unit digits of the number from 9 and subtract the unit place from 10.

For e.g. to know complement of 32,056 (its difference from 100,000), we do:

9-3 = 6; 9-2 = 7; 9-0 = 9; 9-5 = 4; 10-6 = 4;

The result is 67,944. Easier than borrowing them 1’s?

**6. To Multiply a 2 digit number by 11**,for e.g. 35, write it as 3( )5. Inside the ( ), the sum of the two digits goes in. In this case, 3+5 = 8, hence 8 goes inside ( ). So, 35*11 = 382.

In case the sum of the two digits is a two digit number, keep the unit digit and add one to the digit preceding the ( ). For e.g. if we are to multiply 48 by 11, 4( )8. Inside ( ), we have 4+8 which is 12. So we place 2 and add 1 to 4 which precedes the ( ). Hence the result is 528.

The above were just some simple tricks you can apply to for faster calculations. With more practice, one can be sure of the answer and need not verify it by conventional methods.

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