Mathematics is fun…

I was really surprised, here I got some very useful tricks to solve the hardest calculation in seconds. Here I am sharing some tricks which can really prove “Mathematics is fun”.

Multiply Up to 20X20 In 20 second:

Yes you can solve this in seconds. see how

Take 15 x 13 for an example.

Always place the larger number of the two on top in your mind.

Then draw the shape of Africa mentally so it covers the 15 and the 3 from the 13 below. Those covered numbers are all you need.

First add 15 + 3 = 18

Add a zero behind it (multiply by 10) to get 180.

Multiply the covered lower 3 x the single digit above it the “5″ (3×5= 15)

Add 180 + 15 = 195

Square a 2 Digit Number Ending in 5:

For this example we will use 25

Take the “tens” part of the number (the 2 and add 1)=3

Multiply the original “tens” part of the number by the new number (2×3)

Take the result (2×3=6) and put 25 behind it. Result the answer 625.

Try a few more 75 squared … = 7×8=56 … put 25 behind it is 5625.
55 squared = 5×6=30 … put 25 behind it … is 3025. Another easy one! Practice it on paper first!

Multiplying two numbers when a round number is halfway between them:

Suppose you are multiplying two moderately large numbers, 84 and 76. Note that the number 80 is halfway between the two.

This means that 84*76 can be rewritten as
(80 + 4)(80 - 4)
which simplifies to 802 - 42, which is easier to figure out: 6400 - 16 = 6384.

Adding even numbers from two through a selected 2-digit even number:

If the 2-digit even number selected is 24:

Divide 24 by 2 (24/2 = 12) or multiply by 1/2 (1/2 × 24 = 12).

The next number is 13; 12 × 13 = 156.
Ways to multiply 13 by 12:

Square 12, then add 12: 12 × 12 = 144, 144 + 12 = 156.
Multiply left to right. 12 × 13 can be done in steps: 12 × (10+3) = (12 × 10) + (12 × 3) = 120 + 36 = 156.

So the sum of all the even numbers from two through 24 is 156.

Adding the digits of the square of repeating ones:

If the number selected is 1111:

Square the number: 1111 × 1111 = 1234321

Add the digits of the square:
1 + 2 + 3 + 4 + 3 + 2 + 1 = 16

The answer is the square of the number of ones in 1111.

Adding a sequence of consecutive odd numbers:

If the 2-digit odd number selected is 35:

35+1 = 36 (add 1).

36/2 = 18 (divide by 2) or 1/2 × 36 = 18 (multiply by 1/2).

18 × 18 = 324 (square 18): 18 × 18 = (20 - 2)(18) = (20 × 18) - (2 × 18) = 360 - 36 = 360 - 30 - 6 = 324.

So the sum of all the odd numbers from one through 35 is 324.

Adding consecutive numbers between two numbers:

If the two numbers selected are 6 and 19:

Add the numbers: 6 + 19 = 25.

Subtract the numbers: 19 - 6 = 13.

Add 1: 13 + 1 = 14.

Multiply 25 by half of 14: 25 × 7 = 175

So the sum of the numbers from 6 through 19 is 175.

Subtracting the squares of two numbers:

Select a 2-digit number and then choose a number two larger or two smaller.

Multiply the middle number by 4.

Example:

If the the first number selected is 31:

Choose 29.

Multiply the number between them by 4: 4 × 30 = 120

So (31)(31) - (29)(29) = 120.

Reversing/adding/subtracting 3-digit numbers:

Select a number with different 1st and 3rd digits.

Reverse the digits.

Subtract the smaller digit from the larger.

Reverse the digits of this answer.

Add these two numbers.

Subtract a number from this sum.

The final answer will be 1089 minus whatever number you choose in step 6!

Example:

For the last step you say to subtract 22.

The answer is: 1089 - 22 = 1067.

Finding 5 percent of a number:

Choose a large number (or sum of money).

Move the decimal point one place to the left.

Divide by 2 (take half of it).

Example:

If the amount of money selected is 850:

Move the decimal point one place to the left.: 85

Divide by 2: 85/2 = 42.50

So 5% of 850 = 42.50.

Finding 15 percent of a number:

Choose a 2-digit number.

Multiply the number by 3.

Divide by 2.

Move the decimal point one place to the left.

Example:

If the number selected is 43:

Multiply by 3: 3 × 43 = 129

Divide by 2: 129/2 = 64.5

Move the decimal point one place to the left: 6.45

So 15% of 43 = 6.45.

Sum of first n integers:

Another easy formula likely to show up:

1+2+3+4+…+n = n(n+1)/2

Example: 1 + 2 + 3 + … + 12 = 12*13/2 = 6*13 = 78

Sum of the first n square numbers:

1 + 22 + 32 + … + n2 = n(n+1)(2n+1)/6

Example: The sum of the first 10 square numbers:
The long way: 1 + 4 + 9 + 6 + 25 + 36 + 49 + 64 + 81 + 100 = 385
The faster way: 10*(10+1)(20+1)/6 = 10*11*21/6 = 385