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.

Multiplication Sheets – 2 Digits x 11

Here is an opportunity to practice your math tricks skills by multiplying 2 digit numbers by 11. Remember – add the two digits in the number being multiplied by 11, then insert the sum in between the two digits. Don’t forget to carry over if it is required.

These multiplication sheets are meant to be solved in your head. One trick is to speak out loud as you solve the problems; this will help you to remember the partial answers better – especially when you have to carry numbers. With just a little practice, you will soon be able to solve these types of problems very quickly.

The answers to these multiplication problems are at the bottom of the page; just scroll down to check your answers.

Squaring Two-Digit Numbers Quickly

Using this math trick, you will be able to square any two digit number very quickly. With a little practice you can do it in your head, or you can do it on paper and still impress others with your math skills. This method of squaring is very easy, and I will be using as an example squaring the number 23.

First, determine the closest number to your number that ends in a zero. In this example, the number is 20. Next, determine the difference between your number and the closest number with the zero. In this case, it will be (23 – 20) = 3. Add the result to your number (23 + 3 = 26). Now, multiply the number with the zero by the sum of your number and the difference you determined:

20 x 26 = 520

Now square the difference you determined before, and add it to the result above:

(3 x 3) + 520 = 529

Presto! There is the square of your number!

Here are some more examples:

The Square of 25

Closest zero number: 20 (note – 30 will also work in this example)

Difference: 25 – 20 = 5

Sum: 25 + 5 = 30

Answer: (5 x 5) + (20 x 30) = 25 + 600 = 625

The Square of 37

Closest zero number: 40

Difference: 37 – 40 = -3

Sum: 37 + -3 = 34

Answer: (-3 x -3) + (40 x 34) = 9 + 1360 = 1369

The Square of 81

Closest zero number: 80

Difference: 81 – 80 = 1

Sum: 81 + 1 = 82

Answer: (1 x 1) + (80 x 82) = 1 + 6400 + 160 = 6561

Noticed how I broke down the (80 x 82) into (80 x 80) + (2 x 80)!

The Square of 12

Closest zero number: 10

Difference: 12 – 10 = 2

Sum: 12 + 2 = 14

Answer: (2 x 2) + (14 x 10) = 4 + 140 = 144

Multiplying by 5, 25, or 125

Multiplying by 5 is just multiplying by 10 and then dividing by 2. Note: To multiply by 10 just add a 0 to the end of the number.

12x5 = (12x10)/2 = 120/2 = 60.

Another example: 64x5 = 640/2 = 320.

And, 4286x5 = 42860/2 = 21430.

To multiply by 25 you multiply by 100 (just add two 0's to the end of the number) then divide by 4, since 100 = 25x4. Note: to divide by 4 your can just divide by 2 twice, since 2x2 = 4.

64x25 = 6400/4 = 3200/2 = 1600.

58x25 = 5800/4 = 2900/2 = 1450.

To multiply by 125, you multipy by 1000 then divide by 8 since 8x125 = 1000. Notice that 8 = 2x2x2. So, to divide by 1000 add three 0's to the number and divide by 2 three times.

32x125 = 32000/8 = 16000/4 = 8000/2 = 4000.

48x125 = 48000/8 = 24000/4 = 12000/2 = 6000.