# How to multiply any number by 11 in one step

## Impress your friends

Impress your friends - or beat the calculator and win pub-bets...

## First, a few examples

Multiply 11 by 11.

Method, imagine a zero in frontof the first number.

011

This is the number to be multiplied by eleven.

Work from left to right.

Add 0 to 1 = 1

Move to the next number.

Add 1 to 1 = 2

Now we have reached the last digit, write it down: 1

The answer is 121.

That was an extremely easy example, so let's try a longer one:

434211234 X 11

Imagine 0 in front:

0434211234

0+4=4

4+3=7

3+4=7

4+2=6

2+1=3

1+1=2

1+2=3

2+3=5

3+4=7

4

The answer is 4776323574

Now you can do this in-line. Start at the left, add the number to the right, move along until you run out of digits and write the last one down.

Multiply

31231234 x 11

031231234

343543574 = answer

These have been particularly easy because each digit is less than 5.

Here is an example for 555:

0555

5[5+5][5+5]5

I was forced to group the double digit result as [5+5=10]. Clearly this is an odd way to write a number. It's unconventional and confusing. 555 x 11 = 6105. We need to supplement the rules.

What we are really doing is this:

555 +

5550 ---- 6105 Let's examine a longer example: 555555 + 5555550 ------- 6111105

I'll write this out in full so you can see what is going on. After a short time, you will be able to just write down the answer in one hit.

We will use the sawtooth method to explain this.

0 1 2 3 4 5 6 7 8 9 | /| /| /| /| /| /| /| /| /| This is the sawtooth. | / | / | / | / | / | / | / | / | / | At each point, add digits 1 3 5 7 9 11 13 15 17 9 | | | | | / | / | / | / | | Sawtooth again for double | | | | |/ |/ |/ |/ | | digits. 1 3 5 7 10 2 4 6 7 9 | | | | / | | | | | | | | | |/ | | | | | | 1 3 5 8 0 2 4 6 7 9 This is the answer.

This sawtooth method explains the process in detail.As you get used to the method, you can look ahead at the digits to the right to see if you need to add one extra.

Another (easier) way is to start at the right and work left. This is easier because you don't need to look-ahead. If a one needs carrying, then you can note it immediately. The advantage of mastering the left-to-right method allows you to 'speak' the answer in order which is more impressive to an audience. However, have a go at the right-to-left method and compare:

## Right to left method

Again, by example:

(This time I will make a deliberate error for you to spot.)

12378 X 11

Add the leading zero and drop down the rightmost digit.

012378| 8

8+7=15Use the 5 and make a mental note to carry the one. 012378 | 58 3 + 7 (plus the carry) = 11. Use the 1 and make another mental note to carry the one. 012378 | 158 2 + 3 = 5. Use the 5 and nothing to carry. 012378 | 5158 1 + 2 = 3012378 | 35158 0 + 1 = 1. The purpose of the leading zero is to force you to do this last step. 012378 | 135158 This is the answer. OrISit?

Check your answer by casting out 9s!

### Can you spot (and fix) the error?

## Related hubs by Manna In The Wild.

- Russian Multiplication

This is a short article which describes a different way to multiply two numbers. All you need to do is divide by two, double a number, and add a column, and know how to recognize even and odd. Using these... - maths trick how to quickly square a number that ends in 5

You need to compute 35 x 35. Instantly, a child can answer "3 x 4 = 12 so 35 squared is 1,225" The number must end in 5, although numbers over 99 are a little harder, and as they get larger it gets... - Casting out 9s - a way to check your maths quickly

... yet it's rare that one of the easiest ways to check your own arithmetic is taught. Casting out nines is easy. It is a way to quickly do a little checksum operation which will tell you that you have got... - What is all this binary and hexadecimal and octal about anyway?

At one time in my career, I needed to recruit many technical staff. One of the questions that I prepared asked to convert a binary number to octal. I was surprised to find that almost nobody could do it, and...

## More by this Author

- 10
Find out the physics behind a crazy equation that Farnsworth wrote on the blackboard at Mars University. There is a lot more to it that you might realise.

- 8
I wondered how many muscles there are in the human face. It seems like an easy question but in reality there is not a readily useful consensus on the internet. So I decided to use this as an illustration as to why it is...

- 22
In ancient China, craftsmen used skimmed milk and rennet with a little lime to produce a very good water resistant glue. You can do something similar using just skimmed milk and vinegar.

## Comments 1 comment

Great hub!I've been thinking about how to teach math to a naughty pupil these days, and this one inspired me a lot!Thanks!