Simplify calculating percentage

In your head, you may find it difficult to compute 18% of 25. Instead, try solving for 25% of 18.

25% is just half of half of any number. Half of 18 is 9, and half of 9 is 4.5.

Since 25% of 18 is 4.5, it is also true that 18% of 25 is 4.5.

Multiply Up to 20 X 20 In Your Head

Lets try 15 x 13.

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

2. 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.

3. Now add 15 + 3 = 18

4. Add a zero behind it (i.e., multiply by 10) to get 180.

5. Multiply the covered lower 3 by the single digit above it, in this case the "5" (3 x 5 = 15)

6. Add the products from steps 5 and 6 to get your answer. 180 + 15 = 195.

That's it! Wasn't that easy? Practice it on paper first!

Multiplying 3 digits or more by 11

Take for example the number 51236 X 11.
First, write down the number with a zero in front of it.
051236

The zero is necessary so that the rules are simpler.

Draw a line under the number.
Bear with me on this one. It is simple if you work through it slowly. To do this, all you have to do this is "Add the neighbor". Look at the 6 in the "units" position of the number. Since there is no number to the right of it, you can't add to its "neighbor" so just write down 6 below the 6 in the units col.
For the "tens" place, add the 3 to the its "neighbor" (the 6). Write the answer: 9 below the 3.
For the "hundreds" place, add the 2 to the its "neighbor" (the 3). Write the answer: 5 below the 2.
For the "thousands" place, add the 1 to the its "neighbor" (the 2). Write the answer: 3 below the 1.
For the "ten-thousands" place, add the 5 to the its "neighbor" (the 1). Write the answer: 6 below the 5.
For the "hundred-thousands" place, add the 0 to the its "neighbor" (the 5). Write the answer: 5 below the 0.
That's it ... 11 X 051236 = 563596

Sum of digits of a Cube

The sum of any cube when reduced to a single digit will always be either 1, 8, or 9.

For Example:

5³ = 125 = 1+2+5 =8
9³ = 729 = 7+2+9 = 18=1+8=9
17³ = 4913=4+9+1+3=17=1+7=8
4³=64=6+4=10=1+0=1

Also, they follow a cycle. The numbers 1 ,8, and 9 appear in order:

1 - sum of the digits of cube of 1 would be 1
2 - would be 8
3 - would be 9
4 - would be 1 (4³ = 64 = 6+4 = 10= 1+0 = 1)
5 - would be 8 (5³ = 125 = 1+2+5 = 8)
6 - would be 9 (6³ = 216 = 2+1+6 = 9)

so on and so forth.