Many people are terrified of mathematics. This list may help to improve the general knowledge of mathematical methods and speed up mathematical calculations in your head. This knowledge will help you amaze your math teacher.

**Trick #1. Multiplication by 11**

We all know that when multiplied by 10 you simply add 0 to the end of the number. But did you know that there is a simple way to multiply two-digit number by 11? Here it is:

Take the original number and imagine a space between two characters (in this example, we use the number 52):

5_2

Now add the two numbers and write them down in the middle:

5_(5+2)_2

Your answer will be:

572

If adding the numbers in parentheses obtained a two-digit number, just remember the second number and add one to the first number:

9_(9+9)_9

(9+1)_8_9

10_8_9

1089 – it always works!

**Trick #2. Fast Squaring**

This technique helps you quickly square a number that ends in 5. Here is who it goes:

1 – Take the first digit.

2 – Add one to it.

3 – Multiply the result on the first digit by the two digit number.

4 – At the end append 25. That’s it!

Example:

252 = ((2+1) x 2) place the first two “25”

2 x 3 = 6

625 – there you go!

**Trick #3. Multiplication by 5**

Most people memorizes the multiplication table for 5 very easily, but when dealing with large numbers, it gets complicated. Or does it? This technique is incredibly simple.

Take any number, divide by 2 (in other words, divide in half).

If the result is a whole number, assign 0 at the end. If not, do not pay attention to the value on the right side of the decimal point at the end and add 5. It always works:

2682 x 5 = (2682 / 2) & 5 or 0

2682 / 2 = 1341 (integer, so add 0)

13410

Let’s try on another example:

5887 x 5

2943,5 (fractional number, skip the value on the right side of the decimal point, add 5)

29435

**Trick #4. Multiplication by 4 **

This is a very simple technique, although evident only for some. The trick is that you just need to multiply by 2, and then multiply by 2 again:

58 x 4 = (58 x 2) + (58 x 2) = (116) + (116) = 232

**Trick #5. Complex Multiplications**

If you need to multiply large numbers, and one of them – even, you can just rearrange them to get the answer:

32 x 125 is the same as:

16 x 250 is the same as:

8 x 500 ais the same as:

4 x 1000 = 4,000

So, without a calculator: 13 * 11 = 1(1+3)3 = 143… now, I’ve used my calculator. And it’s right. Amazing!

I tried trick #2, fast squaring: 115^2 = 13225.

If I use Lilly technique I get the following:

(1+1) x 1 added “25”

1 added 25

125 (which is not 13225)

Howver, when I use the first 2 instead of only the first digits I get the right result:

(11+1) * 11

13225

So, Lilly your instructions should be refined to:

Cut of the last digit. Add one to the cut-off. Multiply the result on the cut-off number. At the end append 25.

For multiplying by 5, just mmultiply by 10 (I.e. append a 0 to the end), then divide by 2.

Fast squaring, better method:

a^2 = (a-b)(a+b)+b^2

So, e.g:

291 = (291-9)(291+9) + 9^2 = 282*300+81 = 84600+81 = 84681

With a little practice, you can do this in your head.

Thank you! I will include your trick in my next article: 5 more Math tricks to amaze your tutor.

Well it is a method. Do they always work?

84683

Amazing!

These are pretty elemenary techniques . Been using them since 3rd Grade.

Congrtulations, bananahammock. If you’ve been using these techniques since the 3rd grade you are definitely a smart kid!

Hey,

It was my first time reading your blog, about different strategies for teaching.

I really liked your strategies! Especially the way you are showing the logic and fun there is in the world of mathematics. Looking forward to reading more from you.

Thanks.

Sophie