Magic of Numbers- 2

Earlier post about maths made me feel that I have so many people around who have some resonance with my thoughts! Made me feel really enthusiastic to work on and present few more in this

1.Subtracting any number from 100, 1000

1. Subtract 689 from 1000

Step 1: Subtract numbers 6, 8 from 9
Step 2: Subtract unit's place value 9 from 10

1000 - 689 =
9 9 10
-6 8 9
---------
3 1 1

Ans : 1000-689 = 311
2. To divide any number from 9

Example: 32142 / 9

Step 1 : Put down 3 as it is
Step 2 : Add 3 + 2 = 5
Step 3: Add 5(From previous Step) to 1 = 6
Step 4: Add 6(From Previous Step) to 4 = 10 (Carry over 1 to previous Step.So Value in Step 3 becomes 7)
Step 5: Add 10 (From Previous Step) to 2 = 12
Step 6: Divide 12 from 9 and quotient is 1

So The answer is 3 5(6+1)(0+ 1- Quotient value) = 3571

For Demo of this trick check here

3.To quickly divide by 5, 50 and 500

/ 5 - * by 2 and move decimal left 1 time
/50 - * by 2 and move decimal left 2 times
/500 - * by 2 and move decimal left 3 times

Example:

3456 * 5 = (3456 *2) and move decimal left 1 time = > 691.2
3456 * 50 = (3456 *2) and move decimal left 2 times = > 69.12
3456 * 500 = (3456 *2) and move decimal left 3 times = > 6.912

For Demo of this trick check here

4.To add large numbers

238 + 644

238 = 240 - 2 (Number added to 238 to round it off)
644 = 650 - 6 (Number added to 644 to round it off)

240
650
-----
890 - 8 [6+2]
-----
882
-----
This works fine for larger numbers also. But I feel the a better way is

456 + 567

Start adding from left to right

Adding 4 + 5 = 9.Now before concluding the digit see the numbers in next place. It is 5,6 we know that 5+6 = 11 so we have a carry over so the step becomes
(4+5) (5+6) (6+7)
9(1) 1
11 1
Now first place value from left is complete and the sum is 10

See the next place value which is 6, 7 again we have a carry over. So the step becomes
(4+5) (5+6) (6+7)
9(1) 1(1) 3
10 2 3

Ans = 1023
This method is the best and quickest method which can be achieved only with PRACTICE and able to visualize numbers.

5. To get square of a number

(12)^2

Step 1: Square 2 = 4
Step 2: Multiply (1*2) and double it => (2+2 = 4)
Step 3: Square 1 = 1

(12)^2 = 144

(123)^2

Step 1: Square 3=9
Step 2: Consider 12 as a single number. So (12*3) +(12*3) => 36+36 = 72 (Here 7 becomes carryover)
Step 3: Square 12 = 144

(123)^2 = (144+7)29 = 15129

For additional quicker and informative tricks check out Mathemagics videos