How to multiply, in your head, any two-digit number by eleven.

It’s very easy once you know the secret.

Consider the problem: 32 x 11

To solve this problem,
simply add the digits, 3 + 2 = 5,
put the 5 between the 3 and the 2, and there is your answer:

352

---

What could be easier? Now you try:
53 x 11
Since 5 + 3 = 8, your answer is simply
583

One more. Without looking at the answer or writing anything
down, what is
81 x 11?
Did you get 891?

Congratulations!

Now before you get too excited, I have shown you only half
of what you need to know.

Suppose the problem is 85 x 11

Although 8 + 5 = 13, the answer is NOT 8135 !

See how to resolve this


Here is another example. Try 57 x 11.

57 x 11 see the answer


Okay, now it’s your turn. As fast as you can, what is 77 x 11?

If you got the answer 847, then give yourself a pat on the
back. (LoL) You are on your way to becoming a mathematician.

Now, I know from experience that if you tell a friend or
teacher that you can multiply, in your head, any two-digit number
by eleven, it won’t be long before they ask you to do 99 x 11.


See the answer




Okay, take a moment to practice your new skill a few times,
then start showing off. You will be amazed at the reaction you
get. (Whether or not you decide to reveal the secret is up to you!)

Can we use this method for multiplying three-digit numbers
(or larger) by eleven?

Absolutely. For instance, take the problem 314 x 11,

How to resolve this ?

But we’ll save larger problems
like this for later.
More practically, you are probably saying to yourself,

Suppose the problem is 85 x 11

Although 8 + 5 = 13, the answer is NOT 8135 !

As before, the 3 goes in between the numbers, but the 1 needs
to be added to the 8 to get the correct answer:
935

Think of the problem this way:
1
835
===
935

Here is another example. Try 57 x 11.


Since 5 + 7 = 12, the answer is
1
527
===
627

what is 99 x 11 ?

Let’s do this one now, so we are ready for it.
Since 9 + 9 = 18, the answer is:



1
989
====
1089

consider the problem 314 x 11



answer still begins with 3 and ends with 4. Since 3 + 1 = 4, and
1 + 4 = 5, the answer is

3454

Here is another quick trick.
As you probably know, the square of a number is a number multiplied by itself. For example, the square of 7 is 7 x 7 = 49.

Later, I will teach you a simple method that will enable you to easily calculate the square of any two-digit or three-digit (or higher) number. That method is especially simple when the number ends in 5,

so let’s do that trick now.
To square a two-digit number that ends in 5, you need to remember only two things.


1. The answer begins by multiplying the first digit by the next higher digit.
2. The answer ends in 25.


                 35
               x35
3 x 4 = 12
5 x 5 =     25
Answer:1225

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