Cool Maths Tricks.........


Addition
One way to add lots of small numbers is to clump together the ones that add up to multiples of 10. For example, if you have to add 3 + 4 + 5 + 7 + 9 + 11 + 6, that can be arranged as (3 + 7) + (9 + 11) + (4 + 6) + 5 = 10 + 20 + 10 + 5 = 45. This can be really useful when playing dice games like Yahtzee.

Squaring......................................................
In this simple trick we need to modify the equation and make the units digit zero. After all it is easy to multiply when units digit is zero.
For example - Find square of 43
= (43+3) * (43-3) + (3*3)
=(46*40) + 9
= (460*4) + 9
= 1840 + 9 = 1849
Squaring a number ending in 6 
66^2 =_________.
a) Write down 6.
b) 2 x (6 + 1) + 1 = 15. Write 5, carry *1.
c) 6 x (6 + 1) = 42 + *1 = 43. Write 43.
d) The answer is 4356.

 Ex [2] 
86^2 =_________.
a) Write down 6.
b) 2 x (8 + 1) + 1 = 19. Write 9, carry *1.
c) 8 x (8 + 1) = 72 + *1 = 73. Write 73.
d) The answer is 7396.

Multiplication.............................................
There is a misconception that vedic maths multiplication technique helps you multiply faster but in reality it is very difficult to implement this technique during exam.
During exams we need answer in nearest values. So for example  2911 * 304
To make  calculation easy multiply 29*3, you will get a near answer.
Multiplication with 5
Simply multiply the number by 10 and then divide it by 2.
For example 99*5= 990/2= 495
Multiply by 12: Multiply by 10 and add twice the original number.
Multiply by 13: Multiply by 3 and add 10 times original number.
Multiply by 14: Multiply by 7 and then multiply by 2
Multiply by 15: Multiply by 10 and add 5 times the original number, as above.
Multiply by 16: You can double four times, if you want to. Or you can multiply by 8 and then by 2.
Multiply by 17: Multiply by 7 and add 10 times original number.
Multiply by 18: Multiply by 20 and subtract twice the original number (which is obvious from the first step).
Multiply by 19: Multiply by 20 and subtract the original number.
Multiply by 24: Multiply by 8 and then multiply by 3.
Multiply by 27: Multiply by 30 and subtract 3 times the original number (which is obvious from the first step).
Multiplication with 99:Multiply the number with 100 and then minus same number from the result. Let's take an example
Multiply 32*99 = 3200 - 32 = 3168
multiplying special numbers.............
1 x 1 = 1
11 x 11 = 121
111 x 111 = 12321
1111 x 1111 = 1234321
11111 x 11111 = 123454321
111111 x 111111 = 12345654321
1111111 x 1111111 = 1234567654321
11111111 x 11111111 = 123456787654321
111111111 x 111111111 = 12345678987654321
1 x 9 + 2 = 11
12 x 9 + 3 = 111
123 x 9 + 4 = 1111
1234 x 9 + 5 = 11111
12345 x 9 + 6 = 111111
123456 x 9 + 7 = 1111111
1234567 x 9 + 8 = 11111111
12345678 x 9 + 9 = 111111111
123456789 x 9 +10 = 1111111111

THE 11 TRICK...................................
If you encounter a problem where you have to multiply any number with 11, for eg.
36 x 11
write 3 and 6 to both the extremes and write the sum of these two in the middle..
Result==>396
same goes for any two digit number
13 x 11
Result==> 143

Square root....................................................
Best method to find square root of large numbers is by dividing the number into parts. Let's take an example
Find square √ 1936
√ 1936 = √ 4 * √ 484 = √ 4 * √ 4 * √ 121 = 2*2*11 = 44

 Time and Work........................................................
Every question in in time and work chapter can be solved easily by finding efficiency of workers or subject (such as pipes).
For example - A takes 10 days to complete a job. B takes 20 days to complete the same job. In how many days they will complete the job if they work together ?
A's efficiency = 100/10 = 10% per day
B's efficiency = 100/20 = 5% per days
A and B can do 15% of the work in a day if they work together. So they can do the whole job in 100/15 = 6.66 days or 6 days and 18 hours.

Learn fractions.............................................
Learn fractions upto 15. This would improve your calculation speed drastically. Try ity. You can apply it in Time and Work, Time and Distance and many other chapters.
Fraction..............Percentage (%)
1/n......................100/n %
1..........................100%
1/2.......................50%
1/3.......................33.33%
1/4.........................25%
1/5.........................20%
1/6........................16.66%
1/7........................14.28%
1/8.........................12.5%
1/9.......................11.11%
1/10.......................10%
1/11......................9.09%
1/12......................8.25%
1/13.....................7.69%
1/14.....................7.14%
1/15.....................6.66%


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