Next easiest after  multiplication by 11, is multiplication by 2.  Multiplying a number by 2 is also called doubling. Doubling may be done by adding a number to itself but it is easier to apply the “times two” table that we have learned by heart.

Let us call 0, 1, 2, 3 and 4 “small digits” and 5, 6, 7, 8 and 9 “ big digits”. I am sure that there will be no problem in doubling the small digits into 0, 2, 4, 6 and 8 respectively.

Note that if we subtract 5 from a big digit, we will get a small digit. i.e.

• big digit 5 minus 5 = small digit 0.
• big digit 6 minus 5 = small digit 1.
• big digit 7 minus 5 = small digit 2.
• big digit 8 minus 5 = small digit 3.
• big digit 9 minus 5 = small digit 4.

With small digits, doubling is very easy: From the left, we simply double each digit and write the answer below it.

Example 5.1:

             2 4 3 1
             x     2
             4 8 6 2

With big digits, we modify our procedure: Double each digit starting from the left, but before we write our answer, look at the next digit to the right, if it is “big” add 1 to it. Deduct 5 from the next digit,before doubling it.

Example 5.2:

   4  8
   x  2
   9 

   4  8
   x  2
   9  6 

Doubling 4 gives 8 it before putting it down, we note that the next digit to be doubled is 8 which  is big, so we add 1 first to make it 9. We then deduct 5 from 8 to make it 3 before doubling to get 6.

 An important skill that can be developed by first practicing on doubling is distributed multiplication.

Example 5.3:

   4  8
   x  2
    

   4  0     +
   x  2
   8  0     +

   8
x  2
1  6  =  9  6 

Or

   4  8
   x  2
    

   4  5     +
   x  2
   9  0     +

   3
x  2
   6  =  9  6 

Longer numbers can be split.

Example 5.4:

   3  8  4  6
  x         2
    

   3  8  |  4  6     
  x   2  | x   2
   7  6  |  9  2

   3  8  4  6     
  x         2
   7  6  9  2

Exercise 5.1: Double the following  numbers

1. 2,3 4 3
2. 2,5 3 5
3. 4,5 2 7
4. 3,5 5 2
5. 5,5 5 5
6. 8,4 7 7
7. 6,3 8 6
8. 3,0 9 9
9. 3,9 0 9
10. 7,8 9 6

To multiply by 4, we can double two times.

Example 5.5:  237 x 4=

1. 237 x 2 = 474
2. 474 x 2 = 948

To multiply by 8, we can double three times.

Example 5.6: 632 x 8 =

1.    632 x 2 = 1,264
2. 1,264 x 2 = 2,528
3. 2,528 x 2 = 5,056

Exercise 5.2: Find the following products:

1. 142 x 4 =
2. 357 x 4 =
3. 568 x 4 =
4. 742 x 4 =
5. 2468 x 4 =
6. 214 x 8 =
7. 455 x 8 =
8. 773 x 8 =
9. 894 x 8 =
10. 3152 x 8 =

Answers to all exercises are found in the answer key.

Discover the 25 Math Short Cuts ( 25 MSC )!