Some people consider the first three shortcuts too easy, since they involve only addition and subtraction. But one must admit, any multiplication beyond the simple multiplication table is really cool and amazing, and done with some showmanship, is in the realm of the Mathemagical.

Multiplication with a power of 10 is trivial ( just add zeroes, right? ), so let us proceed to the simplest multiplication trick – Multiplying by 11.

To multiply any two digit number by 11, we simply split the two digits and insert their sum in between them.

Example 4.1: 3 5 x 11 = 385

1. Split the two digits (in this case, 3 and 5 ), leaving space for one more digit in the middle.

   3 5  x  1 1  =  3 _ 5
   

2. Insert the sum of the two digits (3 + 5 = 8) between them.

   3 5  x  1 1  =  3 8 5

For longer multiplicands, we follow a similar procedure of placing the sum of the adjacent digits “between” them.

Example 4.2: 34,532 x 11 = 379,852

1. Bring down the first digit slightly to the left:

     3 4 5 3 2  x  11 = 
    3
   

2. Add the first digit to the digit next to (3 + 4 ) it and place the sum underneath the space between them.

     3 4 5 3 2  x  11 = 
    3 7

3. Continue this process until the next to the last digit.

     3 4 5 3 2  x  11 = 
    3 7 9 8 5

4. Bring down the last digit, and we’re done!

     3 4 5 3 2  x  11 = 
    3 7 9 8 5 2

With a little practice multiplication be 11 can be performed mentally

 Exercises 4.1: Perform the following multiplication:

1.        52 x 11 =
2.        36 x 11 =
3.       245 x 11 =
4.     7,261 x 11 =
5.   435,263 x 11 =

But wait!!!!  What if the sum of adjacent digits is greater than 9 and has more than one digit?  Do we insert two digits?

Our procedure for multiplying by 11 will slightly vary if the sum of adjacent digits is 10 or more.

Example 4.3:            39 x 11

1. Separate the two digits.

     3   9  x  11 =
    3

2. Add the two digits. 3 + 9 = 12. But it would be wrong to insert the 12 between 3 and 9.  Only one digit is allowed in the middle.

     3    9  x  11 =
    3 (12) 9 

3. Carry over the 1 of 12 and add it to the 3 giving a final answer of 429.

     3   9  x  11 =
    3+1 2 9 

   or

     3 9  x  11 =
    4 2 9 

For longer numbers, it is best to use a symbol to indicate a “carry” operation when writing the answer.
Example:      39,567 x 11

1. After bringing down the first digit 3, proceed to add it to its right hand neighbor 9 to give 3+9= 12. Put any mark (such as an apostrophe ‘) next to the 3 to indicate the “carry” operation, and put 2 between 3 and 9.

     3  9  5  6  7  x  11 = 
    3' 2

2. Proceed to the right following the above procedure if the sum of the adjacent digits is 10 or more, until the second to the last digit

     3  9  5  6  7  x  11 = 
    3' 2' 4' 1' 3

3. Bring down the last digit.

     3  9  5  6  7  x  11 = 
    3' 2' 4' 1' 3  7

4. Rewrite the answer to take care of the carries. 

     3  9  5  6  7  x  11 = 
    4  3  5  2  3  7

Again, will a little practice, even this type of multiplication can be done mentally.  With a little look-ahead you can skip the carries and amaze your audience by proceeding to write the answer left to right!

Exercise 4.2

1. 46 x 11 =
2. 75 x 11 =
3. 567 x 11 =
4. 7,856 x 11 =
5. 29,586 x 11 =

Answers to all exercises are found in the answer key.

Discover all the 25 Math Short Cuts ( 25 MSC )!