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### Multiplying by 11

```
Date: 09/16/97 at 05:55:04
From: Benjamin Silbert
Subject: A problem my class wants to know

My teacher is a mathematician and one day she asked us to give
her a number times 11. We said: 568 x 11, and after about 5 seconds
she said the answer was 6248, so we checked on our calculators and she
was right!

We want to know how she does it so quickly!
```

```
Date: 10/31/97 at 11:37:11
From: Doctor Trent
Subject: Re: A problem my class wants to know

Multiply it out on paper, and you'll see that she's just adding
digits:

568
x  11
-------
568
568
-------
6248

You can do it like this: in 568, 8 is the last digit, so 8 is the
last digit in the answer.  6 is the second to last digit, so you
add it to 8, and 6 + 8 = 14, so 4 is the tens digit; 5 and 6 are
the first two digits of 568, and 5 + 6 = 11 (plus the carried 1
from before) = 12, so the next digit is 2 with 1 carried.  5 would
be the first digit, but we add the carried one to get 6.

With practice, you can do it in your head quite quickly.

Here's a longer example to help put it together: 7348 x 11

8 is the last digit
4 + 8 = 12   2 is the tens digit, carry a 1
3 + 4 = 7    plus the carried 1 is 8, no carries
7 + 3 = 10   0 is the next digit, carry the 1
7  plus the carried 1 is 8, the first digit
so: 7348 x 11 = 80828

-Doctor Trent,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```

```
Date: 10/31/97 at 17:50:20
From: Benjamin Silbert
Subject: Re: A problem my class wants to know

Dr. Math,

I asked my teacher and then my dad:

Multiply it by 10 and then add the number on.

My teacher said:

use 33 x 11

33

put down the first number (3)

3

6

put down the last number

3

and your total amount is 363.

Benjamin Silbert
```

```
Date: 11/01/97 at 09:10:19
From: Doctor Sonya
Subject: Re: A problem my class wants to know

Dear Benjamin,

Thanks for letting us know the other ways to do this problem.

Your dad's seems to be the simplest, but could be difficult if the
numbers were really big. For example, what if we wanted to find
674 x 11?  We'd have to add 674 + 6740. I like your teacher's way
best.

Write us if you have any more questions.

-Doctor Sonya,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
Elementary Multiplication
Elementary Puzzles
Middle School Puzzles

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